Language：Japanese   Publisher：The Institute of Systems, Control and Information Engineers  

DOI： 10.11509/sci.sci24.0_431

CiNii Research

Publisher：IEEE Control Systems Letters  

This letter proposes a Lyapunov-based method of reducing the number of activation functions of a recurrent neural network (RNN) for its stability analysis. To the best of the authors' knowledge, no method has been presented for pruning RNNs with respecting their stability properties. We are the first to present an effective solution method for this important problem in the control community and machine learning community. The proposed reduction method follows the intuitive policy: compose a reduced RNN by removing some activation functions whose 'magnitudes' with respect to their weighted actions are 'small' in some sense, and analyze its stability to guarantee the stability of the original RNN. Moreover, we theoretically justify this policy by proving several theorems that are applicable to general reduction methods. In addition, we propose a method of rendering the proposed reduction method less conservative, on the basis of semidefinite programming. The effectiveness of the proposed methods is demonstrated on a numerical example.

DOI： 10.1109/LCSYS.2024.3406609

Web of Science

Scopus

Publisher：2024 European Control Conference, ECC 2024  

The study of recent papers brought our attention to an alternative matrix inequality condition for state-feedback design. This condition falls in the category of S-variable results. At the difference of previous conditions it does not involve Schur complement or duality arguments and thus simplifies significantly the mathematical derivations. We provide in this paper a detailed description of the core elements of this new to us result. We then expose some derivations for pole location and time-response performances of uncertain systems with constant or time-varying uncertainties, as well as for some non-linear systems.

DOI： 10.23919/ECC64448.2024.10591320

Scopus

Publisher：IEEE Access  

This paper is an attempt to extend the theory of positive systems to sampled-data systems. Even though where to take the initial time is unimportant in positivity of linear time-invariant systems, this is not the case for sampled-data systems because of their periodically time-varying nature from the perspective of the continuous-time input and output signals. Hence, we first study positivity of sampled-data systems by considering the case where a sampling instant is viewed as the initial time. We then further consider the case where an arbitrary intersample instant is viewed as the initial time, and we finally give the necessary and sufficient conditions for ultimate notions of (i.e., initial-time-independent) internal/external positivity of sampled-data systems. The arguments of this paper are then illustrated through numerical examples.

DOI： 10.1109/ACCESS.2023.3347281

Web of Science

Scopus

Publisher：2024 European Control Conference, ECC 2024  

This paper is concerned with the computation of the local Lipschitz constant of feedforward neural networks (FNNs) with activation functions being rectified linear units (ReLUs). The local Lipschitz constant of an FNN for a target input is a reasonable measure for its quantitative evaluation of the reliability. By following a standard procedure using multipliers that capture the behavior of ReLU s, we first reduce the upper bound computation problem of the local Lipschitz constant into a semidefinite programming problem (SDP). Here we newly introduce copositive multipliers to capture the ReLU behavior accurately. Then, by considering the dual of the SDP for the upper bound computation, we second derive a viable test to conclude the exactness of the computed upper bound. However, these SDPs are intractable for practical FNNs with hundreds of ReLUs. To address this issue, we further propose a method to construct a reduced order model whose input-output property is identical to the original FNN over a neighborhood of the target input. We finally illustrate the effectiveness of the model reduction and exactness verification methods with numerical examples of practical FNNs.

DOI： 10.23919/ECC64448.2024.10590974

Scopus

Language：Japanese   Publisher：The Institute of Systems, Control and Information Engineers  

DOI： 10.11509/sci.sci24.0_1034

CiNii Research

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：Japanese   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)  

<p>This paper addresses the stability analysis problem of recurrent neural networks (RNNs) with activation functions being rectified linear units (ReLUs). In particular, we focus on the linear nonegative properties of the input-output signals of ReLUs. To capture these linear properties within the framework of integral quadratic constraint (IQC), we introduce a copositive multiplier constructed from a copositive matrix. This enables us to capture the linear input-output properties of ReLUs in quadratic form. By using the copositive multipliers in additon to existing multipliers, we can reduce the conservatism of the IQC-based stability analysis for RNNs. We also show that the proposed IQC-based stability condition with copositive multipliers can be viewed as an extension of a recently proposed scaled small-gain stability condition based on the <i>L</i>₂₊induced norm.</p>

DOI： 10.5687/iscie.36.17

CiNii Research

Language：Japanese   Publishing type：Research paper (scientific journal)  

Publisher：IFAC-PapersOnLine  

This paper extends the theory of positive systems to sampled-data systems. When considering positivity of LTI systems, where to take the initial time is unimportant. However, since sampled-data systems are periodically time-varying systems from the perspective of the continuous-time input and output signals, it is important to consider which time should be viewed as the initial time. Therefore, this paper studies positivity of sampled-data systems first by considering the case where a sampling instant is viewed as the initial time, and secondly by further considering the case where an arbitrary intersample instant is viewed as the initial time. The two different situations lead to quite relevant issues of what to take as the initial conditions and what to assume on the initial conditions in appropriately defining the internal/external positivity of sampled-data systems. These arguments are combined to derive the necessary and sufficient conditions for ultimate notions of (i.e., initial-time-independent) internal/external positivity of sampled-data systems.

DOI： 10.1016/j.ifacol.2023.10.1285

Web of Science

Scopus

Publisher：IFAC-PapersOnLine  

This paper is concerned with the optimization of the impulse-to-peak value of positive linear systems. Although the results of the analysis of the peak value of positive linear systems have been reported in the literature, the synthesis problem of impulse-to-peak value remains unresolved. To address this problem, in this paper we show that a cost-constrained minimization problem of the impulse-to-peak value of parameterized positive linear systems can be reduced to a DC (difference of convex functions) program. The derivation utilizes the log-log convexity of posynomial functions and a recent characterization of the impulse-to-peak value of positive systems via a linear program. To illustrate the effectiveness of our results, we study the optimization problem for minimizing the peak infection of networked epidemic spreading processes.

DOI： 10.1016/j.ifacol.2023.10.1286

Web of Science

Scopus

Publisher：IFAC-PapersOnLine  

In this paper, we focus on the lower bounds of the Lp (p ∈ [1, ∞), p = ∞) induced norms of continuous-time LTI systems where input signals are restricted to be nonnegative. This induced norm, called the Lp+ induced norm, is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinearities provide only nonnegative signals for the case p = 2. To have deeper understanding on the Lp+ induced norm, we analyze its lower bounds with respect to the standard Lp induced norm in this paper. As the main result, we show that the Lp+ induced norm of an LTI system cannot be smaller than the Lp induced norm scaled by 2(1−p)/p for ∈ [1, ∞) (scaled by 2−1 for p = ∞). On the other hand, in the case where p = 2, we further propose a method to compute better (larger) lower bounds for single-input systems via reduction of the lower bound analysis problem into a semi-infinite programming problem. The effectiveness of the lower bound computation method, together with an upper bound computation method proposed in our preceding paper, is illustrated by numerical examples.

DOI： 10.1016/j.ifacol.2023.10.1218

Web of Science

Scopus

Language：Japanese   Publisher：The Society of Instrument and Control Engineers  

<p>This paper extends the theory of positive systems to sampled-data systems. When considering positivity of LTI systems, where to take the initial time is unimportant. However, since sampled-data systems are periodically time-varying from the perspective of continuous-time, introducing an adequate definition for their positivity should be relevant to considering which time to take as the initial time. This paper begins by studying positivity of sampled-data systems first by considering the case where a sampling instant is regarded as the initial time, and secondly by further considering the case where an arbitrary intersample instant is regarded as the initial time. These arguments are combined to derive the necessary and sufficient conditions for a unified notion of (i.e., initial-time-independent) positivity of sampled-data systems. This paper then applies this concept to the analysis of the <i>L_q</i>/<i>L</i>_∞ Hankel norm, known as a measure for evaluating the effects of disturbances in dynamical systems. It is shown that positive sampled-data systems lead to concise expressions for the (quasi) <i>L_q</i>/<i>L</i>_∞ Hankel norms not only for <i>q</i> = <i>∞</i> but also for <i>q</i> = 1,2, where the latter are hard to handle for general sampled-data systems. Some relevant properties for these norms are also shown. The theoretical results derived in this paper are confirmed through numerical examples.</p>

DOI： 10.9746/sicetr.59.92

CiNii Research

Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

DOI： 10.11511/jacc.66.0_818

CiNii Research

Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

DOI： 10.11511/jacc.66.0_135

CiNii Research

Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

DOI： 10.11511/jacc.66.0_125

CiNii Research

Language：Japanese   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)  

<p>In this paper, nonlinear controllers are designed for buck converters via the Sum of Squares (SOS) method based on their discretized bilinear model. We first consider a class of control laws in a rational funciton. The condition of Lyapunov stability theory is converted to an SOS condition, and by using the SOS method, a nonlinear stabilizing controller for the discrete-time system is derived to ensure that input constraints on buck converters can also be satisfied. However, with such a control law, the rate of convergence may be poor. To solve this problem, we next obtain through the SOS method a control law satisfying the input constraints and maximizing the Lyapunov function decrement in each sampling time. Finally, simulation and experimental results are shown to confirm the effectiveness of the second control law.</p>

DOI： 10.5687/iscie.35.153

CiNii Research

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：Japanese   Publisher：THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)  

<p>A recurrent neural network (RNN) is a class of deep neural networks and able to imitate the behavior of dynamical systems due to its feedback mechanism. However, the feedback mechanism may cause network instability and hence the stability analysis of RNNs has been an important issue. From control theoretic viewpoint, we can readily apply the small gain theorem for the stability analysis of an RNN by representing it as a feedback connection with a linear time-invariant (LTI) system and a static nonlinear activation function typically being a rectified linear unit (ReLU). It is nonetheless true that the standard small gain theorem leads to conservative results since it does not care the important property that the ReLU returns nonnegative signals only. This motivates us to analyze the <i>L</i>₂induced norm of LTI systems for nonnegative input signals, which is referred to the <i>L</i>₂₊induced norm in this paper. We characterize an upper bound of the <i>L</i>₂₊induced norm by copositive programming, and then derive a numerically tractable semidefinite programming problem for (loosened) upper bound computation. We finally derive an <i>L</i>₂₊-induced-norm-based small gain theorem for the stability analysis of RNNs and illustrate its effectiveness by numerical examples.</p>

DOI： 10.5687/iscie.35.29

CiNii Research

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

Web of Science

Publisher：2022 European Control Conference, ECC 2022  

This paper is concerned with the analysis of the L2 induced norm of continuous-time LTI systems where the input signals are restricted to be nonnegative. This induced norm is referred to as the L2+ induced norm in this paper. It has been shown very recently that the L2+ induced norm is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinear elements only provide nonnegative signals. For the upper bound computation of the L2+ induced norm, an approach with copositive programming has also been proposed. It is nonetheless true that this approach becomes effective only for multi-input systems, and for single-input systems this approach does not bring any improvement over the trivial upper bound, the standard L2 norm. To overcome this difficulty, we newly introduce positive filters to increase the number of positive signals. This enables us to enlarge the size of the copositive multipliers so that we can obtain better (smaller) upper bounds with copositive programming. Keywords: nonnegative signal, L2+ induced norm, positive filter, copositive programming

DOI： 10.23919/ECC55457.2022.9838085

Scopus

Publisher：SICE Journal of Control, Measurement, and System Integration  

In this study, we focus on the (Formula presented.) Hankel norms of linear time-invariant (LTI) discrete-time positive systems across a single switching. The (Formula presented.) Hankel norms are defined as the induced norms from vector-valued (Formula presented.) past inputs to vector-valued (Formula presented.) future outputs across a system switching and a state transition at the time instant zero. A closed-form characterization of the (Formula presented.) Hankel norm in this switching setting for general LTI systems can readily be derived as the natural extension of the standard (Formula presented.) Hankel norm. Thanks to the strong positivity property, we show that we can successfully characterize the (Formula presented.) Hankel norms for the positive system switching case even in some combinations of p, q being (Formula presented.). In particular, some of them are given in the form of linear programming (LP) and semidefinite programming (SDP). These LP- and SDP-based characterizations are particularly useful for the analysis of the (Formula presented.) Hankel norms where the systems of interest are affected by parametric uncertainties.

DOI： 10.1080/18824889.2022.2090801

Scopus

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

This paper investigates the input-output gains, including ℓ1- and ℓ∞-gains and L1- and L∞-gains, of discrete-time and continuous-time positive periodic systems. For the discrete-time case, the input–output gain can be characterized by linear inequalities. For the continuous-time case, the input–output gain characterization problem turns into the existence problem of a positive periodic vector function. Based on some necessary and sufficient input–output gain conditions, we find the ℓ1- (L1-) gain of discrete-time (continuous-time) positive periodic systems is equivalent to the of ℓ∞- (L∞-) gain of the associated dual systems. Finally, two numerical examples are given to illustrate the results.

DOI： https://doi.org/10.1002/rnc.5438

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

This letter shows that, as long as continuous-time linear parameter-varying (LPV) systems are concerned, quadratic-stability-based gain-scheduled state-feedback controller synthesis offers no advantage over quadratic-stability-based fixed (parameter-independent) state-feedback controller synthesis in typical control performance specifications. We derive this counterintuitive result by properly extending the previous results on the robust versions of Finsler's lemma and the elimination lemma. We also show that this counterintuitive result is continuous-time LPV system specific, and in the discrete-time LPV system case quadratic-stability-based gain-scheduled state-feedback controller synthesis does bring improvement. These results give a proper warning about the effectiveness of the quadratic-stability-based gain-scheduled state-feedback controller synthesis.

DOI： 10.1109/LCSYS.2020.2991480

Language：English   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

In the field of control, a wide range of analysis and synthesis problems of linear time-invariant (LTI) systems are reduced to semidefinite programming problems (SDPs). On the other hand, in the field of mathematical programming, a class of conic programming problems, so called the copositive programming problem (COP), is actively studied. COP is a convex optimization problem on the copositive cone, and the completely positive cone, the doubly nonnegative cone, and the Minkowski sum of the positive semidefinite cone and the nonnegative cone are also closely related to COP. These four cones naturally appear when we deal with optimization problems described by nonnegative vectors. In this letter, we show that the stability, the H2 and the H∞ performances of LTI positive systems are basically characterized by the feasibility/optimization problems over these four cones. These results can be regarded as the generalization of well-known LMI/SDP-based results on the positive semidefinite cone. We also clarify that in some performances such direct generalization is not possible due to inherent properties of the copositive or the completely positive cone. We thus capture almost entire picture about how far we can generalize the SDP-based results for positive systems to those on the four cones related to COP.

DOI： 10.1109/LCSYS.2019.2946620

Language：Japanese   Publishing type：Research paper (scientific journal)  

Construction of Externally Positive Systems and Order Reduction for Discrete-Time LTI System Analysis

DOI： 10.5687/iscie.32.284

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1049/iet-cta.2019.0228

Language：Japanese   Publishing type：Research paper (scientific journal)  

Preface to Special Issue on The 5th Multi-symposium on Control Systems

DOI： 10.9746/sicetr.55.147

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1109/MCS.2018.2866649

Language：English   Publishing type：Research paper (scientific journal)  

Motivated by recent advances in the study of linear time-invariant (LTI) positive systems, we explore analysis techniques of general, not necessarily positive, LTI systems using positive system theory. Even though a positive system is characterized by its peculiar property that its impulse response is nonnegative, we often deal with nonnegative impulse responses even in general LTI system analysis. A typical example is the computation of the H-2 norm, where we focus on squared impulse responses. To deal with such products of impulse responses in a systematic fashion, in this paper, we first establish a construction technique of an LTI system whose impulse response is given by the product of impulse responses of two different LTI systems. Then, as the main result, we reduce the H-2 norm computation problem of a general LTI system into the L-\infty-induced norm computation problem (or L-1 problem in short) of a positive system, by which we can derive various formulas for the H-2 norm computation.

DOI： 10.1109/TAC.2017.2767704

Language：Japanese   Publishing type：Research paper (scientific journal)  

H₂ Analysis of LTI Discrete-Time Systems via Conversion to Externally Positive Systems

DOI： 10.5687/iscie.31.75

Language：Japanese   Publishing type：Research paper (scientific journal)  

Nonlinear Output Feedback Control for Average Output Voltage of Boost Converters Based on their Discretized Bilinear Model

DOI： 10.5687/iscie.31.63

Language：English   Publishing type：Research paper (scientific journal)  

This paper presents analysis and synthesis of interconnected systems where the interconnected system of interest consists of discrete-time positive subsystems and an interconnection matrix. The paper gives sufficient conditions for the discrete-time single-input single-output (SISO) subsystems and the interconnection matrix so that the interconnected system has the property of persistence. The fundamental differences for the persistence between the conditions of the discrete-time setting and those of a continuous-time setting are also discussed. The obtained analysis result can apply to formation control for multi-agent systems, which is a synthesis part of the paper. Numerical examples including formation control of mobile robots are shown to illustrate the proposed formation control design method.

DOI： 10.9746/jcmsi.11.91

Language：English   Publishing type：Research paper (scientific journal)  

This paper discusses and compares LMI results built using the S-variable approach starting from equivalent yet different representations of uncertain systems. Using the fact that S-variable results are well suited to handle descriptor systems and that descriptor system modeling is versatile, we compare results in terms of the impact of modeling on the computational burden and on conservatism. Multi-affine representations allow reduced numerical burden while affine representations lead to less conservative results. Numerical examples show that conservatism reduction is not systematic, but is in some cases quite significant without major increase of the numerical burden.

DOI： 10.1016/j.ifacol.2018.11.179

Language：English   Publishing type：Research paper (scientific journal)  

This paper is concerned with analysis techniques of discrete-time LTI systems via construction of relevant externally positive systems. Recently, the author established a construction method of an externally positive system whose impulse response is given by the square of the original discrete-time LTI SISO system to be analyzed. This externally positive system allows us to characterize the H₂ norm of the original system by means of the l_∞-induced norm characterization of externally positive systems. It is nonetheless true that, for the original system of order n, the order of the resulting externally positive system is n² and hence this leads to the increase of associated computational burden. With this important issue in mind, in this paper, we show that the order can be reduced down to n(n + 1)/2 by using the elimination and duplication matrices that are intensively studied by Jan R. Magnus in the 80's. In addition to the computational complexity reduction for the aforementioned H₂ analysis, we show that such construction of externally positive systems with reduced order is quite effective in semidefinite-programming-based peak value analysis of impulse responses of general LTI systems.

DOI： 10.1016/j.ifacol.2018.11.178

Language：English   Publishing type：Research paper (scientific journal)  

This study is concerned with the analysis and synthesis of delay interconnected positive systems. For delay-free cases, it has been shown very recently that the output of the interconnected positive system converges to a positive scalar multiple of a prescribed positive vector under mild conditions on positive subsystems and a non-negative interconnection matrix. This result is effectively used for formation control of multi-agent systems with positive dynamics. The goal of this study is to prove that this steady-state property is essentially preserved under any constant (and hence bounded) communication delay. In the context of formation control, this preservation indicates that the desired formation is achieved robustly against communication delays, even though the resulting formation is scaled depending on initial conditions for the state. To ensure the achievement of the steady-state property, the authors need to prove rigorously that the delay interconnected positive system has stable poles only except for a pole of degree one at the origin, even though it has infinitely many poles, in general. For the rigorous proof, we newly develop frequency-domain (s-domain) analysis for delay interconnected positive systems, which has not been studied for delay-free cases.

DOI： 10.1049/iet-cta.2017.0315

Language：English   Publishing type：Research paper (scientific journal)  

This paper deals with formation control of mobile robots based on interconnected positive systems with SISO subsystems where each robot has a nonlinear dynamics of a MIMO subsystem. To linearize the dynamics, this paper introduces a virtual vehicle of the robot. Then a feedback linearization and a local feedback law transform each dynamics of the virtual vehicle into two SISO positive and stable linear systems. Consequently, the dynamics of the virtual vehicles satisfy the properties of the interconnected positive systems. Experimental results as well as numerical examples including leader-follower formation control for the mobile robots are illustrated.

DOI： 10.1016/j.ifacol.2017.08.755

Language：English   Publishing type：Research paper (scientific journal)  

Recently, the author derived a necessary and sufficient condition for the asymptotic stability of neutral type time-delay positive systems (TDPSs), where the neutral type TDPS of interest is given by a feedback connection between a finite-dimensional LTI positive system and the pure delay The goal of this paper is to extend this result to neutral type TDPSs with multiple commensurate delays. To this end, we first represent a neutral type TDPS with multiple commensurate delays as a neutral type TDPS with a single delay, by augmenting input and output signals in the feedback connection. By this conversion, we can readily apply the latest result already established for single delay neutral type TDPSs. As the main result, we show that a neutral type TDPS with commensurate delays is stable if and only if its delay-free counterpart is stable and an additional “admissibility” condition is satisfied. This result in particular implies that the stability is irrelevant of the length of delays.

DOI： 10.1016/j.ifacol.2017.08.681

Language：English   Publishing type：Research paper (scientific journal)  

This paper addresses the analysis of discrete-time interconnected systems where each subsystem is stable and positive. Admissibility and persistence notions are derived similar to the continuous-time case and a condition for enforcing persistence is derived for the case when all subsystems are single-input single output. Results are applied on numerical examples including the formation control of mobile robots.

DOI： 10.1016/j.ifacol.2017.08.304

Language：English   Publishing type：Research paper (scientific journal)  

Design of controllers in the form of a state-feedback coupled to a state observer is studied in the context of uncertain systems. The classical approach by Luenberger is revisited. Results provide a heuristic design procedure that mimics the independent state-feedback/observer gains design by minimizing the coupling of observation error dynamics on the ideal state-feedback dynamics. The proposed design and analysis conditions apply to linear systems rationally-dependent on uncertainties defined in the cross-product of polytopes. Convex linear matrix inequality results are given thanks to the combination of a descriptor multi-affine representations of systems and the S-variable approach. Stability and H_∞ performances are assessed by multi-affine parameter-dependent Lyapunov matrices.

DOI： 10.1016/j.automatica.2016.10.003

Language：Japanese   Publishing type：Research paper (scientific journal)  

Analysis and Synthesis of Positive Systems and Copositive Programming

DOI： 10.11511/jacc.60.0_78

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1109/MCS.2016.2584278

Language：English   Publishing type：Research paper (scientific journal)  

This paper is concerned with convergence rate analysis of multi-agent positive systems under formation control. Recently, we have shown that very basic multi-agent systems under formation control can be modeled as interconnected positive systems, and desired formation can be achieved by designing interconnection matrices appropriately. In such formation control, the resulting convergence performance (i.e., convergence rate) varies according to the interconnection matrices and this fact motivates us to develop an efficient algorithm for the analysis of the convergence rate. In this paper, assuming that the dynamics of agents are positive and homogeneous, we conceive such an algorithm by problem decomposition. We show that the decomposition to smaller size problems and drastic reduction of computational burden become possible by making full use of the positivity of the agents.

DOI： 10.9746/jcmsi.9.216

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we study H_∞ performance limitation analysis for continuous-time SISO systems using LMIs. By starting from an LMI that characterizes a necessary and sufficient condition for the existence of desired controllers achieving a prescribed H_∞ performance level, we represent lower bounds of the best H_∞ performance achievable by any LTI controller in terms of the unstable zeros and the unstable poles of a given plant. The transfer functions to be investigated include the sensitivity function (1+PK)^-1, the complementary sensitivity function (1+PK)^-1PK, and (1+PK)^-1P, the first and the second of which are well investigated in the literature. As a main result, we derive lower bounds of the best achievable H_∞ performance with respect to (1+PK)^-1P assuming that the plant has unstable zeros. More precisely, we characterize a lower bound in closed-form by means of the first non-zero coefficient of the Taylor expansion of the plant P(s) around its unstable zero.

DOI： 10.9746/jcmsi.9.165

Language：Japanese   Publishing type：Research paper (scientific journal)  

Nonlinear Control with Integral Compensation for Output Voltage of Boost Converters Based on Discretized Bilinear Model―I:―Modeling and Identification

DOI： 10.5687/iscie.28.320

Language：Japanese   Publishing type：Research paper (scientific journal)  

Nonlinear Control with Integral Compensation for Output Voltage of Boost Converters Based on Discretized Bilinear Model―II:―Derivation of a Control Law and Verification by Experiments

DOI： 10.5687/iscie.28.330

Language：Japanese   Publishing type：Research paper (scientific journal)  

Dominant Pole Analysis of Linear Positive Systems with Multiple Time-Delays

DOI： 10.5687/iscie.28.147

Language：English  

Chapter 3 is an extension of the SV-LMIs of the preceding chapter both in terms of generalization of the results and for further conservatism reduction. First the SV results are generalized to descriptor systems. Not only this result is valuable in itself, but, combined to a model manipulation technique, an infinite sequence of SV-LMIs can be build. This sequence of SV-LMIs is shown to be easy to construct and proved to be of decreasing conservatism. Tests are provided for checking if the conservatism gap vanishes. On examples it is shown that the conservatism gap indeed vanishes and this is obtained early elements of the sequence (i.e., the convergence is rather fast).

DOI： 10.1007/978-1-4471-6606-1_3

Language：English  

While the two previous chapters address control design cases which have LMI solutions, Chap. 6 tackles the hard problem of static output-feedback design. No polynomial-time optimization method exists for that problem, and if keeping in the matrix inequality framework, one has to resort to iterative LMI algorithms. For that important and hard problem, the SV approach produces a sophisticated version of such iterative LMI algorithm. In this case, the structuring of the S-variables reveals a virtual stabilizing state feedback. This original design procedure is detailed and tested on examples.

DOI： 10.1007/978-1-4471-6606-1_6

Language：English  

In this chapter, the SV-LMIs of Chap. 2 are reconsidered for robust state-feedback synthesis. The results rely on the structuring of the S-variables. An interpretation in terms of virtual stable model is given to this structure. Moreover, we show the effect of this structuring on conservatism reduction. It happens to be of different nature in the discrete-time and continuous-time cases.

DOI： 10.1007/978-1-4471-6606-1_4

Language：English  

Chapter 7 is dedicated to the analysis of discrete-time periodic systems by means of SV-LMIs. For that special case the SV-LMIs have interesting non-causal system interpretations. Similarly to the LTI case, SV-LMIs are effective for reducing the conservatism of the analysis results when dealing with discrete-time periodic systems affected by polytopic uncertainties.

DOI： 10.1007/978-1-4471-6606-1_7

Language：English  

The primary goal of Chap. 2 is founding the basic idea of the SV approach. Before generalizing the technique (which is done in the following chapters), we show its effectiveness on simple essential control problems. We mainly consider the robust performance analysis problems of linear time-invariant systems affected by parametric uncertainties, and clarify why the SV-LMIs do perform well on these intractable infinite-dimensional semi-infinite problems. We also highlight the improvements in terms of conservatism both theoretically and on examples.

DOI： 10.1007/978-1-4471-6606-1_2

Language：English  

Finally, Chapter 8 deals with state-feedback controller synthesis for discrete-time periodic systems. By introducing S-variables and applying change of variables that is almost identical to the LTI case, we can readily obtain SV-LMIs for periodic state-feedback controller synthesis. We illustrate by numerical examples that the SV-LMIs are indeed effective in conservatism reduction when dealing with discrete-time periodic systems affected by polytopic uncertainties.

DOI： 10.1007/978-1-4471-6606-1_8

Language：English  

Chapter 5 focuses on multiobjective control design problems for discrete-time LTI systems. The goal here is to design a controller that satisfy multiple (and typically conflicting) design specifications. In the state-feedback case, the advantage of the SV-LMIs readily follows from the synthesis results in Chap. 4. To handle output-feedback case, we first extend the results of Chap. 4 and provide SV-LMI-based formulas for dynamic output-feedback controller synthesis. Then, the effectiveness of the SV-LMIs in conservatism reduction can be shown almost the same way as in the state-feedback case.

DOI： 10.1007/978-1-4471-6606-1_5

Language：English   Publishing type：Research paper (scientific journal)  

Chapter 1 is dedicated to the origins of the “ S -variable approach.” We trace the contributions of independent authors that participated to establish the fundamentals and justify our choice for the denomination “ S -variable approach.” This attentive detailed study is the occasion to show several interpretations of the S -variables with respect to technical results such as Finsler’s lemma and elimination lemma. The chapter concludes with the brief exposure of all the problems to be tackled in the remaining part of the book, justifying the importance of these selected problems.

DOI： 10.1007/978-1-4471-6606-1_1

Language：Japanese   Publishing type：Research paper (scientific journal)  

DOI： 10.11509/isciesci.59.1_2_1

Language：Japanese   Publishing type：Research paper (scientific journal)  

Analysis and Synthesis of Interconnected Positive Systems(<Special Issue>Control and Mathematics of Positive Systems)

DOI： 10.11509/isciesci.59.1_21

Language：English   Publishing type：Research paper (scientific journal)  

This study is concerned with the dominant pole analysis of asymptotically stable time-delay positive systems (TDPSs). It is known that a TDPS is asymptotically stable if and only if its corresponding delay-free system is asymptotically stable, and this property holds irrespective of the length of delays. However, convergence performance (decay rate) should degrade according to the increase of delays and this intuition motivates us to analyse the dominant pole of TDPSs. As a preliminary result, in this study, the authors show that the dominant pole of a TDPS is always real. They also construct a bisection search algorithm for the dominant pole computation, which readily follows from recent results on á-exponential stability of asymptotically stable TDPSs. Then, they next characterise a lower bound of the dominant pole as an explicit function of delays. On the basis of the lower bound characterisation, they finally show that the dominant pole of an asymptotically stable TDPS is affected by delays if and only if associated coefficient matrices satisfy eigenvalue-sensitivity condition to be defined in this study. Moreover, they clarify that the dominant pole goes to zero (from negative side) as time-delay goes to infinity if and only if the coefficient matrices are eigenvalue-sensitive.

DOI： 10.1049/iet-cta.2014.0375

Language：English   Publishing type：Research paper (scientific journal)  

This paper is concerned with the decentralized H∞ controller synthesis problem for discrete-time LTI systems. Despite of intensive research efforts over the last several decades, this problem is believed to be nonconvex and still outstanding in general. Therefore, most of existing approaches resort to heuristic optimization algorithms that do not allow us to draw any definite conclusion on the quality of the designed controllers. To get around this difficulty, in this paper, we propose convex optimization procedures for computing lower bounds of the H∞ performance that is achievable via decentralized LTI controllers of any order. In particular, we will show that sharpened lower bounds can be obtained by making good use of structures of the LTI plant typically observed in the decentralized control setting.We illustrate via numerical examples that these lower bounds are indeed useful to ensure the good quality of decentralized controllers designed by a heuristic optimization.

DOI： 10.1002/rnc.2999

Language：English   Publishing type：Research paper (scientific journal)  

This paper shows that, under specific structures of generalized plants, the set of static controllers satisfying internal stability and a certain level of H∞ performance becomes convex. More precisely, we characterize such static H∞ controllers by an LMI with controller variables being kept directly as decision variables. The structural conditions on the generalized plant are not too strict, and we show that generalized plants corresponding to a sort of mixed sensitivity problems indeed satisfy these conditions. For the generalized plants of interest, we further prove that full-order dynamical H∞ controllers can be characterized by an LMI with a simple change of variables. In stark contrast to the known LMI-based H∞ controller synthesis, the change of variables is free from the coefficient matrices of the generalized plant and this property is promising when dealing with a variety of robust control problems. Related issues such as robust controller synthesis against real parametric uncertainties are also discussed.

DOI： 10.1016/j.automatica.2014.04.027

Language：English   Publishing type：Research paper (scientific journal)  

An efficient beamforming algorithm for large-scale phased arrays with lossy digital phase shifters is presented. This problem, which arises in microwave power transmission from solar power satellites, is to maximize the array gain in a desired direction with the gain loss of the phase shifters taken into account. In this paper the problem is first formulated as a discrete optimization problem, which is then decomposed into element-wise subproblems by the real rotation theorem. Based on this approach, a polynomial-time algorithm to solve the problem numerically is constructed and its effectiveness is verified by numerical simulations.

DOI： 10.1587/transcom.E97.B.783

Language：English   Publishing type：Research paper (scientific journal)  

This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron-Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries as the solution of the Lyapunov inequality. This new result leads to an alternative proof of the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the H_∞ performance of continuous-time positive systems. In addition, we further derive a new LMI for the H_∞ performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric. We readily extend these results to discrete-time positive systems and derive new LMIs for the H_∞ performance analysis and synthesis. We finally illustrate their effectiveness by numerical examples on robust state-feedback H_∞ controller synthesis for discrete-time positive systems affected by parametric uncertainties.

DOI： 10.1016/j.sysconle.2013.11.001

Language：Japanese   Publishing type：Research paper (scientific journal)  

Simultaneous Optimization of Phases and Amplitudes for Wireless Power Transmission by a Large-Scale Phased Array Antenna with Lossy Digital Phase Shifters

DOI： 10.11511/jacc.57.0_1935

Language：Japanese   Publishing type：Research paper (scientific journal)  

Maximum Power Point Tracking Control of Photovoltaic Systems Based on Particle Swarm Optimization with Experimental Verication

DOI： 10.5687/iscie.27.237

Language：English   Publishing type：Research paper (scientific journal)  

This paper proposes a unified setup for robust stability and performance analysis and synthesis for periodic polytopic discrete-time systems. Relying on a general formulation for state-feedback periodic memory controllers and a new time-lifting, new sufficient LMI conditions for the existence of robust stability certificates and H₂ guaranteed cost control laws are derived. Comparisons of the efficiency of different controller structures illustrate these developments on a numerical example.

DOI： 10.1109/TAC.2013.2251820

Language：English   Publishing type：Research paper (scientific journal)  

This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established a solid theoretical basis for linear matrix inequality (LMI)-based (robust) H _∞-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H ₂ performance criterion. In the H ₂ case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and the inequalities for bounding traces that characterize the H ₂ norm. We can overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H ₂-PTVMSFC synthesis. On the basis of this result, we also consider robust H ₂-PTVMSFC synthesis for LTI systems with parametric uncertainties.

DOI： 10.1002/asjc.541

Language：Japanese   Publishing type：Research paper (scientific journal)  

LMI-based Stability and H_∞ Performance Analysis of Discrete-time Positive Systems

DOI： 10.5687/iscie.26.45

Language：Japanese   Publishing type：Research paper (scientific journal)  

In this paper, we study the stability analysis of discrete-time interconnected positive systems by means of a weighted l₁-induced norm, where the weighted l₁-induced norm is computed from the l₁ norm of the input and output signals evaluated with given weighting vectors. In the literature,it was shown that the weighted L₁-induced norm of continuous-time LTI positive systems can be characterized by linear programming problem (LP). Moreover, the weighted L₁-induced norm was proved to be useful for the stability analysis of interconnected positive systems. On the basis of these results, we first show that the weighted l₁-induced norm of discrete-time LTI positive systems can be again characterized by LP. From this preliminary result, we can construct a transformation from a given discrete-time positive system to a continuous-time positive system, where the weighted L₁-induced norm of the resulting system is equivalent to the weighted l₁-induced norm of the original system. By means of this key transformation, we can readily extend the continuous-time case results to the stability analysis of discrete-time interconnected positive systems.

DOI： 10.5687/iscie.26.355

Language：Japanese   Publishing type：Research paper (scientific journal)  

The 50th IEEE Conference on Decision and Control and European Control Conference(International Conference)

DOI： 10.11509/isciesci.56.6_338

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we propose a linear periodically time-varying (LPTV) controller synthesis approach for the multiobjective H₂H _∞ control problem of discrete-time linear time-invariant (LTI) systems. By artificially regarding the LTI plant as N-periodic and applying the discrete-time system lifting, we first derive a sequence of semidefinite programmings (SDPs) indexed by N for the synthesis of suboptimal multiobjective LPTV controllers. Furthermore, we show that we can reduce the conservatism and improve the control performance gradually by simply increasing the controller period N. On the other hand, in the latter part of the paper, we propose another sequence of SDPs for the computation of the lower bound of the multiobjective control performance that is achievable via LPTV controllers of any period and order. Similarly to the LPTV controller synthesis, the SDP is derived based on the lifting-based treatment of the LTI plant. Again, it is shown that we can improve the lower bound gradually by increasing the fictitious period N. We validate all of these theoretical results through illustrative examples.

DOI： 10.1016/j.sysconle.2011.05.008

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is "exact" in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.

DOI： 10.1016/j.automatica.2010.10.004

Language：Japanese   Publishing type：Research paper (scientific journal)  

Control System Analysis and Synthesis Based on Linear Matrix Inequalities(<Special Issue>Applications of Numerical/Symbolic Computation Software to Control System Analysis and Synthesis)

DOI： 10.11509/isciesci.55.5_165

Language：Japanese   Publishing type：Research paper (scientific journal)  

Robust H_∞ Performance Analysis of LTI Systems with a Single Uncertain Parameter

DOI： 10.5687/iscie.23.46

Language：English   Publishing type：Research paper (scientific journal)  

In this article, we propose novel linear matrix inequality (LMI) conditions for the stability and l₂ gain performance analysis of discrete-time linear periodically time-varying (LPTV) systems. These LMIs are convex with respect to all of the coefficient matrices of the LPTV systems and this property is promising when we deal with several control system analysis and synthesis problems. For example, we can apply those LMIs straightforwardly to robust performance analysis problems of LPTV systems that are affected by polytopic-type uncertainties. Even though our approach for robust performance analysis is conservative in general, we can reduce the conservatism gradually by artificially regarding the original N-periodic system as pN-periodic and increasing p. In addition, thanks to the simple structure of the LMI conditions, we can readily derive a viable test to verify the exactness of the computation results.

DOI： 10.3166/ejc.16.532-544

Language：Japanese   Publishing type：Research paper (scientific journal)  

Periodically time-varying memory state feedback controller synthesis for discrete-time LTI systems with parametric uncertainties described by LFT

DOI： 10.11509/sci.SCI10.0.318.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Verifying the Effectiveness of the Lower Bounds of the Optimal Performances in the Decentralized H-infinity Control Problems of Discrete-Time LTI Systems

DOI： 10.11509/sci.SCI10.0.315.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Attitude Control of an Experimental Helicopter by a 2DOF Controller with Inverse-System Based Design of the Feedforward

DOI： 10.11509/sci.SCI10.0.352.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Maximization of Wireless Transmitting Power by Phase Optimization of Array Antennas on a Solar Power Satellite

DOI： 10.11511/jacc.53.0.100.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Simple Adaptive Control Synthesis Enhanced by Scaling and Its Application to Positioning Control of Antagonist-Type Pneumatic Actuation Mechanism

DOI： 10.5687/iscie.22.350

Language：English   Publishing type：Research paper (scientific journal)  

This paper addresses robust performance analysis problems of linear time-invariant (LTI) systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, where linear matrix inequality (LMI) plays an important. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution. By pursuing this direction, in this paper, we provide rank conditions on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can be computed. These results come from block-moment matrix structure of the dual variable, which is consistent with the recent results on polynomial optimization. This particular structure enables us to make good use of simultaneous diagonalizability property of commuting diagonalizable matrices so that the sound rank conditions for the exactness verification can be obtained.

DOI： 10.1109/TAC.2009.2017086

Language：English   Publishing type：Research paper (scientific journal)  

This paper addresses robust performance analysis problems of linear time-invariant (LTI) systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, where linear matrix inequality (LMI) plays an important. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution. By pursuing this direction, in this paper, we provide rank conditions on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can be computed. These results come from block-moment matrix structure of the dual variable, which is consistent with the recent results on polynomial optimization. This particular structure enables us to make good use of simultaneous diagonalizability property of commuting diagonalizable matrices so that the sound rank conditions for the exactness verification can be obtained.

Language：Others   Publishing type：Research paper (scientific journal)  

本稿では，バックコンバータに対し，デューティ比を調整することにより出力電圧の定電圧制御を行う．とくに本稿では制御対象に対し目標値追従特性と外乱抑圧特性を独立に設計可能な2自由度LQIサーボ系を構成する．まずはじめに状態平均化法に基づく数式モデルを用いて2自由度LQIサーボ系を設計し，DSPボードに実装することによりコンバータの制御を行う．つぎに，状態平均化法ではモデル化誤差が大きいため，ARXモデルに基づいてシステム同定を行い，得られたモデルを用いて2自由度LQIサーボ系を設計し，同様の制御を行う．同定モデルに基づく制御則の有効性を検証するとともに，2自由度LQIサーボ系の設計法を適用することで，出力電圧を高精度に制御できることを示す．

DOI： 10.11509/sci.SCI09.0.117.0

Language：Others   Publishing type：Research paper (scientific journal)  

本稿では，単一の不確かなパラメータを有する線形時不変系のロバストH∞性能解析問題を取り扱う．既存の多くの手法とは異なり，本研究では双対LMIに基づいて，まずこの解析問題を未知行列と不確かなパラメータを変数とする多項式計画問題に帰着させる．つぎに制約条件として表れる等式条件を利用して，数値計算により容易に解くことのできる緩和問題を階層的に構成する．さらにはこの緩和問題における解の構造に着目し，解析結果の厳密性を保証するランク条件を導出する．また緩和問題を階層的に構成することで緩和による保守性を順次低減できることを，このランク条件を用いて示す．最後に数値例を用いて提案手法の有効性を示す．

DOI： 10.11509/sci.SCI09.0.533.0

Language：Others   Publishing type：Research paper (scientific journal)  

本稿では，離散時間線形周期時変系に対して，系の安定性およびH∞ノルム仕様を満たすメモリー型周期時変状態フィードバック制御器を設計することを考える．メモリー型周期時変状態フィードバック制御器は，現在時刻だけでなく過去の時刻における状態変数の値も用いて入力を決定するという特徴をもつ．本稿では，このような制御器が存在するための必要十分条件をLMIの形で表現し，このLMIをもとにポリトープ型の不確かさを有する系に対してメモリー型周期時変状態フィードバック制御器を設計する．最後に，提案する設計手法が有効であること，とくに周期を大きくすることで不確かさを有する系に対する設計における保守性を順次低減できることを，数値例を用いて示す．

DOI： 10.11509/sci.SCI09.0.281.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Periodically Time-Varying Memory State-Feedback Controller Synthesis for Uncertain Discrete-Time Linear Systems:The H2 Case

DOI： 10.11511/jacc.52.0.60.0

Language：English   Publishing type：Research paper (scientific journal)  

The generalized version of the S-procedure, recently introduced by Iwasaki and co-authors and Scherer independently, has proved to be very useful for robustness analysis and synthesis of control systems. In particular, this procedure provides a nonconservative way to convert specific inequality conditions on lossless sets into numerically verifiable conditions represented by linear matrix inequalities (LMIs). In this paper, we introduce a new notion, one-vector-lossless sets, and propose a generalized S-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized S-procedure, we can examine various properties of matrix-valued functions over some regions on the complex plane. To illustrate the usefulness, we show that full rank property analysis problems of polynomial matrices over some specific regions on the complex plane can be reduced into LMI feasibility problems. It turns out that many existing results such as Lyapunov's inequalities and LMIs for state-feedback controller synthesis readily follow from the suggested generalized S-procedure.

DOI： 10.1137/050627551

Language：Japanese   Publishing type：Research paper (scientific journal)  

Trajectory Tracking Control of a Two-axis Arm Driven by Pneumatic Artificial Muscles

DOI： 10.9746/ve.sicetr1965.44.927

Language：English   Publishing type：Research paper (scientific journal)  

The goal of this paper is to provide an elementary proof for the exactness of the (D,G) scaling. The (D,G) scaling has vast application area around control theory, optimization and signal processing. This is because, by applying the (D,G) scaling, we can convert inequality conditions depending on an uncertain parameter to linear matrix inequalities (LMIs) in an exact fashion. However, its exactness proof is tough, and this stems from the fact that the proof requires an involved matrix formula in addition to the standard Lagrange duality theory. To streamline the proof, in the present paper, we clarify that the involved matrix formula is closely related to a norm preserving dilation under structural constraints. By providing an elementary proof for the norm preserving dilation, it follows that basic results such as Schur complement and congruence transformation in conjunction with the Lagrange duality theory are enough to complete a self-contained exactness proof.

DOI： 10.9746/jcmsi.1.474

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we consider the problem of computing the distance to uncontrollability (DTUC) of a given controllable pair A ∈ C^{n × n} and B ∈ C^{n × m}. It is known that this problem is equivalent to computing the minimum of the smallest singular value of [A - z I B] over z ∈ C. With this fact, Gu et al. proposed an algorithm that correctly estimates the DTUC at a computation cost O (n⁴). From the viewpoints of linear control system theory, on the other hand, this problem can be regarded as a special case of the structured singular value computation problems and thus it is expected that we can establish an alternative LMI-based algorithm. In fact, this paper first shows that we can compute a lower bound of the DTUC by simply applying the existing techniques to solve robust LMIs. Moreover, we show via convex duality theory that this lower bound can be characterized by a very concise dual SDP. In particular, this dual SDP enables us to derive a condition on the dual variable under which the computed lower bound surely coincides with the exact DTUC. On the other hand, in the second part of the paper, we consider the problem of computing the similarity transformation matrix T that maximizes the lower bound of the DTUC of (T^{- 1} A T, T^{- 1} B). We clarify that this problem can be reduced to a generalized eigenvalue problem and thus solved efficiently. In view of the correlation between the DTUC and the numerical difficulties of the associated pole placement problem, this computation of the transformation matrix would lead to an effective and efficient conditioning of the pole placement problem for the pair (A, B).

DOI： 10.1016/j.sysconle.2008.03.002

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we address the H∞ model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the H∞ optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting.

Language：English   Publishing type：Research paper (scientific journal)  

The generalized version of the $mathcal{S}$-procedure, recently introduced by Iwasaki and co-authors and Scherer independently, has proved to be very useful for robustness analysis and synthesis of control systems. In particular, this procedure provides a nonconservative way to convert specific inequality conditions on lossless sets into numerically verifiable conditions represented by linear matrix inequalities (LMIs). In this paper, we introduce a new notion, one-vector-lossless sets, and propose a generalized $mathcal{S}$-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized $mathcal{S}$-procedure, we can examine various properties of matrix-valued functions over some regions on the complex plane. To illustrate the usefulness, we show that full rank property analysis problems of polynomial matrices over some specific regions on the complex plane can be reduced into LMI feasibility problems. It turns out that many existing results such as Lyapunov's inequalities and LMIs for state-feedback controller synthesis readily follow from the suggested generalized $mathcal{S}$-procedure.

Language：Japanese   Publishing type：Research paper (scientific journal)  

Modeling of Cuk Converters based on Discretization ofState Equations and Its Experimental Verification

DOI： 10.11509/sci.SCI08.0.179.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Robust Performance Analysis of Uncertain LTI Systems based on Dual LMIs

DOI： 10.11511/jacc.51.0.172.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Robust H2 Performance Analysis of Continuous-Time LTI Systems Affected by Parametric Uncertainties

DOI： 10.11509/sci.SCI08.0.210.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Atitude Control of a Experimental Helicopter with a 2DOF-LQI Design Method

DOI： 10.11509/sci.SCI08.0.341.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Positioning Control of a Pneumatic Actuation Mechanism of Antagonist-Type Based on Simple Adaptive Control

DOI： 10.11509/sci.SCI07.0.233.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Language：English   Publishing type：Research paper (scientific journal)  

In this note, we propose necessary and sufficient conditions for the asymptotic stability analysis of two-dimensional (2-D) systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions that enable us to analyze the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that, by employing the generalized S-procedure, we can derive smaller size of LMIs so that the computational burden can be reduced.

DOI： 10.1109/TAC.2006.880789

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we consider the robust Hurwitz stability analysis problems of a single parameter-dependent matrix A (θ) {colon equals} A₀ + θ A₁ over θ ∈ [- 1, 1], where A₀, A₁ ∈ R^{n × n} with A₀ being Hurwitz stable. In particular, we are interested in the degree N of the polynomial parameter-dependent Lyapunov matrix (PPDLM) of the form P (θ) {colon equals} ∑_{i = 0}^N θⁱ P_i that ensures the robust Hurwitz stability of A (θ) via P (θ) > 0, P (θ) A (θ) + A^T (θ) P (θ) < 0 (∀ θ ∈ [- 1, 1]). On the degree of PPDLMs, Barmish conjectured in early 90s that if there exists such P (θ), then there always exists a first-degree PPDLM P (θ) = P₀ + θ P₁ that meets the desired conditions, regardless of the size or rank of A₀ and A₁. The goal of this paper is to falsify this conjecture. More precisely, we will show a pair of the matrices A₀, A₁ ∈ R^{3 × 3} with A₀ + θ A₁ being Hurwitz stable for all θ ∈ [- 1, 1] and prove rigorously that the desired first-degree PPDLM does not exist for this particular pair. The proof is based on the recently developed techniques to deal with parametrized LMIs in an exact fashion and related duality arguments. From this counter-example, we can conclude that the conjecture posed by Barmish is not valid when n ≥ 3 in general.

DOI： 10.1016/j.automatica.2006.04.011

Language：Japanese   Publishing type：Research paper (scientific journal)  

A Redundant Descriptor Approach to H_∞ State-Feedback Controller Synthesis

Language：Japanese   Publishing type：Research paper (scientific journal)  

Robust H_∞ Performance Analysis of Linear Time-Invariant Uncertain Systems via Polynomially Parameter-Dependent Lyapunov Functions

Language：Others   Publishing type：Research paper (scientific journal)  

In this paper, we shall provide a new redundant descriptor approach to H_∞ state-feedback controller synthesis based on the strategy of the recently developed dilated LMIs. It is known that both of the redundant descriptor and the dilated LMI approaches are effective for robust/gain-scheduled H_∞ state-feedback controller synthesis when the state-space matrices of the plant are affected by uncertain/scheduling parameters. These approaches are closely related in the sense that they enlarge the size of LMIs and employ additional matrix variables to obtain more tractable LMI conditions. However, in the existing redundant descriptor approaches, some assumptions have been imposed on the the state-space matrices of the plant to avoid difficulties arising from the fictious direct feedthrough term from the disturbance inputs to the performance outputs of the resulting descriptor form. This is in sharp contrast with the dilated LMI approaches that do not require any specific assumptions on the state space matrices. To fill the gap between these two approaches, in the present paper, we revisit the redundant descriptor approaches and provide a new way to recast the state-space representations into descriptor forms by employing yet new additional variables. By employing those new additional variables, it turns out that those LMIs resulting from the descriptor approaches coincide with the known dilated LMI conditions. The role of those additional variables can be seen clearly if we view from the standpoint of the redundant descriptor approaches.

DOI： 10.9746/sicetr1965.42.750

Language：Others   Publishing type：Research paper (scientific journal)  

DOI： 10.11511/jacc.49.0.65.0

Language：Others   Publishing type：Research paper (scientific journal)  

In this paper, we address robust H_∞ performance analysis problems of linear time-invariant polytopic-type uncertain systems. We employ polynomially parameter-dependent Lyapunov functions to assess the robust H_∞ performance and derive sufficient conditions for the existence of those Lyapunov functions in terms of numerically verifiable finitely many linear matrix inequalities (LMIs). To this end, we first consider to analyze the H_∞ performance of uncertainty-free systems by means of Lyapunov functions of a particular form, and explore the existence condition of such Lyapunov functions. We show that, by considering a suitable redundant system description, the existence condition of such Lyapunov functions can be reduced into constrained inequality conditions to which Finsler's Lemma can be applied. It turns that we can readily obtain novel LMI conditions for the H_∞ performance analysis of uncertainty-free systems. The LMI-based conditions that enable us to assess the robust H_∞ performance of uncertain systems by means of polynomially parameter-dependent Lyapunov functions follow immediately from these newly obtained LMIs. The LMI conditions obtained in this paper can be regarded as a natural extension of those known as extended or dilated LMIs in the literature.

DOI： 10.9746/sicetr1965.42.618

Language：Others   Publishing type：Research paper (scientific journal)  

制御対象の保護のために制御入力の大きさを制限する必要がある場合や，操作器の出力の物理的な限界のために制御入力が飽和して，制御性能の劣化（ワインドアップ現象）が発生する恐れがあるとき，既存の2 自由度L Q I サーボ系の設計法では，設計パラメータを試行錯誤的に調整しなければならない．本稿では，L2性能保証領域の考え方を採用し，制御入力の飽和を陽に考慮した2 自由度L Q I サーボ系の設計法の1 つとして，制御入力の非飽和を達成する設計法を提案する．

DOI： 10.11509/sci.SCI06.0.285.0

Language：Others   Publishing type：Research paper (scientific journal)  

本稿では，不確かさを有する線形時不変系のロバストH∞性能を多項式型パラメータ依存リアプノフ関数を用いて解析することを可能とする新たなLMI条件を提案する．また，この提案条件の解析結果の保守性は前もって指定する行列に依存する．そこで，提案条件によるH∞性能解析を繰り返し計算に帰着させることによって，指定する行列を望ましい値に更新し、さらに厳密な(保守的でない)解析結果を得るための改善法を提案する．

DOI： 10.11509/sci.SCI06.0.52.0

Language：Others   Publishing type：Research paper (scientific journal)  

2軸型空圧人工筋アームは軽量で柔軟であるという特長を持ち，2つの軸をもつことから手先位置をある平面内で自由に動かすことが可能である．しかし，圧縮空気や人工筋を用いることから剛性が低く，運動学に非線形性を含むことから正確な軌道追従制御をすることが容易ではない．これに対して本稿では，LQ最適制御理論に基づくサーボ系の設計法と人工筋の圧力に関するマイナーループを併用した軌道追従制御を試みた．

DOI： 10.11509/sci.SCI06.0.288.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Stability Analysis for 2-D Discrete Systems

DOI： 10.11509/isciesci.50.11_412

Language：Others   Publishing type：Research paper (scientific journal)  

本稿では不確かな線形時不変系に対する状態フィードバックH∞制御系設計問題について考察する．過去の研究において提案されたLMI(線形行列不等式)による設計法に基づいて(D,G)スケーリングを用いた設計法を提案する．さらに，その提案手法を繰り返し用いることにより，従来の手法に比べてより良いH∞性能を達成するフィードバックゲインを求めることができることを示す．

DOI： 10.11509/sci.SCI06.0.266.0

Language：English   Publishing type：Research paper (scientific journal)  

This paper studies robust performance analysis problems of linear time-invariant systems affected by real parametric uncertainties. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is know that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. This paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated LMI conditions even in the case of rational parameter dependence. In particular, it turns out that the proposed dilated LMIs enable us to assess the robust performance via multiaffine parameter-dependent Lyapunov variables so that less conservative analysis results can be achieved. Connections among the proposed conditions and existing results are also discussed concretely. Several existing results can be viewed as particular cases of the proposed conditions.

DOI： 10.1016/j.automatica.2005.05.023

Language：Japanese   Publishing type：Research paper (scientific journal)  

A Study to Assess the Disturbance Response of Control Systems across Switching

Language：Japanese   Publishing type：Research paper (scientific journal)  

The 16th IFAC World Congress

DOI： 10.11509/isciesci.49.9_389

Language：Others   Publishing type：Research paper (scientific journal)  

In this paper, we discuss robust D-stability analysis of uncertain polynomial matrices. By introducing polynomial-type multipliers, we show that it is possible to obtain varieties of LMI conditions for D-stability analysis in a constructive way according to the order/structure of the multipliers to be employed. Then, we show the effectiveness of the proposed LMI conditions when dealing with robust D-stability analysis problems of polytopic-type uncertain polynomial matrices.

DOI： 10.11509/sci.SCI05.0.208.0

Language：Others   Publishing type：Research paper (scientific journal)  

In this paper, we aim at achieving accurate positioningcontrol of a pneumatic artificial antagonist-type actuation mechanism. This system has favorable characteristics such as safe interaction with humans and high flexibility. However, due to the nonlinearity of the system behavior as well as the weak rigidity of the compressed air, it is quite difficult to achieve accurate positioning control. To overcome these difficulties, in our preceding studies, we adopted the design method of two-degree-of-freedom (2DOF) LQI servo systems, by which satisfactory tracking performance for step references was achieved under various load conditions.In this paper, we consider ramp references and apply the design method of plant-variable (PV) optimal control, which could be regarded as a natural extension of the design method of 2DOF-LQI servo systems. It is demonstrated that accurate and quick tracking can be achieved for step and ramp references by this method.

DOI： 10.11509/sci.SCI05.0.219.0

Language：Others   Publishing type：Research paper (scientific journal)  

In recent studies, Asai proposed a strategy to analyze disturbance response of control systems across switching. It was shown that the performance deterioration caused by the disturbance can be assessed quantitatively by a sort of L₂ gain of the control system, which can be regarded as a generalization of the well-studied Hankel norm of linear time-invariant systems. In addition, explicit formulas to compute the L₂ gain have also been derived. The derivation explored there is, however, rather involved and does not conform to the elegant results already known in the analysis of Hankel operators. Motivated by these facts, in the present note, we give a concise proof for the results by Asai based on linear operator representations. It turns out that the results can readily be obtained by describing a procedure to compute the norm of the associated compact linear operator.

DOI： 10.9746/sicetr1965.41.937

Language：Japanese   Publishing type：Research paper (scientific journal)  

American Control Conference 2004

Language：English   Publishing type：Research paper (scientific journal)  

This paper provides new dilated linear matrix inequality (LMI) characterizations for continuous-time controller synthesis. The dilated LMIs enable us to parametrize controllers without involving the Lyapunov variables in the parametrizations. Taking advantage of this feature, we can readily design multiobjective controllers with non-common Lyapunov variables, whereas we are forced to employ a common one in the well-known Lyapunov shaping paradigm. In particular, it is shown that the proposed dilated-LMI-based approach to H₂/D-stability synthesis encompasses the corresponding Lyapunov shaping paradigm as a special case. In this sense, the results of this paper can be viewed as partial counterparts of those obtained in the discrete-time setting.

DOI： 10.1016/j.automatica.2004.06.009

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we propose new LMI-based conditions to design output-feedback controllers under structural constraints. The conditions are represented in terms of LMIs with rank constraints and we apply the alternating projection method to solve them. Even though the alternating projection algorithm does not ensure global convergence, extensive numerical experiments demonstrate that the proposed design method is promising in designing structured controllers. The difficulties and limitations linked with the proposed design method is also discussed.

DOI： 10.1080/00207170412331298947

Language：English   Publishing type：Research paper (scientific journal)  

In this note, we deal with the problem of approximating a given nth-order linear time-invariant system G by an rth-order system G_r where r < n. It is shown that lower bounds of the H_∞ norm of the associated error system can be analyzed by using linear matrix ineqaulity (LMI)-related techniques. These lower bounds are given in terms of the Hankel singular values of the system G and coincide with those obtained in the previous studies where the analysis of the Hankel operators plays a central role. Thus, this note provides an alternative proof for those lower bounds via simple algebraic manipulations related to LMIs. Moreover, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the problem is essentially convex and the optimal reduced-order models can be constructed via LMI optimization.

DOI： 10.1109/TAC.2004.831116

Language：Others   Publishing type：Research paper (scientific journal)  

本稿では，2×2のエルミート行列に関する2次形式で表現される複素平面上のある領域において、与えられたマトリクスペンシルが正則となるためのLMI条件を導出する．さらにこの条件を応用した線形時不変系のLyapunovの安定性理論の新しい証明，およびパラメータ変動系のロバスト安定性解析に関する新たなLMI条件を示す．

DOI： 10.11509/sci.SCI04.0.47.0

Language：Others   Publishing type：Research paper (scientific journal)  

本稿では離散時間系のモデル低次元化について考察する．はじめに，系G(z)に対して低次元化モデルGr(z)を求める場合，誤差系のH無限大ノルムの下界が行列不等式を用いて解析できることを示す．さらに系 G(z) のハンケル特異値の最小値の重複度分だけ低次元化を行う場合には，上述の下界が下限となり，かつ下限を達成する最適な低次元化モデルがLMI最適化によって求まることを示す．

DOI： 10.11509/sci.SCI04.0.70.0

Language：Others   Publishing type：Research paper (scientific journal)  

This paper is concerned with model reduction methods taking account of positive realness and minimum-phase properties, while keeping the H infinity norm of the associated error system (||E(s)||)as small as possible with the LMI optimization technique. These methods are applied to the reduction of an Euler-Bernoulli beam system to demonstrate their effectiveness.In the application of the proposed methods,we first need to obtain apositive real or minimum-phase reduced-order model such that ||E(s)|| is reasonably small.A way for obtaining such a reduced-order modelis via the truncated positive real balanced realization method,but it sometimes leads toa reduced-order model with very large ||E(s)||.Thus, this paper also tackles this problem from the numerical pointof view.

DOI： 10.11509/sci.SCI04.0.71.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Control System Analysis and Synthesis Using Dilated LMIs

DOI： 10.11509/isciesci.48.9_355

Language：Japanese   Publishing type：Research paper (scientific journal)  

Model Reduction Method Preserving the Steady-State Gain and Its Application to Electric Power Systems

DOI： 10.5687/iscie.16.476

Language：English   Publishing type：Research paper (scientific journal)  

Language：Others   Publishing type：Research paper (scientific journal)  

A two-degree-of-freedom design method of LQI servo systems has been proposed based on optimal control theory. The feature of this method is that tracking characteristics are determined optimally with respect to a quadratic-integral performance index while the integral compensator (i.e., the integral gain) can be designed independently without affecting tracking characteristics. This paper considers to apply the H∞ techniques to the design of the integral compensator. We apply such a design scheme to positioning control of a pneumatic servo system and show its effectiveness through experiments.

DOI： 10.11509/sci.SCI03.0.2004.0

Language：Others   Publishing type：Research paper (scientific journal)  

To design gain scheduled controllers in a less conservative fashion, a dilated-LMI-based approach has been proposed recently. However, this approach is still conservative due to the use of multi-affine parameter-dependent Lyapunov variables. In this paper, we revisit the dilated LMI condition and provide a yet less conservative design method that enables us to design gain scheduled controllers via polynomial-type parameter-dependent Lyapunov variables.

DOI： 10.11509/sci.SCI03.0.7005.0

Language：Others   Publishing type：Research paper (scientific journal)  

本稿ではモデル低次元化について考察する．最適Hankelノルム近似手法においては，モデル低次元化の際の誤差システムのH_∞ノルムの下界値がHankel特異値を用いて表現できることが示されている．本稿では，LMIに関連した代数的手法を適用することにより，これらの下界値が容易に導出できることを示す．さらに，低次元化の次数が１の場合には，LMI最適化問題を解くことにより誤差システムのH_∞ノルムを最小にする低次元化モデルが得られることを示す．

DOI： 10.11511/jacc.46.0.185.0

Language：English   Publishing type：Research paper (scientific journal)  

This paper addresses robust performance analysis problems for linear time-invariant systems depending on uncertain parameters. It is well known that, in the case of affine parameter dependence, we can deal with such problems based on standard LMI (Linear Matrix Inequalities) characterizations and the concept of quadratic stability. However, in the case of rational parameter dependence, we need another effort to arrive at numerically tractable conditions. This paper clarifies that recently developed dilated LMI characterizations are useful in dealing with such robust performance analysis problems. The dilated LMI’s also allow us to employ parameter-dependent Lyapunov variables, which are known to be quite effective to reduce the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.

DOI： 10.11499/sicep.2002.0.569.0

Language：Others   Publishing type：Research paper (scientific journal)  

This paper is concerned with a model reduction method taking account of the steady-state gain, while keeping the H_∞ norm of the associated error system as small as possible with the LMI optimization technique. An existing method to achieve this objective is such that only the input and output matrices are modified iteratively, and the state matrix remains unchanged. The extension of this method provided in this paper enables one to modify the state matrix as well. The method is applied to the reduction of a multi-machine electric power system to demonstrate the effectiveness of the proposed method.

DOI： 10.11509/sci.SCI02.0.147.0

Language：Others   Publishing type：Research paper (scientific journal)  

A number of design methods for output-feedback decentralized stabilizing controllers have been proposed for large-scale linear systems. In the centralized case, it is well known that this output-feedback synthesis problem is reduced to an optimization problem of linear matrix inequalities (LMI’s). In this paper, to design decentralized controllers, we restrict some variables of those LMI’s to block-diagonal forms. However, since this restriction is not enough to obtain decentralized controllers, we also introduce a certain replacement of variables. Since the latter causes the LMI’s to turn into bilinear matrix inequalities (BMI’s), we convert BMI’s into LMI’s by fixing some variables in the BMI’s. We get two kinds of LMI’s which are obtained by fixing some variables and solve those LMI’s alternately. The effectiveness of this design method is illustrated by numerical examples.

DOI： 10.11509/sci.SCI02.0.14.0

Language：Japanese   Publishing type：Research paper (scientific journal)  

Simple Adaptive Control Method with Automatic Tuning of PFC and Its Application to Positioning Control of a Pneumatic Servo System

DOI： 10.5687/iscie.14.102

Language：English   Publishing type：Research paper (scientific journal)  

In this study, we propose such sequential tuning methods of multivariable optimal regulators that can be applied to the tuning of control systems under operation. In such tuning, it is desirable to change feedback gains only step by step, confirming that the control performance is actually improved in each step. The first method we propose is such that we design an optimal single-input regulator in each step, by paying attention to only one input of the plant while the feedback laws to other inputs are fixed to those obtained in the previous sequential tuning steps. On the other hand, the second method is such that all elements of the feedback gain are changed at once, while we are given the design freedom about how much we are to change the gain. These two methods as well as their combined use are shown to lead to the optimal gain as a multivariable control system eventually, provided that the sequential tuning steps are repeated sufficiently many times. We apply these methods to the tuning of LQI servo systems, and carry out the simulation study of the control of a hot strip mill to illustrate the tuning law and show its effectiveness.

DOI： 10.1080/002071700445415

Language：Japanese   Publishing type：Research paper (scientific journal)  

A Sequential Tuning Method of Controller based on H_2 Performance

Language：Japanese   Publishing type：Research paper (scientific journal)  

Sequential Tuning Methods for Optimal Control Systems and their Application to Hot Strup Mills

Event date： 2024.3

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2024.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2024.3

Language：Japanese  

Country：Japan  

Event date： 2023.4 - 2023.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2023.3 - 2024.3

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：宮城   Country：Japan  

Event date： 2023.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.11 - 2021.11

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.9

Language：English   Presentation type：Oral presentation (general)  

Venue：Bayreuth   Country：Germany  

Event date： 2022.9

Language：English   Presentation type：Oral presentation (general)  

Venue：Kumamoto   Country：Japan  

Event date： 2022.7

Language：English   Presentation type：Oral presentation (general)  

Venue：Virtual   Country：United Kingdom  

Event date： 2022.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2021.12

Language：English   Presentation type：Oral presentation (general)  

Country：United States  

Event date： 2021.11

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2021.11

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2021.11

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2021.6

Language：English   Presentation type：Oral presentation (general)  

Venue：Virtual   Country：Netherlands  

Event date： 2021.5

Language：English   Presentation type：Oral presentation (general)  

Venue：Virtual   Country：Korea, Republic of  

Event date： 2021.5

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2021.5

Language：English   Presentation type：Oral presentation (general)  

Venue：Virtual   Country：Germany  

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2019.6

Language：English  

Venue：Naples   Country：Italy  

This study is concerned with the H{2} state-feedback controller synthesis problem under positivity constraint on the closed-loop system. This problem is believed to be a nonconvex problem in both continuous-and discrete-time system settings and hence remains to be the most challenging issue in positive system theory. For this hard problem, in the discrete-time system setting, the authors recently proposed a technique for the lower bound computation of the best achievable H{2} performance by a specific treatment of finite impulse responses (FIRs) of the closed-loop systems. The goal of this paper is to extend this idea to the continuous-time system setting. Even though there is no notion of FIR in (finite-dimensional) continuous-time system impulse responses, the truncation of the Taylor series expansion of the matrix exponential function in the impulse response paves the way for obtaining a semidefinite programming problem (SDP) for the lower bound computation. We show that, by increasing the truncation degree, we can construct a sequence of SDPs that generates a monotonically non-decreasing sequence of the lower bounds. By combining this lower bound computation technique with heuristic upper bound and suboptimal gain computation techniques, it becomes possible to draw definite conclusion on the quality of the computed suboptimal gains.

Event date： 2018.9

Language：English  

Venue：Nara   Country：Japan  

This study is concerned with decentralized stabilizing controller synthesis problem for interconnected systems constructed from positive subsystems. The main issue is how to design a controller for each subsystem locally so that positivity and stability of the overall interconnected system can be attained. Under a specific interconnection structure, the author has already shown that such a controller can be designed locally without any information about the rest of the positive subsystems. Namely, under the specific interconnection structure, we can reduce the original problem into a set of L-1- induced-norm optimal controller synthesis problems for subsystems each of which can be solved indeed locally via linear programming. On the basis of these preceding results, in this study, we show an optimality property of such local L-1 -induced-norm optimal controllers in a global sense. More precisely, we prove that the set of L-1 -induced-norm optimal controllers is indeed globally optimal in the sense that it minimizes the abscissa of the coefficient matrix of the overall interconnected closed-loop system.

Event date： 2018.6

Language：English  

Venue：Limassol   Country：Cyprus  

This paper is concerned with the H-{2} state- feedback synthesis problem under positivity constraint on the closed-loop system. This problem is believed to be a non-convex problem and hence exact treatment is not known to this date. With this difficulty in mind, in this paper, we first derive several semidefinite programs (SDPs) for the computation of the upper bounds of the achievable performance as well as suboptimal gains. However, if we rely only on the upper bound computation, we cannot say anything quantitatively on the quality of the computed suboptimal gains. For such quantitative evaluation, we next derive an SDP for the lower bound computation of the achievable performance. The key idea in deriving such an SDP is that, if the closed-loop system is positive, then the Lya- punov variable in the standard SDP for the H-{2} state-feedback synthesis should be (elementwise) nonnegative. By numerical examples, we illustrate the effectiveness and limitation of the proposed strategy with upper and lower bounds computation. Keywords: H-{2} state-Feedback synthesis, positivity constraint, upper and lower bound computation.

Event date： 2018.3

Language：English  

Venue：Tokyo   Country：Japan  

This paper is concerned with the H₂ state-feedback synthesis problem for discrete-time systems under positivity constraint on the closed-loop systems. This problem is believed to be a non-convex problem and hence exact treatment is not known to this date. With this difficulty in mind, in this paper, we first derive semidefinite programs (SDPs) for the computation of the upper bounds of the achievable H₂ performance as well as suboptimal gains. However, if we merely rely on the upper bound computation, we cannot draw any definite conclusion on the quality of the computed suboptimal gains. Thus the main issue of the present paper is the lower bound computation, and to this end we derive an SDP for that computation via specific treatment of the finite impulse resonse (FIR) with the idea of time-varying gain synthesis. We show that the lower bounds become tighter as we increase the length of the FIR. By numerical examples we show the soundness of the proposed strategy with upper and lower bounds computation.

Event date： 2017.12

Language：English  

Venue：Melbourne   Country：Australia  

This paper is concerned with dominant pole analysis of neutral-type time delay positive systems (TDPSs). The neutral-type TDPS of interest is constructed by feedback connection between a finite-dimensional linear time-invariant positive system (FDLTIPS) and the pure delay, where the FDLTIPS has a nonzero direct feedthrough term. It has been shown very recently that this neutral-type TDPS is asymptotically stable if and only if its delay-free finite-dimensional counterpart is stable and admissible, where the latter means that the direct feedthrough term is Schur stable. This result in particular implies that the stability is irrelevant of the length of the delay. However, it is strongly expected that convergence or divergence rate depends on the delay length and this is the motivation for the dominant pole analysis. In this paper, we show that one of the dominant poles of the neutral-type TDPS is real irrespective of the stability, and we derive closed-form formulas that relate the real dominant pole with the delay length for both stable and unstable neutral-type TDPSs.

Event date： 2017.9

Language：English  

Venue：Kanazawa   Country：Japan  

Motivated by recent drastic advances in the study of linear-time invariant (ETI) positive systems, we explore analysis techniques of general, not necessarily positive ETI systems using positive system theory. Even though a positive system is characterized by its peculiar property that its impulse response is nonnegative, we often deal with nonnegative impulse responses even in general ETI system analysis. A typical example is the computation of the H₂ norm where we focus on squared impulse responses. To deal with such products of impulse responses in a systematic fashion, in this paper, we first establish a construction technique of an ETI system whose impulse response is given by the product of impulse responses of two different ETI systems. Then, as the main result, we reduce the H₂ norm computation problem of a general ETI system into the L_∞-induced norm computation problem (or L₁ problem in short) of a positive system, by which we can derive a closed-form formula for the H_∞ norm computation.

Event date： 2016.12

Language：English  

Venue：Las Vegas   Country：United States  

In SDP-based H_∞ control, we often encounter numerical difficulties when solving SDPs by various pieces of software. It is empirically known that such numerical difficulty occurs if an SDP at hand or its dual has no interior point feasible solutions, and this is indeed the case of some SDPs in H_∞ control. To conceive a way for getting around such numerical difficulties in a concrete problem setting, in this paper, we focus on the dual SDP for the H_∞ control problem of the transfer function (1 + PK)-1P and simplify it. More precisely, by actively using the information of unstable zeros (non-minimum phase zeros) of the plant P, we reduce the original dual SDP into a set of simplified SDPs each of which and its dual have interior point feasible solutions. In this way, we show by numerical experiments that reliable numerical computation can be done by SDP software. On the other hand, once we have obtained simplified SDPs, it becomes possible to further reduce them into the computation of maximum singular values of matrices determined by unstable zeros. In this way, if the number of unstable zeros is moderate, we can obtain analytical expressions of the best achievable H_∞ performance or its lower bounds in terms of the unstable zeros. Keywords: H_∞ control, SDP, numerical reliability, best achievable performance.

Event date： 2016.9

Language：English  

Venue：Buenos Aires   Country：Argentina  

In this paper, we study a dual-LMI-based approach to H_∞ performance limitation analysis of SISO systems. The scope includes the analysis of the sensitivity function S = (1 + PK)^-1 and the complementary sensitivity function T = (1 + PK)^-1 PK where P and K stand for the plant and the controller, respectively. The H_∞ performance limitations for these transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero (i.e., non-minimum phase zero) of degree one or the sole unstable pole of degree one. The goal of this paper is to show that such exact bounds can be reproduced by a dual LMI approach. To this end, we study a Lagrange dual of the standard SDP that is usually used to design H_∞ optimal controllers by numerical computation. By characterizing the structure of dual feasible solutions in terms of unstable zeros and unstable poles of the plant, we clarify that we can construct an optimal solution for the dual SDP analytically. It follows that we obtain exact H_∞ performance bounds that are consistent with the known results.

Event date： 2016.9

Language：English  

Venue：Rome   Country：Italy  

This chapter is concerned with asymptotic stability analysis of neutral type time-delay positive systems (TDPSs). We focus on a neutral type TDPS represented by a feedback system constructed from a finite-dimensional LTI positive system and the pure delay, and give a necessary and sufficient condition for the stability. In the case where we deal with a retarded type TDPS, i.e., if the direct-feedthrough term of the finite-dimensional LTI positive system is zero, it is well known that the retarded type TDPS is stable if and only if its delay-free finite-dimensional counterpart is stable. In the case of neutral type TDPS, i.e., if the direct-feedthrough term is nonzero, however, we clarify that the neutral type TDPS is stable if and only if its delay-free finite-dimensional counterpart is stable and the direct-feedthrough term is Schur stable. Namely, we need additional condition on the direct-feedthrough term.

Event date： 2016.7

Language：English  

Venue：Boston   Country：United States  

In this paper, we study a dual-LMI-based approach to H∞ performance limitations analysis of SISO systems with multiple (i.e., duplicated) unstable zeros and poles. The scope includes the analysis of the transfer functions M = (1+PK)-1 P, S = (1+PK)-1, and T = (1+PK)-1 PK where P and K stand for the plant and the controller, respectively. The latter two transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero of degree one or the sole unstable pole of degree one. However, such exact bounds are hardly available for the cases where the plant has multiple (i.e., duplicated) unstable zeros and poles. To obtain a lower bound of the best achievable H∞ performance for such involved cases, in this paper, we study a dual of the standard LMI that represents the existence of H∞ controllers achieving a prescribed H∞ performance level. By deriving a parametrization of dual feasible solutions and constructing a dual suboptimal solution analytically, we can readily obtain a lower bound of the best achievable H∞ performance.

Event date： 2015.12

Language：English  

Venue：Osaka   Country：Japan  

This paper is concerned with the analysis and synthesis of time-delay interconnected positive systems with external inputs. The interconnected system of interest is constructed from positive subsystems and a nonnegative interconnection matrix, where we assume delays on communications over subsystems. We first analyze the output behavior of the time-delay interconnected positive systems with step and ramp inputs. Then, we second show that the analysis results can be applied to leader-follower-type formation control of moving objects. More precisely, we show a linear-programming-based synthesis condition of the interconnection matrix to achieve a desired formation. We finally demonstrate the effectiveness of the synthesis technique by numerical simulation on time-headway control of a platoon of vehicles.

Event date： 2015.12

Language：English  

Venue：Osaka   Country：Japan  

In a very recent study by the first author and his colleagues, a novel LMI-based approach has been proposed to the best achievable H∞ performance limitations analysis for continuous-time SISO systems. Denoting by P and K a plant and a controller, respectively, and assuming that the plant P has an unstable zero, it was shown that a lower bound of the best achievable H∞ performance with respect to the transfer function (1+PK)-1P can be given analytically in terms of the real part of the unstable zero and the first non-zero coefficient of the Taylor expansion of P around the unstable zero. The goal of this paper is to show that, if the plant P has no unstable zeros except for the sole real unstable zero of degree one, then the lower bound shown there is exact. The exactness proof relies on the detailed analysis on the Lagrange dual problem of the SDP characterizing H∞ optimal controllers. More precisely, we show that we can construct an optimal dual solution proving the exactness analytically in terms of the state-space matrices of the plant P and the unstable zero. This analytical expression of the dual optimal solution is also a main result of this study.

Event date： 2015.7

Language：English  

Venue：Bratislava   Country：Slovakia  

In this paper, we deal with an interconnected system constructed from positive subsystems and a nonnegative interconnection matrix. In particular, motivated by leader-follower-type formation control of multi-agent systems, we concentrate our attention on the case where external inputs are applied to the interconnected system. By analyzing the steady-state output of the interconnected system with respect to step and ramp inputs, respectively, we derive synthesis conditions on the interconnection matrix to achieve formation-control-oriented design objectives. We finally illustrate the usefulness of theoretical results via numerical simulation on time-head way control of vehicle platoons.

Event date： 2015.5 - 2015.6

Language：English  

Venue：Kota Kinabalu   Country：Malaysia  

This paper is concerned with the analysis of interconnected systems where positive subsystems are connected by a nonnegative interconnection matrix with communication delays. Recently, we have shown that, under mild assumptions on the positive subsystems and the interconnection matrix, the delay interconnected system has stable poles only except for a simple pole at the origin, and the output of the interconnected system converges to a scalar multiple of a prescribed positive vector. This result is effectively used for formation control of multi-agent systems with positive dynamics, where the desired formation is basically achieved irrespective of the length of the delays. However, the rate of convergence varies according to the length of the delays and hence quantitative evaluation of the convergence rate is an important issue. For the quantitative evaluation of the convergence rate, in this paper, we provide an efficient method for the computation of the lower bounds of the second largest real part of the (infinitely many) poles of the delay interconnected positive systems.

Event date： 2014.12

Language：English  

Venue：Los Angeles   Country：United States  

This is a continuation of our preceding studies on the analysis of interconnected positive systems. Under mild conditions on positive subsystems and a nonnegative interconnection matrix, we showed that the state of the interconnected positive system converges to a positive scalar multiple of a prescribed positive vector. As a byproduct of this property, called persistence, it turned out that the output converges to the positive right eigenvector of the interconnection matrix. This result is effectively used in the formation control of multi-agent positive systems. The goal of this paper is to prove that the essential property of persistence is still preserved under arbitrary (time-invariant) communication delays. In the context of formation control, this preservation indicates that the desired formation is achieved robustly against communication delays, even though the resulting formation is scaled depending upon initial conditions for the state. From a mathematical point of view, the key issue is to prove that the delay interconnected positive system has stable poles only except for a pole of degree one at the origin, even though it has infinitely many poles in general. To this end, we develop frequency-domain (s-domain) analysis for delay interconnected positive systems.

Event date： 2014.8

Language：English  

Venue：Cape Town   Country：South Africa  

This paper addresses the formation control problem of multi-agent systems whose dynamics are all positive. Recently, as a byproduct of the analysis of interconnected positive systems, we have shown an effective way for designing a communication scheme (i.e., an interconnection matrix) over the positive agents so that a prescribed formation can be achieved. For the convergence rate analysis of such multi-agent positive systems under formation control, we propose an efficient algorithm to compute the dominant pole of interconnected positive systems by actively using the positive property of each agent. We illustrate by numerical examples that the proposed algorithm is definitely efficient particularly when the number of agents gets larger.

Event date： 2014.8

Language：English  

Venue：Cape Town   Country：South Africa  

Robust stability analysis is investigated for discrete-time linear systems with rational dependency with respect to polytopic type uncertainties. Two type of uncertainties are considered: constant parametric uncertainties and time-varying switching uncertainties. Results are in LMI formalism and proofs involve parameter-dependent, quadratic in the state, Lyapunov functions. The new proposed conditions are shown to extend and merge two important existing results. Conservatism reduction is tackled via a model augmentation technique. Numerical complexity is contained by exploiting the structure of the models with respect to the uncertainties.

Event date： 2014.8

Language：English  

Venue：Cape Town   Country：South Africa  

Design of robust observers is considered in the context of linear discrete-time, time invariant systems. Robustness is achieved with respect to polytopic type uncertainties that affect the dynamics of the plant. At the difference with the uncertainty-free situation, state-feedback/observer separation principle does not hold. Therefore, the observer design has to take into account the state-feedback gain. Results are derived with linear matrix inequality formalism and involve up-to-date slack-variables approach. A numerical example illustrates the results. Limitations of the method are discussed and prospective work for improving these is exposed.

Event date： 2014.6

Language：English  

Venue：Strasbourg   Country：France  

This paper is concerned with the dominant pole analysis of asymptotically stable time-delay positive systems (TDPSs). It is known that a TDPS is asymptotically stable if and only if its corresponding delay-free system is asymptotically stable, and this property holds irrespective of the length of delays. However, convergence performance (decay rate) should degrade according to the increase of delays and this intuition motivates us to analyze the dominant pole of TDPSs. As a preliminary result, in this paper, we show that the dominant pole of a TDPS is always real. We also construct a bisection search algorithm for the dominant pole computation, which readily follows from recent results on α-exponential stability of asymptotically stable TDPSs. Then, we next characterize a lower bound of the dominant pole as an explicit function of delays. On the basis of the lower bound characterization, we finally show that the dominant pole of an asymptotically stable TDPS is affected by delays if and only if associated coefficient matrices satisfy eigenvalue-sensitivity condition to be defined in this paper. Moreover, we clarify that the dominant pole goes to zero (from negative side) as time-delay goes to infinity if and only if the coefficient matrices are eigenvalue-sensitive.

Event date： 2013.12

Language：English  

Venue：Florence   Country：Italy  

This paper addresses the analysis and synthesis of interconnected systems constructed from SISO positive subsystems and a nonnegative interconnection matrix. We focus on the case where the interconnection matrix switches over a finite set of given nonnegative matrices. By analyzing the existence of a first integral, we clarify a condition under which the state of the interconnected system, starting from any nonnegative initial state, becomes nonnegative and bounded under arbitrary switching. By extending this result, we establish a linearprogramming- based method to synthesize the interconnection matrices to achieve a switching formation control of multi-agent positive systems.

Event date： 2013.7

Language：English  

Venue：Zurich   Country：Switzerland  

This paper is concerned with the analysis of large-scale interconnected systems constructed from positive subsystems and a nonnegative interconnection matrix. We first show that the interconnected system is admissible and stable if and only if a Metzler matrix built from the coefficient matrices of the positive subsystems and the interconnection matrix is Hurwitz stable. By means of this key lemma, we further provide several results that characterize the admissibility and stability of interconnected systems in terms of the weighted L₁-induced norm of each positive subsystem and the Frobenius eigenvalue of the interconnection matrix. Moreover, in the case where every subsystem is SISO, we provide explicit conditions under which the interconnected system has the property of persistence, i.e., the state of the interconnected system converges to a unique strictly positive vector (up to a strictly positive constant multiplicative factor) irrespective of nonnegative and nonzero initial states. We illustrate the effectiveness of the persistence results via formation control of multi-agent systems.

Event date： 2013.5

Language：English  

Venue：Hiroshima   Country：Japan  

An efficient algorithm was developed for transmitting power maximization of phased arrays including amplitude degradation. A large-scale phased array will be adopted as transmitting antenna of a solar power satellite project. The amplitude of each antenna element will be degraded at every phase shift due to long-term operation and failure of antenna units. This array problem is formulated as a discrete optimization problem, and decomposed into element-wise subproblems by utilizing the real rotation theorem. Then a polynomial-time algorithm to solve the problem numerically was constructed.

Event date： 2012.12

Language：English  

Venue：Maui, HI   Country：United States  

This study concerns decentralized control of interconnected positive systems. The main issue is how to design a controller for each subsystem locally so that positivity and stability of the overall interconnected system can be attained. Under a specific interconnection structure, we will show that such a controller can be designed optimally without any information about the rest of the positive subsystems. This achievement is based on our recent characterization of stability of interconnected positive systems in terms of the L₁-induced norm of each subsystem, where the L₁-induced norm is evaluated with positive weighting vectors that are coupled mutually over the subsystems. The key observation in this study is that, under the specific interconnection structure, we can decouple the L₁-induced norm conditions completely. We thus reduce the original stabilization problem into a set of L₁-induced norm optimal controller synthesis problems each of which can be solved indeed locally. In particular, the L₁-induced norm optimal controller synthesis can be done efficiently by solving a semidefinite programming problem.

Event date： 2012.12

Language：English  

Venue：Maui, HI   Country：United States  

This paper is devoted to H_∞ analysis and synthesis conditions of state-feedback periodic memory controllers, in the framework of periodic uncertain discrete-time systems. The proposed conditions are such that the user is allowed to freely add degrees-of-freedom to the control law which effectively reduces the conservatism of the synthesis condition and decreases the guaranteed H_∞ induced norm of the obtained uncertain closed-loop systems. Numerical examples show that for a particular structure of controllers the efficiency of the design theorem can be significantly enhanced by relaxing the structure of slack-variables.

Event date： 2012.10

Language：English  

Venue：Jeju   Country：Korea, Republic of  

This paper is concerned with the dual-LMI-based analysis of linear positive systems. As the first contribution, we will show that the cerebrated Perron-Frobenius theorem can be proved concisely via a duality-based argument. On the other hand, in the second part of the paper, we extend the well-known result that a stable Metzler matrix admits a diagonal Lyapunov matrix as the solution of the Lyapunov inequality. More precisely, again via a duality-based argument, we will clarify a necessary and sufficient condition under which a stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries. This new result leads to an alternative proof for the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the L₂ gain of positive systems.

Event date： 2012.6

Language：English  

Venue：Montreal, QC   Country：Canada  

In a recent study, we introduced an L₁-induced norm (L ₁ gain in short) as a performance index for linear time-invariant positive systems, where the L₁-norm of the disturbance input and the performance output signals is evaluated with positive weighting vectors. Moreover, we showed that the L₁ gain with the weighting vectors plays an essential role in stability analysis of interconnected positive systems. Aiming at extending this result for stabilization of interconnected positive systems, in this paper, we study L₁-optimal feedback controller synthesis for positive systems with given weighing vectors. In particular, we will show that an L₁-optimal state-feedback gain designed for a fixed positive system and a fixed pair of weighing vectors is robustly optimal against variations on the input matrix, the direct feedthrough matrix of the controlled positive system as well as variations on the weighting vector for the disturbance input signal. This property is of course promising for robust L₁-optimal control of uncertain positive systems. We illustrate the robust optimality property by numerical examples.

Event date： 2012.6

Language：English  

Venue：Aalborg   Country：Denmark  

In this paper, the general formulation of periodically time-varying state-feedback controllers with memory is considered for the first time. New analysis and synthesis conditions for robust stability are proposed. The exibility of these new results allows the user to freely add degrees-of-freedom to the control law which appears to effectively reduce the conservatism of the synthesis condition and to increase the stability domain of the closed-loop system in the presence of uncertainties. Furthermore, it is shown that for a particular structure of controllers a more efficient version of the design theorem can be derived by enriching the matrix of slack-variables.

Event date： 2011.12

Language：English  

Venue：Orlando, FL   Country：United States  

In this paper, we focus on L ₁ gain analysis problems of linear time-invariant continuous-time positive systems. A positive system is characterized by the strong property that its output is always nonnegative for any nonnegative input. Because of this peculiar property, it is natural to evaluate the magnitude of positive systems by the L ₁ gain (i.e. the L ₁ induced norm) in terms of the input and output signals. In contrast with the standard L ₁ gain, in this paper, we are interested in L ₁ gains with weightings on the input and output signals. It turns out that the L ₁ gain with weightings plays an essential role in the stability analysis of interconnected positive systems. More precisely, as a main result of this paper, we show that an interconnected positive system is stable if and only if there exists a set of weighting vectors that renders the L ₁ gain of each positive subsystem less than unity. As such, using a terminology in the literature, the weighting vectors work as 'separators,' and thus we establish solid separator-based conditions for the stability of interconnected positive systems. We finally illustrate that these separator-based conditions are effective particularly when we deal with robust stability analysis of positive systems against both L ₁ gain bounded and parametric uncertainties.

Event date： 2011.12

Language：English  

Venue：Orlando, FL   Country：United States  

Particularly attractive for small satellites, the use of magnetic torquers for attitude control is still a difficult problem. Indeed, equations are naturally time-varying and suffers from controllability issues. In this paper, a generic model, taking different kinds of pointing and different kinds of actuators into account, is proposed, linearized and then discretized. Recent studies demonstrate how combining magnetorquers and reaction wheels is attractive. Following this line, latest LMI synthesis techniques for static periodic controller are applied in this paper to the attitude control problem of a spacecraft equipped with both actuation systems. Simulation results are provided, showing the performance of the obtained control law.

Event date： 2011.12

Language：English  

Venue：Orlando, FL   Country：United States  

This paper is concerned with robust state-feedback controller synthesis for discrete-time linear periodic/time-invariant systems subject to polytopic-type parametric uncertainties. In recent studies, some of the authors conceived an LMI-based approach to periodically time-varying memory controller (PTVMC) synthesis and proved that this approach is indeed effective to get less conservative robust controller design procedures. However, since the peculiar controller structure requires to reset memory to zero in a periodic way, it is pointed out that the control performance depends on the timing of implementation. In this paper we tackle this issue and propose a reset-less state-feedback Periodic FIR Controller (PFIRC), which turns out to be suitable to improve robustness on periodic and time-invariant systems. Moreover, as a special case, a design condition is provided for FIR-type LTI controllers that robustly stabilize uncertain LTI systems. Numerical examples illustrate the efficiency of the proposed approaches.

Event date： 2011.8

Language：English  

Venue：Istanbul   Country：Turkey  

A large-scale phased array antenna will be adopted as a microwave power transmitter of solar power satellites. The objective of the present study is to maximize transmitting power of a large-scale phased array antenna including lossy digital phase shifters. In the present paper, we describe a newly developed algorithm for transmitting power maximization, and demonstration experiments of a one-dimensional 12-elements phased array antenna including 4-bit lossy digital phase shifters. We confirmed effectiveness of the developed algorithm through the demonstration experiments as well as numerical simulations.

Event date： 2010.12

Language：English  

Venue：Atlanta, GA   Country：United States  

In the preceding studies we proposed a dual LMI approach for robust performance analysis problems of LTI systems that are affected by parametric uncertainties. By starting from a dual LMI that characterizes a dissipation performance of uncertainty-free LTI systems, we showed that the robust dissipation performance analysis problem can be reduced into a feasibility problem of a polynomial matrix inequality (PMI). Moreover, by applying a linearization to the PMI, we derived an infinite sequence of LMI relaxation problems that allows us to reduce the relaxation gap gradually. Nevertheless, the asymptotic behaviour of this infinite sequence has been open, and this motivates us to study mutual relationship among the dual LMI approach and existing approaches. As the main result of this paper, we prove that our dual LMI approach corresponds to the dual of the polynomial parameter-dependent Lyapunov function approach with matrix sum-of-squares (SOS) relaxations, which is known to be asymptotically exact. Thus we clarify a close relationship between these two approaches that are seemingly very different. This relationship readily leads us to the desired conclusion that the proposed dual LMI approach is asymptotically exact as well.

Event date： 2010.9

Language：English  

Venue：Yokohama   Country：Japan  

This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established a solid theoretical basis for the LMI-based (robust) H_∞-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H₂ performance criterion. In the H₂ case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and inequalities for bounding traces that characterize the H₂ norm. We can indeed overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H₂-PTVMSFC synthesis. Based on this result, we also consider robust H₂-PTVMSFC synthesis for polytopictype uncertain LTI systems.

Event date： 2010.6 - 2010.7

Language：English  

Venue：Baltimore, MD   Country：United States  

This paper is concerned with the decentralized H_∞ controller synthesis problem for discrete-time linear time-invariant (LTI) systems. In spite of intensive research efforts over the last several decades, this problem is believed to be non-convex and still outstanding in general. Therefore most existing approaches resort to heuristic optimization algorithms that do not allow us to draw any definite conclusion on the quality of the designed controllers. To get around this difficult situation, in this paper, we propose convex optimization procedures for computing lower bounds of the H _∞ performance that is achievable via decentralized LTI controllers of any order. In particular, we show that sharpened lower bounds can be obtained by making good use of structures of the LTI plant typically observed in the decentralized control setting. We illustrate via numerical examples that these lower bounds are indeed useful to ensure the good quality of decentralized controllers designed by a heuristic optimization.

Event date： 2010.6 - 2010.7

Language：English  

Venue：Baltimore, MD   Country：United States  

In this note, we address two design problems for Linear Parameter-Varying (LPV) systems; Gain-Scheduled (GS) H₂ state-feedback controller design and GS H_∞ state-feedback controller design. In sharp contrast to the methods in the literature, the scheduling parameters are supposed to be inexactly measured. The LPV systems are supposed to have polynomially parameter-dependent statespace matrices, and the controllers to be designed are supposed to be rationally parameter-dependent. Using a parametrically affine matrix, which is the inverse of Lyapunov variable, we give formulations for the design of GS H₂ and H_∞ state-feedback controllers which are robust against the uncertainties in the measured scheduling parameters, in terms of parametrically affine Linear Matrix Inequalities (LMIs). As a special case, our methods include robust controller design using constant Lyapunov variables. Simple numerical examples are included to illustrate our results.

Event date： 2009.12

Language：English  

Venue：Shanghai   Country：China  

This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these PMI problems are non-convex and hence computationally intractable in general. To get around this difficulty, we construct a sequence of LMI relaxation problems via a simple idea of linearization. In addition, we derive a rank condition on the LMI solution under which the exactness of the analysis result is guaranteed. From the LMI solution satisfying the rank condition, we can easily extract the worst case parameters.

Event date： 2009.12

Language：English  

Venue：Shanghai   Country：China  

In this paper, we enhance the quality of our preceding results on periodically time-varying memory state-feedback controller (PTVMSFC) synthesis for discrete-time linear periodic/time-invariant systems. We firstly revisit PTVMSFC synthesis for certain systems and derive a necessary and sufficient LMI condition for the existence of the desired H_∞-PTVMSFCs. Based on these LMIs, we next consider robust H_∞-PTVMSFC synthesis for polytopic-type uncertain systems and demonstrate that we can obtain less conservative results. We finally derive a test to verify that the designed PTVMSFC is "exact" in the sense that it attains the best achievable robust H_∞ performance. This exactness verification test works fine in practice, and we show via numerical examples that exact robust control is indeed possible via PTVMSFCs, even for those problems where the standard static state-feedback fails.

Event date： 2009.8

Language：English  

Venue：Fukuoka   Country：Japan  

In this paper, we propose novel LMI conditions for the stability and l2 gain performance analysis of discretetime linear periodically time-varying (LPTV) systems. These LMIs are convex with respect to all of the coefficient matrices of the LPTV systems and this property is expected to be promising when dealing with several control system analysis and synthesis problems. For example, we can apply those LMIs straightforwadly to robust performance analysis problems of LPTV systems that are affected by polytopic-type uncertainties. Even though our approach for robust performance analysis is conservative in general, we can reduce the conservatism gradually by artificially regarding the original N -periodic system as pN -periodic and increasing p. In addition, thanks to the simple structure of the LMI conditions, we can readily derive a viable test to verify the exactness of the computation results.

Event date： 2009.6

Language：English  

Venue：St. Louis, MO   Country：United States  

The goal of this paper is to provide an elementary proof for the exactness of the (D,G) scaling applied to the uncertainty structure with one repeated real scalar block and one full complex matrix block. The (D,G) scaling has vast application area around control theory, optimization and signal processing. This is because, by applying the (D,G) scaling, we can convert inequality conditions depending on an uncertain parameter to linear matrix inequalities (LMIs) in an exact fashion. However, its exactness proof is tough, and this stems from the fact that the proof requires an involved matrix formula in addition to the standard Lagrange duality theory. To streamline the proof, in the present paper, we clarify that the involved matrix formula is closely related to a norm preserving dilation under structural constraints. By providing an elementary proof for the norm preserving dilation, it follows that basic results such as Schur complement and congruence transformation in conjunction with the Lagrange duality theory are enough to complete a self-contained exactness proof.

Event date： 2008.12

Language：English  

Venue：Cancun   Country：Mexico  

This is a continuation of our preceding study dealing with robust stabilizing controller synthesis for uncertain discrete-time linear periodic/time-invariant systems. In this preceding study, we dealt with the case where the underlying systems are affected by polytopic-type uncertainties and revealed a particular periodically time-varying dynamical controller (PTVDC) structure that allows LMI-based robust stabilizing controller synthesis. Based on these preliminary results, in this paper, we provide LMI conditions for robust H₂ and H∞ PTVDC synthesis. One of the salient features of the proposed method is that we can reduce the conservatism and improve the control performance gradually by increasing the period of the controller to be designed. In addition, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we illustrate that our design method is indeed effective to achieve less conservative results under both the periodic and time-invariant settings. keywords: Robust control, periodic systems, polytopic uncertainties, linear matrix inequalities.

Event date： 2008.7

Language：English  

Venue：Seoul   Country：Korea, Republic of  

In this paper, we deal with robust performance analysis problems of LTI systems depending on uncertain parameters. By following existing scaling-based approaches, we firstly derive computationally tractable parameter-independent LMI conditions to assess the robust performance, which are conservative in general. What makes the present approach novel is to take the dual of those LMIs so that we can conclude the exactness of the analysis results. More precisely, we clarify that if the computed dual solution satisfies a certain rank condition, then we can ensure that the robust performance is never attained. In particular, we can extract the worst case perturbation that violates the underlying performance. Thus we provide viable tests for the exactness verification of LMI-based robust performance analysis.

Event date： 2008.7

Language：English  

Venue：Seoul   Country：Korea, Republic of  

Recent papers in the field of LMI-based robust control have provided extensions of known results for linear time-invariant systems to the case of periodically time varying linear systems. These results, theoretically satisfactory because formulated in terms of optimization problems of polynomial complexity, may still have limited applications in practice because the number of variables and constraints is very large. The present paper proposes a new formulation of these results that allows to reduce the computational burden both by reducing the number of decision variables and the size of the constraints. Along with this numerical improvement, the paper produces a new modeling of periodic discrete-time systems in descriptor form that is believed promising for future research.

Event date： 2008.7

Language：English  

Venue：Seoul   Country：Korea, Republic of  

In this paper, we propose a new LMI-based method for robust state-feedback controller synthesis of discrete-time linear periodic/time-invariant systems subject to polytopic uncertainties. In stark contrast with existing approaches that are confined to static controller synthesis, we explore dynamic controller synthesis and reveal a particular periodically time-varying dynamical controller structure that allows LMI-based synthesis. In particular, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective to achieve less conservative results.

Event date： 2007.12

Language：English  

Venue：New Orleans, LA   Country：United States  

This paper addresses robust performance analysis problems of LTI systems affected by real parametric uncertainties. These problems, known also as a special class of structured singular value computation problems, are inherently intractable (NP-hard problems). As such intensive research effort has been made to obtain computationally tractable and less conservative analysis conditions, where linear matrix inequality (LMI) plays an important role. Nevertheless, since LMI-based conditions are expected to be conservative in general, it is often the case that we cannot conclude anything directly if the LMI at hand turns out to be infeasible. This motivates us to consider the dual of the LMI and examine the structure of the dual solution, which does exist if the primal LMI is infeasible. By pursuing this direction, in this paper, we provide a rank condition on the dual solution matrix under which we can conclude that the underlying robust performance is never attained. In particular, a set of uncertain parameters that violates the specified performance can readily be obtained. The key idea to derive these results comes from simultaneous diagonalizability property of commuting diagonalizable matrices. The block-moment matrix structure of the dual variable plays an essential role to make good use of this property.

Event date： 2007.7

Language：English  

Venue：New York, NY   Country：United States  

This paper concerns the computation of the distance to uncontrollability (DTUC) of a given controllable pair A ∈ C^n×n and B ∈ C^n×m. This problem can be regarded as a special case of the structured singular value computation problems and motivated from this fact, in our preceding work, we derived an semidefinite program (SDP) to compute the lower bounds of the DTUC. In the first part of this paper, we show via convex duality theory that the lower bounds can be computed by solving a very concise dual SDP. In particular, this dual SDP enables us to derive a rank condition on the dual variable under which the computed lower bound coincides with the exact DTUC. This rank condition is surely effective in practice, and we will show thorough numerical examples that we can obtain exactness certificate even for those problems where the common rank-one exactness principle fails. On the other hand, in the second part of the present paper, we consider the problem to compute the similarity transformation matrix T that maximizes the lower bound of the DTUC of (T^-1AT,T^-1B). Based on the SDP for the lower bounds computation, we clarify that this problem can be reduced to generalized eigenvalue problem and thus solved efficiently. In view of the correlation between the DTUC and the numerical difficulties of the associated pole placement problem, this computation of the similarity transformation matrix would lead to an effective and efficient conditioning of the pole placement problem for the pair (A, B).

Event date： 2006.12

Language：English  

Venue：San Diego, CA   Country：United States  

In this paper, we consider the problem to compute the distance to uncontrollability of a given controllable pair A ∈ C^n×n and B ∈ C^n×m. It is known that this problem is equivalent to computing the minimum of the smallest singular value of [A - zI B] over z ∈ C. With this fact, Gu proposed an algorithm that correctly estimates the distance at a computation cost ο(n⁶). On the other hand, in the community of control theory, remarkable advances have been made on the techniques to deal with parametrized linear matrix inequalities (LMIs) as well as the analysis of positive polynomials. This motivates us to explore an alternative LMI-based algorithm and shed more insight on the problem to estimate the distance to uncontrollability. In fact, this paper shows that we can establish an effective method to compute a lower bound of the distance by simply applying the existing techniques to solve parametrized LMIs. To obtain an upper bound, on the other hand, we analyze in detail the solutions resulting from the LMI optimization carried out to compute the lower bound. This enables us to estimate the location of the local, but potentially global optimizer z* ∈ C in a reasonable fashion. We thus provide a novel technique to obtain an upper bound of the distance by evaluating the smallest singular value on the estimated optimizer z*. It turns out that the lower and upper bounds are very close in all tested numerical examples. We finally derive an algebraic condition under which the exactness of the suggested computation method of the lower bound can be ensured, based on the convex duality theory. Furthermore, we show that the suggested computation method of the upper bound is closely related to the obtained algebraic condition for the exactness verification.

Event date： 2006.7

Language：English  

Venue：Toulouse   Country：France  

In this paper, we address the robust H₂ performance analysis problems of linear time-invariant polytopic-type uncertain systems. To obtain numerically verifiable and less conservative analysis conditions, we employ polynomially parameter-dependent Lyapunov functions (PPDLFs) to assess the robust H₂ performance and give a sufficient condition for the existence of such PPDLFs in terms of finitely many linear matrix inequalities (LMIs). The resulting LMI conditions turn out to be a natural extension of those known as extended or dilated LMIs in the literature, where the PDLFs employed were restricted to those depending affinely on the uncertain parameters. It is shown that, by increasing the degree of PPDLFs, we can obtain more accurate (no more conservative) analysis results at the expense of increased computational burden. Exactness of the proposed analysis conditions as well as their computational complexity will be examined through numerical experiments.

Event date： 2004.12

Language：English  

Venue：Nassau   Country：Bahamas  

In this paper, we propose necessary and sufficient conditions for asymptotic stability analysis of 2-D systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions to verify the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that we can reduce the size of LMIs by employing the generalized S-procedure.

Event date： 2004.12

Language：English  

Venue：Nassau   Country：Bahamas  

The generalized S-procedure, introduced by Iwasaki et al., has proved to be very useful for robustness analysis and synthesis of control systems. This procedure provides a nonconservative way to convert inequality conditions on lossless sets into numerically verifiable conditions represented by linear matrix inequalities (LMIs). In this paper, we introduce a new notion, one-vector-lossless sets, and propose a generalized S-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized S-procedure, we can examine various properties of matrix-valued functions over some regions on the complex plane. To illustrate the usefulness, we show that full rank property analysis problems of polynomial matrices over some specific regions on the complex plane can be reduced into LMI feasibility problems. It turns out that many existing results such as Lyapunov's inequalities for stability analysis of linear systems and LMIs for state-feedback controller synthesis can be viewed as particular cases of this result.

Event date： 2004.6 - 2004.7

Language：English  

Venue：Boston, MA   Country：United States  

In this paper, we deal with the problem of approximating a given n-th order LTI system G by an r-th order system G_r where r < n. It is shown that lower bounds of the H∞ norm of the associated error system can be analyzed by using LMI-related techniques. These lower bounds are given in terms of the Hankel singular values of the system G and coincide with those obtained in the previous studies where the analysis of the Hankel operators plays a central role. Thus, this paper provides an alternative proof for those lower bounds via simple algebraic manipulations related to LMI's. Moreover, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the problem is essentially convex and the optimal reduced-order models can be constructed via LMI optimization.

Event date： 2003.12

Language：English  

Venue：Maui, HI   Country：United States  

In this paper, we propose new LMI-based conditions to design output-feedback controllers under structural constraints. The conditions are given in terms of LMI's with rank constraints and we solve them by means of the alternating projection algorithm. Even though the algorithm does not ensure global convergence, extensive numerical experiments demonstrate that the proposed design method is promising in designing structured and/or multiobjective controllers, provided that the dimension of the closed-loop systems is not excessively large.

Event date： 2003.6

Language：English  

Venue：Milan,   Country：Italy  

This paper is concerned with the gain-scheduled controller synthesis for linear parameter varying (LPV) systems. In the case where the state space matrices of the system depend afrinely on the time-varying parameters, the standard linear matrix inequalities (LMI's) are helpful in dealing with such problems provided that we accept the notion of quadratic stability. However, in the case of rational parameter dependence, the standard LMI's carry some deficiency and do not lead to numerically tractable conditions in a straightforward fashion. This paper clarifies that recently developed dilated LMI's are effective in overcoming the difficulties and deriving numerically tractable conditions The dilated LMI's enable us also to employ parameterdependent Lyapunov variables to achieve control objectives, which are known to be promising to alleviate the conservatism stemming from a quadratic (parameter-independent) Lyapunov variable.

Event date： 2003.6

Language：English  

Venue：Denver, CO   Country：United States  

This paper studies LMI-based robust performance analysis of linear time-invariant systems depending on uncertain parameters. In the case where the coefficient matrices of the system are affine with respect to the uncertain parameters, the standard LMI's are helpful in dealing with such analysis problems provided that we accept the notion of quadratic stability. On the other hand, in the case of rational parameter dependence, the standard LMI's carry some deficiency and thus we need another effort to derive numerically tractable conditions. This paper shows that recently developed dilated LMI's are effective in attacking such robust performance analysis problems. Indeed, applying dilated LMI's leads directly to numerically tractable conditions regardless of the form of the dependence on uncertain parameters. In addition, dilated LMI's enable us to employ parameter-dependent Lyapunov variables to test robust performance, which are known to be quite effective to alleviate the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.

Event date： 2002.12

Language：English  

Venue：Las Vegas, NV   Country：United States  

This paper enhances our previous results on dilated LMI's so that we can address robust controller synthesis problems for continuous-time LTI systems subject to real polytopic uncertainties. The replacement of a constant scalar involved in the previous dilated LMI's by an adjustable parameter is the key to accomplish this extension. The particular form of the extension enables the use of parameter-dependent Lyapunov variables in such a sound way that an advantage of the dilated LMI approach is ensured explicitly in attacking such robust controller synthesis problems. Namely, the dilated LMI approach is shown to achieve better (no worse) results than the conventional one which is restricted to parameter-independent Lyapunov variables, provided that the adjustable parameter is taken to meet a certain simple condition.

Event date： 2002.5

Language：English  

Venue：Anchorage, AK   Country：United States  

It has been recognized recently that the dilation of the LMI characterizations has new potentials in dealing with such involved problems as multiobjective control, robust performance analysis or synthesis for real polytopic uncertainty and so on. Contrary to the success in this direction in the discrete-time setting, analogous characterizations in the continuous-time setting are still open and challenging. The main contribution of this paper is to propose a general procedure to construct such dilated LMI characterizations for continuous-time control design. Because of our particular procedure, the dilated LMI characterizations are proved to have some very nice and interesting features that are to some extent analogous to the ones already obtained in the discrete-time setting.

Event date： 2001.6

Language：English  

Venue：Arlington, VA   Country：United States  

This paper presents a new approach with non-common linear matrix inequality (LMI) solutions to the multiobjective state-feedback control design problem. A conventional approach is adopting common LMI solutions to avoid a difficulty of non-convex constraints at the sacrifice of conservatism. To get around the conservatism, in this paper, we perform a standard procedure called change of variables and represent the resulting variables as a set of affine functions of new variables. These affine functions are such that they satisfy the non-convex constraints regardless of the new variables. With these affine functions, we readily derive a set of LMI conditions that allow non-common LMI solutions.

Event date： 1999.12

Language：English  

Venue：Phoenix, AZ, USA   Country：Other  

In this study, we propose such sequential tuning methods of multivariable optimal regulators that can be applied to the tuning of control systems under operation. We apply one of these methods to the tuning of LQI servo systems, and carry out the simulation study of the control of a hot strip mill to illustrate the tuning law and show its effectiveness.

Language：English  

Country：Other  

This paper addresses robust D-stability analysis problems of uncertain polynomial matrices. The underlying idea we follow is that a given polynomial matrix is D-stable if and only if there exist polynomial-type multipliers that render the resulting polynomial matrices to be strictly positive over a specific region on the complex plane. By applying the generalized S-procedure technique, we show that those positivity analysis problems can be reduced into feasibility tests of linear matrix inequalities (LMIs). Thus we can obtain varieties of LMI conditions for (robust) D-stability analysis of polynomial matrices according to the degree/structure of the multipliers to be employed. in particular, we show that existing LMI conditions for robust D-stability analysis can be viewed as particular cases of the proposed conditions, where the degree of the multipliers chosen to be the same as those of the polynomial matrices to be examined. It turns out that, by increasing the degree of the multipliers, we can readily obtain less conservative LMI conditions than the one found in the literature.

Language：English  

Country：Other  

Multipurpose aviation laboratory-α (MuPAL-α) is an experimental aircraft developed by the Japan aerospace exploration agency (JAXA). Its one of the most important functions is to realize in-flight simulation, i.e., to simulate maneuverability of other aircraft via practical flight experiments. To achieve the desired maneuverability matching under model uncertainty and gust disturbance, in this paper, we construct reference feedforward type 2DOF (RFF-2DOF) control system. We will show via numerical simulation that satisfactory results are obtained by constructing RFF-2DOF control system.

Language：English  

Country：Other  

In this paper, we show that a set of static controllers satisfying a certain level of H_∞ performance becomes convex when the underlying generalized plant satisfy several structural conditions. More precisely, we characterize such static H_∞ controllers by an LMI with the controller parameters being kept directly as decision variables. The conditions on the generalized plant are not too strict as illustrated by the fact that a sort of mixed sensitivity problems indeed satisfies these conditions. In addition, for the generalized plant of interest, we prove that full-order dynamical H_∞ controllers can be characterized by an LMI with simple change of variables. In stark contrast to known LMI formulations, the change of variables does not involve coefficient matrices of the generalized plant. This property is promising when dealing with a whole variety of robust control problems. As an illustration, the real μ synthesis problem is discussed.

Language：English  

DOI： 10.1109/MCS.2016.2584278

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

Language：Japanese   Publishing type：Article, review, commentary, editorial, etc. (scientific journal)  

Language：Japanese