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   Publisher：The Institute of Systems, Control and Information Engineers  

DOI： 10.11509/sci.sci24.0_431

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)  

DOI： 10.1109/LCSYS.2020.2991480

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

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

DOI： 10.1109/LCSYS.2019.2946620

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

This paper is concerned with the analysis of discrete-time LTI systems via construction of associated externally positive systems. Recently, the authors 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 closed-form 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, incurring a drastic increase in computational burden of computer-aided analysis and synthesis. 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 J. 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： 10.5687/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)  

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)  

DOI： 10.1109/TAC.2017.2767704

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

In this paper, we explore H₂ analysis techniques of general, not necessarily positive, discrete-time linear time-invariant (LTI) systems by means of positive system theory. While externally positive systems are a particular class of systems whose impulse responses take only nonnegative values, we often encounter such impulse responses even in the analysis of general LTI systems. A typical example is the computation of the H₂ norm where we focus on squared impulse responses. In view of this observation, we first clarify that we can construct an SISO externally positive system whose impulse response is given by the square of the impulse response of a given SISO LTI system. This system conversion allows us to reduce the H₂ norm computation problem of a general LTI system to the l_∞-induced norm computation problem (or l₁ problem in short) of the resulting externally positive system. It also turns out that this problem reduction enables us to derive various alternative formulas for the H₂ norm of general discrete-time LTI systems.

DOI： 10.5687/iscie.31.75

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

This paper is concerned with nonlinear output feedback control for the average output voltage of boost converters through their discretized bilinear models. We first propose a bilinear observer synthesis method for the discretized bilinear model by effectively using the fact that the control input corresponds to the duty ratio and hence has upper and lower bounds whose values can be exploited in the synthesis. We next employ a kind of Lyapunov method for the synthesis of state-feedback controllers with integral compensation. Here, the integral compensation aims at making the (approximate) average output voltage track its reference input and is introduced with its implementability taken into account under limited data acquisition performance and operational speed of digital signal processors. Finally, we carry out control experiments with the combined use of the designed state feedback and bilinear observer and verify the effectiveness of the overall control strategy.

DOI： 10.5687/iscie.31.63

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

DOI： 10.9746/jcmsi.11.91

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

DOI： 10.1016/j.ifacol.2018.11.179

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

DOI： 10.1016/j.ifacol.2018.11.178

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

DOI： 10.1049/iet-cta.2017.0315

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

DOI： 10.1016/j.ifacol.2017.08.755

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

DOI： 10.1016/j.ifacol.2017.08.681

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

DOI： 10.1016/j.ifacol.2017.08.304

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

DOI： 10.1016/j.automatica.2016.10.003

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

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)  

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)  

The ultimate subject of the present study is concerned with the design of a nonlinear control law with integral compensation for the output voltage of boost converters through the use of their discretized bilinear model. In this first part of the study, we begin with a discretized model of boost converters obtained by rigorously taking account of the switching action in the converters. Since the control input, the duty cycle, is involved in this model in a highly nonlinear fashion,however, designing a discrete-time control law with this model is rather unrealistic. To circumvent this difficulty, we approximate the discretized model and introduce a simplified model, a discretized bilinear model, and discuss its favorable property. We further give a method for experimentally determining the discretized bilinear model through system identification. With an experiment on identifying an actual boost converter, we then discuss the effectiveness of the discretized bilinear model and its identification method. The resulting model will be used for discrete-time control law design to verify effectiveness of the overall scheme of the present study in an accompanying paper.

DOI： 10.5687/iscie.28.320

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

This paper is concerned with nonlinear control with integral compensation for the output voltage of boost converters through the use of their discretized bilinear model. We first derive a nonlinear state feedback control law through Lyapunov stability theory, where we introduce a Lyapunov function candidate and maximize its decrement at each switching instant under a penalty on the control input. This approach is then modified to incorporate an integral action in the control law,and a method is provided for confirming the closed-loop stability under the modified control law. We next apply the design method of the control law with integral compensation to the identified discretized bilinear model of a boost converter. Finally, we carry out control experiments with the designed control law, through which the effectiveness of the overall scheme of the present study is demonstrated.

DOI： 10.5687/iscie.28.330

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

This paper is concerned with the dominant pole analysis of asymptotically stable time-delay positive systems (TDPSs) with multiple delays. It has been shown recently that the dominant pole of a stable TDPS with a single delay increases and hence the convergence performance degrades according to the increase of the delay, if and only if the associated state space matrices satisfy an eigenvalue-sensitivity condition. This paper extends these preceding results to TDPSs with multiple delays. As a main result, we show that the dependence of the dominant pole upon the variation of multiple delays can be completely determined by the eigenvalue-sensitivity condition with respect to the state space matrices corresponding to the varying delays.

DOI： 10.5687/iscie.28.147

Language：English  

DOI： 10.1007/978-1-4471-6606-1_3

Language：English  

DOI： 10.1007/978-1-4471-6606-1_6

Language：English  

DOI： 10.1007/978-1-4471-6606-1_4

Language：English  

DOI： 10.1007/978-1-4471-6606-1_7

Language：English  

DOI： 10.1007/978-1-4471-6606-1_2

Language：English  

DOI： 10.1007/978-1-4471-6606-1_8

Language：English  

DOI： 10.1007/978-1-4471-6606-1_5

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

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)  

DOI： 10.11509/isciesci.59.1_21

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

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)  

DOI： 10.1587/transcom.E97.B.783

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

DOI： 10.1016/j.sysconle.2013.11.001

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

宇宙太陽光発電では，宇宙空間で発電した電力を大規模なフェーズドアレイアンテナによりマイクロ波に変換し，地上の受電設備へ無線伝送する．著者らはすでに，損失のあるディジタル移相器を用いたフェーズドアレイアンテナにおいて，各素子の励振位相を適切に調整して望ましい方向への伝送電力を最大化する問題を組合せ最適化問題として定式化するとともに，効率のよいアルゴリズムを提案している．本研究では，各素子の励振振幅も同時に最適化する問題に対して本アルゴリズムを拡張する．そして，計算機実験を用いてその有効性を検証する．

DOI： 10.11511/jacc.57.0_1935

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

This paper is concerned with the maximum power point tracking control of photovoltaic systems. In solar power generation using photovoltaic systems, DC-DC converters are usually inserted between photovoltaic systems and loads so that we can change operation points and thereby increase efficiency. However, the characteristic of the output power with respect to the duty ratio of DC-DC converters has multiple local maxima and drastically changes according to weather variation. In this paper, we propose an algorithm for online tuning of the duty ratio based on particle swarm optimization so that we can realize maximum power point tracking under such intractable circumstances. We finally verify the effectiveness of the algorithm by practical experiments.

DOI： 10.5687/iscie.27.237

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

DOI： 10.1109/TAC.2013.2251820

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

DOI： 10.1002/asjc.541

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

This paper is concerned with the stability and H_∞ performance analysis of discrete-time positive systems. In the literature, it is shown that the stability and H_∞ performance of continuous-time positive systems can be characterized by LMIs with diagonal Lyapunov matrices. Recently, new LMIs allowing asymmetric matrix solutions have been reported as well. In this paper, by means of the Perron-Frobenius theorem, we first show that the Schur stability of a given positive matrix is equivalent to the Hurwitz stability of an appropriately constructed Metzler matrix. Then, we secondly prove that we can construct a continuous-time positive system preserving the stability and H_∞ norm of the original discrete-time positive system. By applying existing results to the resulting continuous-time positive systems, we can readily obtain useful LMIs for the stability and H_∞ performance analysis of discrete-time positive systems.

DOI： 10.5687/iscie.26.45

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

DOI： 10.5687/iscie.26.355

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

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)  

DOI： 10.1016/j.automatica.2010.10.004

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

DOI： 10.11509/isciesci.55.5_165

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

This paper addresses the robust H_∞ performance analysis problem of linear time-invariant (LTI) systems whose state-space coefficient matrices depend polynomially on a single uncertain parameter. By means of a dual LMI that characterizes the H_∞ performance of uncertainty-free LTI systems, we firstly formulate this analysis problem as a polynomial matrix inequality (PMI) optimization problem. However, this PMI problem is non-convex and hence intractable in general. Therefore, we apply linearization and construct an infinite sequence of relaxation problems, represented by SDPs, with theoretical guarantee of asymptotic exactness in the limit. In order to detect whether an arbitrary relaxation problem in the sequence is “exact” in the sense that it provides the same optimal value as that of the original problem, we derive a rank condition on the SDP solution under which we can conclude the exactness.

DOI： 10.5687/iscie.23.46

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

DOI： 10.3166/ejc.16.532-544

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

本稿では，不確かなパラメータにLFT形式で依存する離散時間線形時不変系に対して，H2ノルム仕様を満足するメモリー型周期時変状態フィードバック制御器(PTVMSFC)を設計する方法について述べる．これは，既存研究において提案されているLMI条件に伸張を施すことで，LFT形式の不確かさを扱うことを可能とするものである．本稿ではとくにLFT形式で不確かさを含む連続時間線形時不変系を離散化し，提案手法を適用してPTVMSFCを設計することで，保守性の低いロバスト制御が可能となることを数値例を用いて示す．

DOI： 10.11509/sci.SCI10.0.318.0

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

本研究では，離散時間線形時不変系の分散型Ｈ∞制御問題に対して近年提案された，達成可能なＨ∞性能の下界値を解析するための手法の有効性を検証する．この手法は，下界値を解析するためのＳＤＰを制御対象の構造に基づいて導くというものであり，とくに制御対象が分散制御問題においてしばしば見受けられるような特徴的な構造を有する場合には，より保守性の低い下界値を求めることが可能であることが示唆されている．本研究では，制御対象がいくつかの特徴的な構造を有する場合には実際に保守性の低い下界値が得られることを，数値例を用いて実証する．

DOI： 10.11509/sci.SCI10.0.315.0

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

本研究では，前後傾斜運動および旋回が可能な2自由度ヘリコプタ実験機の高精度の姿勢制御を達成することを目的とする．2つの運動のダイナミクスの間に強い干渉があることや正確なモデリングが困難であることが，高精度の姿勢制御を妨げる大きな要因となっている．本稿では，この制御対象に対して逆システムに基づくフィードフォワード項を有する2自由度制御系を構成し，H∞制御理論に基づいてフィードバック制御器をシステマティックに設計することにより，高精度の姿勢制御が達成可能であることを示す．

DOI： 10.11509/sci.SCI10.0.352.0

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

宇宙太陽光発電において，発電した電力は，アンテナ素子を多数配列したフェーズドアレイアンテナによりマイクロ波に変換して地上の受電設備へ送電することが想定されている．本研究では，フェーズドアレイアンテナによるマイクロ波無線電力伝送において，受電設備の方向への送電電力が最大となるよう各アンテナ素子の位相を決定する問題を対象とする．本研究ではまず，この問題を組合せ最適化問題として定式化し，実回転定理を適用して各アンテナ素子ごとの部分問題に分解する．そして，この分解に基づいて効率的な解法を提案し，数値実験によりその有効性を実証する．

DOI： 10.11511/jacc.53.0.100.0

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

In this paper, we aim at achieving accurate positioning control of a pneumatic actuation mechanism of antagonist-type by means of the simple adaptive control (SAC) method. Since this plant does not satisfy the ASPR-ness condition, we introduce a parallel feedforward compensator (PFC) so that the SAC strategy can be applied. However, the introduction of PFC leads to performance deterioration and in particular causes a steady state error. To suppress the steady-state error while keeping the fundamental structure of the SAC system, we introduce a “constant scaling” to the SAC system. We also consider a “dynamic scaling” so that the transient response of the controlled system can be improved. Through experiments, we show that the SAC strategy with these scalings is indeed effective in achieving accurate positioning control.

DOI： 10.5687/iscie.22.350

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

DOI： 10.1109/TAC.2009.2017086

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

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)  

DOI： 10.1137/050627551

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

This paper is concerned with trajectory tracking control of a two-axis arm driven by pneumatic artificial muscles, in which it is important for the plant output to track general reference inputs other than step signals. To comply with this control objective, this paper applies the plant-variable-optimal (PV-optimal) servo system derived in the framework of two-degree-of-freedom optimal control, and shows that trajectory tracking can be achieved with high accuracy by taking the intrinsic features of the arm into account in the design. That is, we first apply a minor feedback loop based on the pressure measurements about the pneumatic muscles, and then derive a plant model taking account of the relationship between the link angles and pressure measurements. We then adjust the weighting matrices for the PV-optimal servo system according to the physical meaning of the plant state, and design an observer that uses pressure measurements as well as link angle measurements. It is demonstrated with experiments that trajectory tracking with high accuracy can be achieve with such design procedures.

DOI： 10.9746/ve.sicetr1965.44.927

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

DOI： 10.9746/jcmsi.1.474

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

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)  

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

本稿では，状態方程式の離散化に基づくチュックコンバータのモデル化手法を提案する．チュックコンバータには制御スイッチと状態依存スイッチがあり，スイッチの動作に伴い等価回路が遷移する．そこで，各等価回路の振舞を表す状態方程式を離散化し，サンプル点上での電流, 電圧値を解析することで，時間と状態に応じた遷移を実現するモデルを構築する．また，実際に回路を作成し，実験結果とモデルによるシミュレーション結果を比較することで，モデルの妥当性を検証する．

DOI： 10.11509/sci.SCI08.0.179.0

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

In this paper, we study a robust performance analysis problemof linear time-invariant (LTI) systems whose state space matrices depend polynomially on an uncertain parameter. Most of existing approaches to this problem is such thatwe recast the problem into a robust SDP by means of standard LMIs that characterize the performance. On the other hand, in the present paper, we firstly consider the dual of those LMIs and show that the robust performance analysis problem can be naturally reduced to an polynomial optimization problem with matrix variables. For this problem, we can readily construct a hierarchy of LMI relaxations whose infeasibility imply the fulfillment of the robust performance. In addition, in the case where the LMI relaxation has a feasible solution, we derive a rank condition with respect to the solution under which the robust performance is never attained.

DOI： 10.11511/jacc.51.0.172.0

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

本稿では，不確かなパラメータを有する連続時間線形時不変系のロバストH2性能を解析するための新たな手法を提案する．既存の手法の多くがロバストH2性能の上界値計算に留まり，その厳密性の評価が不十分であるのに対し，本稿では上界値計算のためのLMIの双対LMIを考えることで，計算された上界値がロバストH2性能の真値と一致していることを帰結し得る双対解に関する条件を明らかにする．さらに広範な数値例をもとに提案手法の有効性を示す．

DOI： 10.11509/sci.SCI08.0.210.0

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

本研究で対象とするヘリコプタ実験機はピボット型の支軸に取付けられており,2つのロータを用いて旋回および前後傾斜動が可能である.本研究の目的は，この実験機の高精度の姿勢制御を達成することであるが,各軸間に相互干渉が存在することが大きな障壁となる.これに対して本稿では，目標値追従特性と外乱抑制特性とを独立に設計できるという特長をもつ2自由度LQIサーボ系の設計法を適用し,高精度の姿勢制御を達成した.

DOI： 10.11509/sci.SCI08.0.341.0

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

本研究では，単純適応制御(SAC)に基づき，拮抗型空圧人工筋駆動機構の高精度の位置決め制御を目指す．SAC系を構成する上では並列フィードフォワード補償要素(PFC)の導入が不可欠となるが，一方でPFCの導入により定常偏差が生じるという問題がある．本研究では，制御対象およびPFCの定常ゲインに基づいたスケーリングを施すことで，SAC系の基本的な構成を維持しつつ定常偏差を0とすることが可能であることを示し，実機での実験を通して提案手法の有効性を示す．

DOI： 10.11509/sci.SCI07.0.233.0

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

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

DOI： 10.1016/j.automatica.2006.04.011

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

DOI： 10.1109/TAC.2006.880789

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

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

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)  

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)  

DOI： 10.1016/j.automatica.2005.05.023

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

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

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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)  

DOI： 10.1016/j.automatica.2004.06.009

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

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

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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

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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)  

DOI： 10.11509/isciesci.48.9_355

Language：Japanese   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. Taking account of the steady-state gain leads to decreasing the integrated square error between the step response of the original system and that of the reduced order system. The proposed method is applied to the reduction of the model of a multi-machine electric power system to demonstrate its effectiveness.

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)  

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)  

The simple adaptive control (SAC) method being applied to non-ASPR plants including pneumatic servo systems, it becomes indispensable to furnish a parallel feedforward compensator (PFC) to the system. Also, a fine adjustment of parameters in PFC is required to keep stability and to attain a desirable performance. It is, however, difficult to adjust them suitably with little information on the plant. In this paper, we propose an algorithm which tunes them automatically with a watch of improvement of the actual performance. An experiment is also carried out to show the effectiveness of our proposal.

DOI： 10.5687/iscie.14.102

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

DOI： 10.1080/002071700445415

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

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

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)  

Country：Germany  

Event date： 2022.9

Language：English   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2022.7

Language：English   Presentation type：Oral presentation (general)  

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)  

Country：Netherlands  

Event date： 2021.5

Language：English   Presentation type：Oral presentation (general)  

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)  

Country：Germany  

Event date： 2021.3

Language：Japanese   Presentation type：Oral presentation (general)  

Country：Japan  

Event date： 2019.6

Language：English  

Country：Italy  

Event date： 2018.9

Language：English  

Country：Japan  

Event date： 2018.6

Language：English  

Country：Cyprus  

Event date： 2018.3

Language：English  

Country：Japan  

Event date： 2017.12

Language：English  

Country：Australia  

Event date： 2017.9

Language：English  

Country：Japan  

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  

Country：Italy  

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  

Country：Japan  

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  

Country：Slovakia  

Event date： 2015.5 - 2015.6

Language：English  

Country：Malaysia  

Event date： 2014.12

Language：English  

Country：United States  

Event date： 2014.8

Language：English  

Country：South Africa  

Event date： 2014.8

Language：English  

Country：South Africa  

Event date： 2014.8

Language：English  

Country：South Africa  

Event date： 2014.6

Language：English  

Country：France  

Event date： 2013.12

Language：English  

Country：Italy  

Event date： 2013.7

Language：English  

Country：Switzerland  

Event date： 2013.5

Language：English  

Country：Japan  

Event date： 2012.12

Language：English  

Country：United States  

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  

Country：Korea, Republic of  

Event date： 2012.6

Language：English  

Country：Canada  

Event date： 2012.6

Language：English  

Country：Denmark  

Event date： 2011.12

Language：English  

Country：United States  

Event date： 2011.12

Language：English  

Country：United States  

Event date： 2011.12

Language：English  

Country：United States  

Event date： 2011.8

Language：English  

Country：Turkey  

Event date： 2010.12

Language：English  

Country：United States  

Event date： 2010.9

Language：English  

Country：Japan  

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  

Country：China  

Event date： 2009.12

Language：English  

Country：China  

Event date： 2009.8

Language：English  

Country：Japan  

Event date： 2009.6

Language：English  

Country：United States  

Event date： 2008.12

Language：English  

Country：Mexico  

Event date： 2008.7

Language：English  

Country：Korea, Republic of  

Event date： 2008.7

Language：English  

Country：Korea, Republic of  

Event date： 2008.7

Language：English  

Country：Korea, Republic of  

Event date： 2007.12

Language：English  

Country：United States  

Event date： 2007.7

Language：English  

Country：United States  

Event date： 2006.12

Language：English  

Country：United States  

Event date： 2006.7

Language：English  

Country：France  

Event date： 2004.12

Language：English  

Country：Bahamas  

Event date： 2004.12

Language：English  

Country：Bahamas  

Event date： 2004.6 - 2004.7

Language：English  

Country：United States  

Event date： 2003.12

Language：English  

Country：United States  

Event date： 2003.6

Language：English  

Country：Italy  

Event date： 2003.6

Language：English  

Country：United States  

Event date： 2002.12

Language：English  

Country：United States  

Event date： 2002.5

Language：English  

Country：United States  

Event date： 2001.6

Language：English  

Country：United States  

Event date： 1999.12

Language：English  

Country：Other  

Language：English  

Country：Other  

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