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論文一覧
蛯原 義雄 （えびはら よしお）
教授
システム情報科学研究院
電気システム工学部門
データ更新日：2024.04.03
原著論文教授
システム情報科学研究院
電気システム工学部門
データ更新日：2024.04.03
| 1. | R. Shiga, T. Hagiwara, and Y. Ebihara, Internal/External Positivity of Sampled-Data Systems: Definitions and the Necessary and Sufficient Conditions, IEEE Access, 2024.01. |
| 2. | 志賀亮介，萩原朋道，蛯原義雄, サンプル値系の外部非負性とLq/L∞ ハンケルノルム解析, 計測自動制御学会論文集, 2023.02. |
| 3. | 高尾亮太，藤井達希，本岡駿人，蛯原義雄, 積分二次制約と共正値マルチプライアを用いた連続時間再帰型ニューラルネットワークの安定性解析, システム制御情報学会論文誌, 2023.01. |
| 4. | 楊熙，蛯原義雄，萩原朋道, 離散化双線形モデルに基づくバックコンバータ出力電圧のSOS 手法による非線形制御, システム制御情報学会論文誌, 35, 6, 153-164, 2022.06. |
| 5. | 本岡駿人，蛯原義雄, 非負値入力に対するL2 誘導ノルムの解析と再帰型ニューラルネットワークの安定性解析への応用, システム制御情報学会論文誌, 2022.02. |
| 6. | Y. Ebihara, The lq/lp Hankel Norms of Discrete-Time Positive Systems Across Switching, SICE Journal of Control, Measurement, and System Integration, 15, 2, 109-118, 2022.02. |
| 7. | Y. Ebihara, H. Waki, V. Magron, N. H. A. Mai, D. Peaucelle, S. Tarbouriech, l2 induced norm analysis of discrete-time LTI systems for nonnegative input signals and its application to stability analysis of recurrent neural networks, European Journal of Control, 2021.10. |
| 8. | 志賀亮介，加藤光樹，蛯原義雄，萩原朋道, 離散時間非負システムのlq/lp Hankel ノルム解析, 計測自動制御学会論文集, Vol. 57, No. 3, pp. 128–137, 2021.03. |
| 9. | Bohao Zhu, James Lam, Yoshio Ebihara, Input–output gain analysis of positive periodic systems, International Journal of Robust and Nonlinear Control, https://doi.org/10.1002/rnc.5438, 31, 8, 2928-2945, 2021.02, 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.. |
| 10. | H. Waki, Y. Ebihara, N. Sebe, Reduction of SISO H-infinity Output Feedback Control Problem, Linear Algebra and Its Application, 2021.02. |
| 11. | Yoshio Ebihara, Noboru Sebe, Hayato Waki, On Gain-Scheduled State-Feedback Controller Synthesis with Quadratic Stability Condition, IEEE Control Systems Letters, 10.1109/LCSYS.2020.2991480, 4, 3, 662-667, Vol. 4, No. 3, pp. 662–667, 2020.07, [URL], 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.. |
| 12. | Y. Ebihara, B. Zhu, J. Lam, The Lq/Lp Hankel Norms of Positive Systems, IEEE Control Systems Letters, Vol. 4, No. 2, pp. 462–467, 2020.05. |
| 13. | Teruki Kato, Yoshio Ebihara, Tomomichi Hagiwara, Analysis of Positive Systems Using Copositive Programming, IEEE Control Systems Letters, 10.1109/LCSYS.2019.2946620, 4, 2, 444-449, Vol. 4, No. 2, pp. 444–449, 2020.04, [URL], 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.. |
| 14. | 蛯原 義雄, 脇 隼人, 瀬部 昇, 半正定値計画によるH∞ 性能限界解析, 計測と制御 = Journal of the Society of Instrument and Control Engineers, 10.11499/sicejl.59.218, 59, 3, 218-225, 2020.03, [URL]. |
| 15. | 蛯原 義雄, 瀬部 昇, 増淵 泉, 脇 隼人, 管野 政明, 椿野 大輔, 離散時間線形時不変システム解析のための外部非負システムの構成と低次元化, システム制御情報学会論文誌, 10.5687/iscie.32.284, 32, 7, 284-293, 2019.07, [URL], 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.. |
| 16. | Xingwen Liu, Jun Shen, Zhan Shu, Mustapha Ait Rami, Yoshio Ebihara, Guest editorial Theory of positive systems and applications, IET Control Theory and Applications, 10.1049/iet-cta.2019.0228, 13, 7, 889-890, 2019.04, [URL]. |
| 17. | 蛯原 義雄, 大木 健太郎, 巻頭言：特集号「第5回制御部門マルチシンポジウム論文特集号」について, 計測自動制御学会論文集, 10.9746/sicetr.55.147, 55, 3, 147-147, 2019, [URL]. |
| 18. | Yoshio Ebihara, Technical Committee on Systems with Uncertainty [Technical Activities], IEEE Control Systems, 10.1109/MCS.2018.2866649, 38, 6, 18 and 144, 2018.12, [URL]. |
| 19. | Yoshio Ebihara, H2 Analysis of LTI systems via conversion to externally positive systems, IEEE Transactions on Automatic Control, 10.1109/TAC.2017.2767704, 63, 8, 2566-2572, 2018.08, [URL], 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.. |
| 20. | 蛯原 義雄, 瀬部 昇, 増淵 泉, 脇 隼人, 管野 政明, 椿野 大輔, 外部非負システムへの変換による離散時間線形時不変システムのH2 解析, システム制御情報学会論文誌, 10.5687/iscie.31.75, 31, 2, 75-84, 2018.02, [URL], 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.. |
| 21. | 反甫 透, 蛯原 義雄, 萩原 朋道, 離散化双線形モデルに基づくブーストコンバータ平均出力電圧の非線形出力フィードバック制御, システム制御情報学会論文誌, 10.5687/iscie.31.63, 31, 2, 63-74, 2018.02, [URL], 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.. |
| 22. | Hiroyuki Ichihara, Shoya Tanabe, Yoshio Ebihara, Dimitri Peaucelle, Analysis and Synthesis of Discrete-Time Interconnected Positive Systems, SICE Journal of Control, Measurement, and System Integration, 10.9746/jcmsi.11.91, 11, 2, 91-99, 2018.01, [URL], 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.. |
| 23. | D. Peaucelle, Y. Ebihara, Affine Versus Multi-Affine Models for S-Variable LMI Conditions, IFAC-PapersOnLine, 10.1016/j.ifacol.2018.11.179, 51, 25, 453-458, 2018, [URL], 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.. |
| 24. | Yoshio Ebihara, Construction of Externally Positive Systems for Discrete-Time LTI System Analysis, IFAC-PapersOnLine, 10.1016/j.ifacol.2018.11.178, 51, 25, 447-452, 2018, [URL], 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.. |
| 25. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Steady-state analysis of delay interconnected positive systems and its application to formation control, IET Control Theory and Applications, 10.1049/iet-cta.2017.0315, 11, 16, 2783-2792, 2017.11, [URL], 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.. |
| 26. | Hiroyuki Ichihara, Shinya Kajihara, Yoshio Ebihara, Dimitri Peaucelle, Formation Control of Mobile Robots Based on Interconnected Positive Systems, IFAC-PapersOnLine, 10.1016/j.ifacol.2017.08.755, 50, 1, 8441-8446, 2017.07, [URL], 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.. |
| 27. | Shoya Tanabe, Hiroyuki Ichihara, Yoshio Ebihara, Dimitri Peaucelle, Persistence Analysis of Discrete-Time Interconnected Positive Systems and its Application to Mobile Robot Formation, IFAC-PapersOnLine, 10.1016/j.ifacol.2017.08.304, 50, 1, 3105-3110, 2017.07, [URL], 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.. |
| 28. | Yoshio Ebihara, Stability Analysis of Neutral Type Time-Delay Positive Systems with Commensurate Delays, IFAC-PapersOnLine, 10.1016/j.ifacol.2017.08.681, 50, 1, 3093-3098, 2017.07, [URL], 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.. |
| 29. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Analysis and synthesis of interconnected positive systems, IEEE Transactions on Automatic Control, 10.1109/TAC.2016.2558287, 62, 2, 652-667, 2017.02, [URL], This paper is concerned with the analysis and synthesis of interconnected systems constructed from heterogeneous positive subsystems and a nonnegative interconnection matrix. We first show that admissibility, to be defined in this paper, is an essential requirement in constructing such interconnected systems. Then, we clarify that the interconnected system is admissible and stable if and only if a Metzler matrix, which is built from the coefficient matrices of positive subsystems and the nonnegative interconnection matrix, is Hurwitz stable. By means of this key result, we further provide several results that characterize the admissibility and stability of the interconnected system in terms of the Frobenius eigenvalue of the interconnection matrix and the weighted L1- induced norm of the positive subsystems again to be defined in this paper. 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., its state converges to a unique strictly positive vector (that is known in advance up to a strictly positive constant multiplicative factor) for any nonnegative and nonzero initial state. As an important consequence of this property, we show that the output of the interconnected system converges to a scalar multiple of the right eigenvector of a nonnegative matrix associated with its Frobenius eigenvalue, where the nonnegative matrix is nothing but the interconnection matrix scaled by the steady-stage gains of the positive subsystems. This result is then naturally and effectively applied to formation control of multiagent systems with positive dynamics. This result can be seen as a generalization of a well-known consensus algorithm that has been basically applied to interconnected systems constructed from integrators.. |
| 30. | Dimitri Peaucelle, Yoshio Ebihara, Yohei Hosoe, Robust observed-state feedback design for discrete-time systems rational in the uncertainties, Automatica, 10.1016/j.automatica.2016.10.003, 76, 96-102, 2017.02, [URL], 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.. |
| 31. | 蛯原 義雄, 非負システムの解析・設計と共正値計画, 自動制御連合講演会講演論文集, 10.11511/jacc.60.0_78, 60, 0, 78-81, 2017, [URL]. |
| 32. | Yoshio Ebihara, Technical Committee on Systems with Uncertainty [Technical Activities], IEEE Control Systems, 10.1109/MCS.2016.2584278, 36, 5, 2016.10, [URL]. |
| 33. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Convergence Rate Analysis of Multi-Agent Positive Systems under Formation Control An Efficient Algorithm by Exploiting Positivity, SICE Journal of Control, Measurement, and System Integration, 10.9746/jcmsi.9.216, 9, 5, 216-224, 2016.09, [URL], 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.. |
| 34. | Yoshio Ebihara, Keisuke Matsuo, Tomomichi Hagiwara, LMI-Based Lower Bound Analysis of the Best Achievable H∞ Performance for SISO Systems, SICE Journal of Control, Measurement, and System Integration, 10.9746/jcmsi.9.165, 9, 4, 165-172, 2016.07, [URL], 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.. |
| 35. | 後藤 良介, 蛯原 義雄, 萩原 朋道, 離散化双線形モデルに基づくブーストコンバータ出力電圧の積分補償付非線形制御―I:―モデル化と同定, システム制御情報学会論文誌, 10.5687/iscie.28.320, 28, 7, 320-329, 2015.07, [URL], 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.. |
| 36. | 後藤 良介, 蛯原 義雄, 萩原 朋道, 離散化双線形モデルに基づくブーストコンバータ出力電圧の積分補償付非線形制御―II:―制御則の導出と実験による検証, システム制御情報学会論文誌, 10.5687/iscie.28.330, 28, 7, 330-339, 2015.07, [URL], 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.. |
| 37. | 西尾 直也, 蛯原 義雄, 萩原 朋道, 複数のむだ時間を有する線形非負システムの支配極解析, システム制御情報学会論文誌, 10.5687/iscie.28.147, 28, 4, 147-154, 2015.04, [URL], 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.. |
| 38. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Descriptor case and system augmentation, Communications and Control Engineering, 10.1007/978-1-4471-6606-1_3, 61-106, 2015.01, [URL], 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).. |
| 39. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Introduction, Communications and Control Engineering, 10.1007/978-1-4471-6606-1_1, 9781447166054, 1-8, 2015.01, [URL], 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.. |
| 40. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Multiobjective controller synthesis for LTI systems, Communications and Control Engineering, 10.1007/978-1-4471-6606-1_5, 139-164, 2015.01, [URL], 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.. |
| 41. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Robust controller synthesis of periodic discrete-time systems, Communications and Control Engineering, 10.1007/978-1-4471-6606-1_8, 229-244, 2015.01, [URL], 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.. |
| 42. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Robust performance analysis of LTI systems, Communications and Control Engineering, 10.1007/978-1-4471-6606-1_2, 9-59, 2015.01, [URL], 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.. |
| 43. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Robust performance analysis of discrete-time periodic systems, Communications and Control Engineering, 10.1007/978-1-4471-6606-1_7, 199-227, 2015.01, [URL], 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.. |
| 44. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Robust state-feedback synthesis for LTI systems, Communications and Control Engineering, 10.1007/978-1-4471-6606-1_4, 107-137, 2015.01, [URL], 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.. |
| 45. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Static output-feedback synthesis, Communications and Control Engineering, 10.1007/978-1-4471-6606-1_6, 165-198, 2015.01, [URL], 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.. |
| 46. | 蛯原 義雄, 特集号「非負システムの制御と数理」を企画して(非負システムの制御と数理), システム／制御／情報, 10.11509/isciesci.59.1_2_1, 59, 1, 2, 2015, [URL]. |
| 47. | 蛯原 義雄, 結合非負システムの解析と設計(非負システムの制御と数理), システム／制御／情報, 10.11509/isciesci.59.1_21, 59, 1, 21-26, 2015, [URL]. |
| 48. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Frédéric Gouaisbaut, Dominant pole analysis of stable time-delay positive systems, IET Control Theory and Applications, 10.1049/iet-cta.2014.0375, 8, 17, 1963-1971, 2014.11, [URL], 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.. |
| 49. | Yoshio Ebihara, Noboru Sebe, Lower bound analysis of H∞ performance achievable via decentralized LTI controllers, International Journal of Robust and Nonlinear Control, 10.1002/rnc.2999, 24, 16, 2423-2437, 2014.11, [URL], 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.. |
| 50. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, On the structure of generalized plant convexifying static H∞ control problems, Automatica, 10.1016/j.automatica.2014.04.027, 50, 6, 1706-1714, 2014.06, [URL], 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.. |
| 51. | Shunji Tanaka, Tomohiko Mitani, Yoshio Ebihara, An efficient beamforming algorithm for large-scale phased arrays with lossy digital phase shifters, IEICE Transactions on Communications, 10.1587/transcom.E97.B.783, E97-B, 4, 783-790, 2014.01, [URL], 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.. |
| 52. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, LMI approach to linear positive system analysis and synthesis, Systems and Control Letters, 10.1016/j.sysconle.2013.11.001, 63, 1, 50-56, 2014.01, [URL], 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.. |
| 53. | 田中 俊二, 三谷 友彦, 蛯原 義雄, 励振位相と励振振幅の同時最適化によるフェーズドアレイアンテナの無線伝送電力最大化, 自動制御連合講演会講演論文集, 10.11511/jacc.57.0_1935, 57, 0, 1935-1939, 2014, [URL], 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．. |
| 54. | 島本 拓和, 蛯原 義雄, 萩原 朋道, 粒子群最適化手法に基づく太陽光発電装置の最大電力点追従制御と実機実験による検証, システム制御情報学会論文誌, 10.5687/iscie.27.237, 27, 6, 237-245, 2014, [URL], 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.. |
| 55. | Jean François Trégouët, Dimitri Peaucelle, Denis Arzelier, Yoshio Ebihara, Periodic memory state-feedback controller New formulation, analysis, and design results, IEEE Transactions on Automatic Control, 10.1109/TAC.2013.2251820, 58, 8, 1986-2000, 2013.08, [URL], 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.. |
| 56. | Yoshio Ebihara, Periodically time-varying memory state-feedback for Robust H2 control of uncertain discrete-time linear systems, Asian Journal of Control, 10.1002/asjc.541, 15, 2, 409-419, 2013.03, [URL], 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.. |
| 57. | 松村 大気, 蛯原 義雄, 萩原 朋道, LMIを用いた離散時間非負システムの安定性とH_∞性能解析, システム制御情報学会論文誌, 10.5687/iscie.26.45, 26, 1, 45-51, 2013.01, [URL], 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.. |
| 58. | Taiki Matsumura, Yoshio Ebihara, Tomomichi Hagiwara, Stability Analysis of Discrete-time Interconnected Positive Systems using Weighted l1-induced Norm, システム制御情報学会論文誌, 10.5687/iscie.26.355, 26, 10, 355-364, 2013, [URL], 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.. |
| 59. | 蛯原 義雄, The 50th IEEE Conference on Decision and Control and European Control Conferenceに参加して(国際会議の報告), システム／制御／情報, 10.11509/isciesci.56.6_338, 56, 6, 338, 2012, [URL]. |
| 60. | Yoshio Ebihara, Jun Yamaguchi, Tomomichi Hagiwara, Periodically time-varying controller synthesis for multiobjective H 2 H∞ control of discrete-time systems and analysis of achievable performance, Systems and Control Letters, 10.1016/j.sysconle.2011.05.008, 60, 9, 709-717, 2011.09, [URL], 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.. |
| 61. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems, Automatica, 10.1016/j.automatica.2010.10.004, 47, 1, 14-25, 2011.01, [URL], 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.. |
| 62. | 川田 昌克, 蛯原 義雄, LMIに基づく制御系解析・設計(制御系解析・設計における数値計算/数式処理ソフトウェアの活用), システム／制御／情報, 10.11509/isciesci.55.5_165, 55, 5, 165-173, 2011, [URL]. |
| 63. | 松田 雄介, 田原 雅人, 蛯原 義雄, 萩原 朋道, 単一の不確定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 双対LMIに基づく緩和問題の漸近的に厳密な階層的構成と非漸近的な厳密性検証, システム制御情報学会論文誌, 10.5687/iscie.23.46, 23, 3, 46-55, 2010.03, [URL], 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.. |
| 64. | Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Analysis of uncertain discrete-time linear periodic systems based on system lifting and LMIs, European Journal of Control, 10.3166/ejc.16.532-544, 16, 5, 532-544, 2010.01, [URL], 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.. |
| 65. | 高柳 徹, 蛯原 義雄, 萩原 朋道, 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するメモリー型周期時変状態フィードバック制御器設計, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI10.0.318.0, 10, 0, 318-318, 2010, [URL], 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．. |
| 66. | 田中 俊二, 三谷 友彦, 蛯原 義雄, 宇宙太陽光発電の送電アレイアンテナ位相最適化による無線伝送電力最大化, 自動制御連合講演会講演論文集, 10.11511/jacc.53.0.100.0, 53, 0, 100-100, 2010, [URL], 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．. |
| 67. | 丸岡 信晃, 蛯原 義雄, 萩原 朋道, 逆システムに基づくフィードフォワード項を有する2自由度制御系によるヘリコプタ実験機の姿勢制御, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI10.0.352.0, 10, 0, 352-352, 2010, [URL], 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．. |
| 68. | 小野 幹典, 蛯原 義雄, 萩原 朋道, 瀬部 昇, 離散時間線形時不変系の分散型H∞制御問題に対する下界値解析手法の有効性検証, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI10.0.315.0, 10, 0, 315-315, 2010, [URL], 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．. |
| 69. | 札場 勇大, 蛯原 義雄, 萩原 朋道, 岡崎 安直, 小松 真弓, 単純適応制御系設計におけるスケーリングの導入と拮抗型空圧人工筋駆動機構の位置決め制御への応用, システム制御情報学会論文誌, 10.5687/iscie.22.350, 22, 10, 350-356, 2009.10, [URL], 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.. |
| 70. | Yoshio Ebihara, Yusuke Onishi, Tomomichi Hagiwara, Robust performance analysis of uncertain LTI systems Dual LMI approach and verifications for exactness, IEEE Transactions on Automatic Control, 10.1109/TAC.2009.2017086, 54, 5, 938-951, 2009.05, [URL], 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.. |
| 71. | Yoshio Ebihara, Yusuke Onishi, Tomomichi Hagiwara, Robust Performance Analysis of Uncertain LTI Systems Dual LMI Approach and Verifications for Exactness, IEEE Transactions on Automatic Control, 54, 5, 938-951, 2009.05, 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.. |
| 72. | 小山 めぐみ, 蛯原 義雄, 萩原 朋道, 2自由度LQIサーボ系によるバックコンバータの出力電圧制御, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI09.0.117.0, 9, 0, 117-117, 2009, [URL], 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．. |
| 73. | 蛯原 義雄, Periodically Time-Varying Memory State-Feedback Controller Synthesis for Uncertain Discrete-Time Linear Systems:The H2 Case, 自動制御連合講演会講演論文集, 10.11511/jacc.52.0.60.0, 52, 0, 60-60, 2009, [URL], This study is concerned with the synthesis of periodically time-varyingmemory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established basic strategiesfor LMI-based (robust) H-infinity PTVMSFCs synthesis, and in this paper we 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 a common solutionfor multiple LMI conditions that are related toLyapunov inequality and inequalities for bounding traces of Lyapunov matrix. We overcome this difficulty by deriving an analytic representationof LMI solutions and derive a necessary and sufficientLMI condition for the H2-PTVMSFCs synthesis. Based on these results, we also consider robust H2-PTVMSFC synthesis for polytopic-type uncertain LTI systems.. |
| 74. | 久保山 祐紀, 蛯原 義雄, 萩原 朋道, ポリトープ型の不確かさを有する線形離散時間系に対するメモリー型周期時変状態フィードバック制御器の設計, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI09.0.281.0, 9, 0, 281-281, 2009, [URL], 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．. |
| 75. | 田原 雅人, 松田 雄介, 蛯原 義雄, 萩原 朋道, 単一の不確定パラメータを有する線形時不変系の双対LMIに基づくロバストH∞性能解析, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI09.0.533.0, 9, 0, 533-533, 2009, [URL], 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．. |
| 76. | Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara, Generalized S-procedure for inequality conditions on one-vector-lossless sets and linear system analysis, SIAM Journal on Control and Optimization, 10.1137/050627551, 47, 3, 1547-1555, 2008.11, [URL], 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.. |
| 77. | Yoshio Ebihara, On the Exactness Proof of (D, G) Scaling, SICE Journal of Control, Measurement, and System Integration, 10.9746/jcmsi.1.474, 1, 6, 474-478, 2008.11, [URL], 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.. |
| 78. | 金盛 且洋, 清田 将五郎, 蛯原 義雄, 萩原 朋道, 岡崎 安直, 小松 真弓, プラント変数最適ロバストサーボ系に基づく2軸型空圧人工筋アームの軌道追従制御 圧力情報を利用したオブザーバによる追従性能の向上, Transactions of the Society of Instrument and Control Engineers, 10.9746/ve.sicetr1965.44.927, 44, 11, 927-935, 2008.11, [URL], 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.. |
| 79. | Yoshio Ebihara, Computing the distance to uncontrollability via LMIs Lower bound computation with exactness verification, Systems and Control Letters, 10.1016/j.sysconle.2008.03.002, 57, 9, 763-771, 2008.09, [URL], In this paper, we consider the problem of computing the distance to uncontrollability (DTUC) of a given controllable pair A ∈ Cn × n and B ∈ Cn × 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).. |
| 80. | Yoshio Ebihara, Yoshito Hirai, Tomomichi Hagiwara, On H∞ model reduction for discrete-time linear time-invariant systems using linear matrix inequalities, Asian Journal of Control, 10, 3, 291-300, 2008.05, 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.. |
| 81. | Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara, Generalized $mathcal{S}$-Procedure for Inequality Conditions on One-Vector-Lossless Sets and Linear System Analysis, SIAM Journal on Control and Optimization, 47, 3, 1547-1555, 2008, 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.. |
| 82. | 藤原 佳典, 蛯原 義雄, 萩原 朋道, ヘリコプタ実験機の2自由度LQIサーボ系による姿勢制御, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI08.0.341.0, 8, 0, 341-341, 2008, [URL], 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.. |
| 83. | 大隈 正寛, 蛯原 義雄, 萩原 朋道, 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性能解析, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI08.0.210.0, 8, 0, 210-210, 2008, [URL], 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．. |
| 84. | 蛯原 義雄, 松田 雄介, 双対LMIに基づく線形時不変系のロバスト性能解析, 自動制御連合講演会講演論文集, 10.11511/jacc.51.0.172.0, 51, 0, 172-172, 2008, [URL], 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.. |
| 85. | 松田 雄介, 蛯原 義雄, 萩原 朋道, 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と実験によるその妥当性の検証, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI08.0.179.0, 8, 0, 179-179, 2008, [URL], 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．. |
| 86. | 札場 勇大, 蛯原 義雄, 萩原 朋道, 岡崎 安直, 単純適応制御に基づく拮抗型空圧人工筋駆動機構の位置決め制御, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI07.0.233.0, 7, 0, 233-233, 2007, [URL], 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．. |
| 87. | 蛯原 義雄, 〓 貴生, PID制御のパラメータチューニング特集号を企画して, システム／制御／情報, 50, 12, 471, 2006.12. |
| 88. | Yoshio Ebihara, Yoshimichi Ito, Tomomichi Hagiwara, Exact stability analysis of 2-D systems using LMIs, IEEE Transactions on Automatic Control, 10.1109/TAC.2006.880789, 51, 9, 1509-1513, 2006.09, [URL], 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.. |
| 89. | Yoshio Ebihara, Tomomichi Hagiwara, On the degree of polynomial parameter-dependent Lyapunov functions for robust stability of single parameter-dependent LTI systems A counter-example to Barmish's conjecture, Automatica, 10.1016/j.automatica.2006.04.011, 42, 9, 1599-1603, 2006.09, [URL], 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 ∈ Rn × 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 = 0N θi Pi that ensures the robust Hurwitz stability of A (θ) via P (θ) > 0, P (θ) A (θ) + AT (θ) P (θ) 0 + 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 ∈ R3 × 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.. |
| 90. | 川田 昌克, 蛯原 義雄, 陳 幹, H_∞状態フィードバック設計のための冗長なディスクリプタアプローヂ 伸張型LMIに基づく既存結果の拡張, 計測自動制御学会論文集, 42, 7, 750-757, 2006.07. |
| 91. | 平井 義人, 蛯原 義雄, 萩原 朋道, 多項式型パラメータ依存 Lyapunov 関数を用いた不確かな線形時不変系のロバストH_∞性能解析, 計測自動制御学会論文集, 42, 6, 618-627, 2006.06. |
| 92. | 川田 昌克, 蛯原 義雄, 陳 幹, H∞状態フィードバック設計のための冗長なディスクリプタアプローチ:伸張型LMIに基づく既存結果の拡張, 計測自動制御学会論文集, 10.9746/sicetr1965.42.750, 42, 7, 750-757, 2006, [URL], 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.. |
| 93. | 朴 サンウク, 蛯原 義雄, 萩原 朋道, (D,G)スケーリングを用いた状態フィードバックH∞制御系設計と反復計算による改良, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI06.0.266.0, 6, 0, 266-266, 2006, [URL], 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．. |
| 94. | 伊藤 義道, 蛯原 義雄, 2-D離散システムの安定性解析, システム／制御／情報, 10.11509/isciesci.50.11_412, 50, 11, 412-417, 2006, [URL]. |
| 95. | 清田 将五郎, 蛯原 義雄, 萩原 朋道, 岡崎 安直, 足達 勇治, LQ最適制御理論を用いた2軸型空圧人工筋アームの軌道追従制御, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI06.0.288.0, 6, 0, 288-288, 2006, [URL], 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．. |
| 96. | 平井 義人, 蛯原 義雄, 萩原 朋道, 不確かな線形時不変系のロバストH∞性能解析:多項式型パラメータ依存リアプノフ関数を用いた解析と繰り返し計算による改善, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI06.0.52.0, 6, 0, 52-52, 2006, [URL], 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．. |
| 97. | 前田 雄俊, 蛯原 義雄, 萩原 朋道, 制御入力の飽和を考慮した2自由度LQIサーボ系のL2性能保証領域に基づく設計法, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI06.0.285.0, 6, 0, 285-285, 2006, [URL], 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．. |
| 98. | 平井 義人, 蛯原 義雄, 萩原 朋道, 多項式型パラメータ体存Lyapunov関数を用いた不確かな線形時不変系のロバストH∞性能解析, 計測自動制御学会論文集, 10.9746/sicetr1965.42.618, 42, 6, 618-627, 2006, [URL], 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.. |
| 99. | 金盛 且洋, 蛯原 義雄, 萩原 朋道, 線形行列不等式を用いたサンプル値 H2/H∞ 制御系の設計法に関する考察, 自動制御連合講演会講演論文集, 10.11511/jacc.49.0.65.0, 49, 0, 65-65, 2006, [URL]. |
| 100. | Yoshio Ebihara, Tomomichi Hagiwara, A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems, Automatica, 10.1016/j.automatica.2005.05.023, 41, 11, 1933-1941, 2005.11, [URL], 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.. |
| 101. | 蛯原 義雄, 萩原 朋道, 制御系の切換時における外乱応答の評価手法に関する検討 線形作用素表現に基づくL_2ゲイン解析, 計測自動制御学会論文集, 41, 11, 937-938, 2005.11. |
| 102. | 蛯原 義雄, The 16th IFAC World Congress, システム／制御／情報, 10.11509/isciesci.49.9_389, 49, 9, 389, 2005, [URL]. |
| 103. | 蛯原 義雄, 萩原 朋道, 制御系の切換時における外乱応答の評価手法に関する検討:線形作用素表現に基づくL2ゲイン解析, 計測自動制御学会論文集, 10.9746/sicetr1965.41.937, 41, 11, 937-938, 2005, [URL], 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.. |
| 104. | 和田 康宏, 蛯原 義雄, 萩原 朋道, 岡崎 安直, 足達 勇治, 拮抗型空圧人工筋駆動機構の2自由度LQI制御, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI05.0.219.0, 5, 0, 219-219, 2005, [URL], 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.. |
| 105. | 藤村 勇樹, 蛯原 義雄, 萩原 朋道, 高次の多項式型マルチプライヤを用いた多項式行列のロバストD安定解析, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI05.0.208.0, 5, 0, 208-208, 2005, [URL], 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.. |
| 106. | 蛯原 義雄, American Control Conference 2004, 計測と制御 = Journal of the Society of Instrument and Control Engineers, 43, 12, 1007, 2004.12. |
| 107. | Yoshio Ebihara, Tomomichi Hagiwara, New dilated LMI characterizations for continuous-time multiobjective controller synthesis, Automatica, 10.1016/j.automatica.2004.06.009, 40, 11, 2003-2009, 2004.11, [URL], 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.. |
| 108. | Yoshio Ebihara, Kazuma Tokuyama, Tomomichi Hagiwara, Structured controller synthesis using LMI and alternating projection method, International Journal of Control, 10.1080/00207170412331298947, 77, 12, 1137-1147, 2004.08, [URL], 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.. |
| 109. | Yoshio Ebihara, Tomomichi Hagiwara, On H∞ model reduction using LMIs, IEEE Transactions on Automatic Control, 10.1109/TAC.2004.831116, 49, 7, 1187-1191, 2004.07, [URL], In this note, we deal with the problem of approximating a given nth-order linear time-invariant system G by an rth-order system Gr where r ∞ 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.. |
| 110. | 前田 雄俊, 蛯原 義雄, 萩原 朋道, マトリクスペンシルの正則性解析と線形時不変系の安定解析への応用, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI04.0.47.0, 4, 0, 47-47, 2004, [URL], 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．. |
| 111. | 蛯原 義雄, 萩原 朋道, 伸張型線形行列不等式を用いた制御系の解析と設計, システム／制御／情報, 10.11509/isciesci.48.9_355, 48, 9, 355-360, 2004, [URL]. |
| 112. | 桑原 丈, 蛯原 義雄, 萩原 朋道, 正実性・最小位相性を考慮したモデル低次元化手法, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI04.0.71.0, 4, 0, 71-71, 2004, [URL], 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.. |
| 113. | 平井 義人, 蛯原 義雄, 萩原 朋道, 行列不等式を用いた離散時間線形時不変系のモデル低次元化, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI04.0.70.0, 4, 0, 70-70, 2004, [URL], 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．. |
| 114. | 桑原 丈, 細川 琢磨, 蛯原 義雄, 萩原 朋道, 森岡 靖夫, 定常ゲインを考慮したモデル低次元化手法とその電力系統縮約への応用, システム制御情報学会論文誌, 10.5687/iscie.16.476, 16, 9, 476-483, 2003.09, [URL], 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.. |
| 115. | Yoshio Ebihara, Tomomichi Hagiwara, A Dilated LMI Approach to Continuous-Time Gain-Scheduled Controller Synthesis with Parameter-Dependent Lyapunov Variables, 計測自動制御学会論文集, 39, 8, 734-740, 2003.08. |
| 116. | 和田 康宏, 蒲地 誠, 蛯原 義雄, 萩原 朋道, 2自由度最適積分型サーボ系におけるH∞制御の利用と空気圧シリンダの位置決め制御, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI03.0.2004.0, 3, 0, 2004-2004, 2003, [URL], 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.. |
| 117. | 蛯原 義雄, 萩原 朋道, On Model Reduction Using LMI’s, 自動制御連合講演会講演論文集, 10.11511/jacc.46.0.185.0, 46, 0, 185-188, 2003, [URL], 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．. |
| 118. | 冨岡 一貴, 蛯原 義雄, 萩原 朋道, 多項式型パラメータ依存リアプノフ変数を用いたゲインスケジューリング制御系の設計, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI03.0.7005.0, 3, 0, 7005-7005, 2003, [URL], 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.. |
| 119. | Yoshio Ebihara, Tomomichi Hagiwara, A Dilated LMI Approach to Robust Performance Analysis of Linear Time-Invariant Uncertain Systems, SICE Annual Conference Program and Abstracts, 10.11499/sicep.2002.0.569.0, 2002, 0, 569-569, 2002, [URL], 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.. |
| 120. | 野崎 尚広, 蛯原 義雄, 萩原 朋道, LMIによる分散安定化制御装置の一設計法, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI02.0.14.0, 2, 0, 14-14, 2002, [URL], 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.. |
| 121. | 桑原 丈, 蛯原 義雄, 萩原 朋道, 森岡 靖夫, 定常ゲインを考慮したモデル低次元化手法の拡張とその電力系統縮約への応用, システム制御情報学会 研究発表講演会講演論文集, 10.11509/sci.SCI02.0.147.0, 2, 0, 147-147, 2002, [URL], 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.. |
| 122. | 京和泉 宏三, 藤田 行茂, 蛯原 義雄, 単純適応制御手法による空圧サーボ位置決め制御 - PFC のオートチューニング機構の導入, システム制御情報学会論文誌, 10.5687/iscie.14.102, 14, 3, 102-109, 2001.03, [URL], 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.. |
| 123. | Yoshio Ebihara, Tomomichi Hagiwara, Mituhiko Araki, Sequential tuning methods of LQ/LQI controllers for multivariable systems and their application to hot strip mills, International Journal of Control, 10.1080/002071700445415, 73, 15, 1392-1404, 2000.10, [URL], 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.. |
| 124. | 蛯原 義雄, 荻原 朋道, H_2パフォーマンスに基づいたコントローラの逐次調整法, 材料とプロセス : 日本鉄鋼協会講演論文集 = Current advances in materials and processes : report of the ISIJ meeting, 13, 2, P14, 2000.03. |
| 125. | 蛯原 義雄, 萩原 朋道, 荒木 光彦, 多変数最適制御系の逐次調整法とその圧延システムへの応用, 材料とプロセス : 日本鉄鋼協会講演論文集 = Current advances in materials and processes : report of the ISIJ meeting, 12, 5, P-13, 1999.09. |
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