Exact Solution Method for Robust Semidefinite Programming Problemsand Its Application to Control System Synthesis

• Project/Area Number: 21760328
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Control engineering
• Research Institution: Kyoto University
• Principal Investigator: EBIHARA Yoshio 京都大学, 大学院・工学研究科, 准教授 (80346080)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: ロバスト半正定値計画 / 制御系解析・設計 / 厳密解法 / 半正定値計画問題 / 線形計画問題 / システム解析 / システム設計 / 非負システム / 周期時変制御器設計 / ロバスト半正値計画

Research Abstract

In this study we dealt with robust semidefinite programming problems (robust SDPs) that naturally appear when we analyze robust performance of control systems affected by parametric uncertainties. For the robust SDPs, we successfully constructed a sequence of SDPs that is ensured to be asymptotically exact. On the other hand, to achieve better robust performance for uncertain discrete-time systems, we conceived a novel memory-type periodically time-varying controller structure and established a concrete way to design such controllers by means of SDPs. Dr. Yoshio Ebihara received SICE Annual Conference International Award for his paper dealing with robust performance analysis of uncertain discrete-time systems.

Research Products

• [Journal Article] Periodic Memory State-feedback Controller: New Formulation, Analysis and Design Results (2013)
  • Author(s): J.F. Tregouet, D. Peaucelle, D. Arzelier and Y. Ebihara
  • Journal Title: IEEE Transactions on Automatic Control Pages: 14-14
  • URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6475980&tag=1
  • Peer Reviewed
• [Journal Article] Periodically Time-Varying Memory State-Feedback for Robust H2 Control of Uncertain Discrete-Time Linear Systems (2013)
  • Author(s): Y. Ebihara
  • Journal Title: Asian Journal of Control Volume: Vol. 15, No. 2 Pages: 409-419
  • Peer Reviewed
• [Journal Article] LMIを用いた離散時間非負システムの安定性とH-infinity性能解析 (2013)
  • Author(s): 松村大気,蛯原義雄,萩原朋道
  • Journal Title: システム制御情報学会論文誌 Volume: Vol. 26, No. 1 Pages: 45-51
  • Peer Reviewed
• [Journal Article] Lower Bound Analysis of H-infinity Performance Achievable via Decentralized LTI Controllers (2013)
  • Author(s): Y. Ebihara
  • Journal Title: International Journal of Robust and Nonlinear Control Volume: 未定 Issue: 16 Pages: 15-15
  • DOI: 10.1002/rnc.2999
  • Peer Reviewed
• [Journal Article] Periodic Memory State-Feedback Controller: New formulation, Analysis and Design Results (2013)
  • Author(s): J.F. Tregouet
  • Journal Title: IEEE Transactions on Automatic Control Volume: 未定 Issue: 8 Pages: 14-14
  • DOI: 10.1109/tac.2013.2251820
  • Peer Reviewed
• [Journal Article] 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 (2013)
  • Author(s): 松村大気
  • Journal Title: システム制御情報学会論文誌 Volume: Vol. 26, No. 1 Pages: 45-51
  • Peer Reviewed
• [Journal Article] Periodically Time-Varying Controller Synthesis for Multiobjective H2/H-infinity Control of Discrete-Time Systems and Analysis of Achievable Performance (2011)
  • Author(s): Y. Ebihara, Y. Yamaguchi and T. Hagiwara
  • Journal Title: Systems and Control Letters Volume: Vol. 60, No. 9 Pages: 709-717
  • Peer Reviewed
• [Journal Article] Periodically Time-Varying Memory State-Feedback ControllerSynthesis for Discrete-Time Linear Systems (2011)
  • Author(s): Y. Ebihara, D. Peaucelle and D. Arzelier
  • Journal Title: Automatica Volume: Vol. 47, No. 1 Pages: 14-25
  • Peer Reviewed
• [Journal Article] Periodically Time-Varying Controller Synthesis for Multiobjective H2/H-infinity Control of Discrete-Time Systems and Analysis of Achievable Performance (2011)
  • Author(s): Y.Ebihara, J.Yamaguchi, T.Hagiwara
  • Journal Title: Systems and Control Letters Volume: Vol.60 Issue: 9 Pages: 709-717
  • DOI: 10.1016/j.sysconle.2011.05.008
  • Peer Reviewed
• [Journal Article] Periodically Time-Varying Memory State-Feedback Controller Synthesis for Discrete-Time Linear Systems (2011)
  • Author(s): Y.Ebihara, D.Peaucelle, D.Arzelier
  • Journal Title: Automatica Volume: Vol.47 Pages: 14-25
  • Peer Reviewed
• [Journal Article] Analysis of Uncertain Discrete-Time Linear Periodic Systemsbased on System Lifting and LMIs (2010)
  • Author(s): Y. Ebihara, D. Peaucelle and D. Arzelier
  • Journal Title: European Journal of Control Volume: Vol. 16, No. 5 Pages: 532-544
  • Peer Reviewed
• [Journal Article] 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- (2010)
  • Author(s): 松田雄介,田原雅人, 蛯原義雄,萩原朋道
  • Journal Title: システム制御情報学会論文誌 Volume: Vol. 23, No. 3 Pages: 46-55
  • Peer Reviewed
• [Journal Article] Analysis of Uncertain Discrete-Time Linear Periodic Systems based on System Lifting and LMIs (2010)
  • Author(s): Y.Ebihara, D.Peaucelle, D.Arzelier
  • Journal Title: European Journal of Control Volume: Vol.16 Pages: 532-544
  • Peer Reviewed
• [Journal Article] 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 (2010)
  • Author(s): 松田雄介, 田原雅人, 蛯原義雄, 萩原朋道
  • Journal Title: システム制御情報学会論文誌 Vol.23 Pages: 46-55
  • NAID: 10026495704
  • Peer Reviewed
• [Journal Article] Robust Performance Analysis of Uncertain LTI Systems: Dual LMI Approach and Verifications for Exactness (2009)
  • Author(s): Y. Ebihara, Y. Onishi and T. Hagiwara
  • Journal Title: IEEE Transactions on Automatic Control, Special Issue on Positive Polynomials in Control Volume: Vol. 54, No. 5 Pages: 938-951
  • NAID: 120002086027
  • Peer Reviewed
• [Presentation] Stability and Persistence Analysis of Large Scale InterconnectedPositive Systems (2013)
  • Author(s): Y. Ebihara, D. Peaucelle and D. Arzelier
  • Organizer: Proc. of the European Control Conference
  • Place of Presentation: Zurich, Switzerland
  • Year and Date: 2013-07-19
• [Presentation] Stability and Persistence Analysis of Large Scale Interconnected Positive Systems (2013)
  • Author(s): Y. Ebihara
  • Organizer: European Control Conference
  • Place of Presentation: Zurich, Switzerland
• [Presentation] Robust H-infinity Performance of Periodic Systems with Memory: New Formulations, Analysis and Design Results (2012)
  • Author(s): J.F. Tregouet, D. Arzelier, D. Peaucelle, Y. Ebihara, C. Pittet and A. Falcoz
  • Organizer: Proc. of the 51th IEEE Conference on Decision and Control
  • Place of Presentation: Maui, Hawaii, USA
  • Year and Date: 2012-12-13
• [Presentation] Decentralized Control ofInterconnected Positive Systems Using L1-induced Norm Characterization (2012)
  • Author(s): Y. Ebihara, D. Peaucelle and D. Arzelier
  • Organizer: Proc.of the 51th IEEE Conference on Decision and Control
  • Place of Presentation: Maui, Hawaii, USA
  • Year and Date: 2012-12-13
• [Presentation] Dual LMI Approach to Linear Positive System Analysis (2012)
  • Author(s): Y. Ebihara
  • Organizer: Proc. of 12th International Conference on Control, Automation and Systems (ICCAS 2012)
  • Place of Presentation: Jeju, Korea
  • Year and Date: 2012-10-18
• [Presentation] Optimal L1-Controller Synthesis for Positive Systems and Its Robustness Properties (2012)
  • Author(s): Y. Ebihara, D. Peaucelle and D. Arzelier
  • Organizer: Proc. of the American Control Conference
  • Place of Presentation: Montreal, Canada
  • Year and Date: 2012-06-29
• [Presentation] Robust Stability of Periodic Systems with Memory: New Formulations, Analysis and Design Results (2012)
  • Author(s): J.F. Tregouet, Y. Ebihara, D. Arzelier, D. Peaucelle, C. Pittet and A. Falcoz
  • Organizer: Proc. of the 7th IFAC Symposium on Robust Control Design
  • Place of Presentation: Aalborg, Denmark
  • Year and Date: 2012-06-22
• [Presentation] Decentralized Control of Interconnected Positive Systems Using L1-induced Norm Characterization (2012)
  • Author(s): Y. Ebihara
  • Organizer: The 51th IEEE Conference on Decision and Control
  • Place of Presentation: Maui, Hawaii
• [Presentation] Robust H-infinity Performance of Periodic Systems with Memory: New Formulations, Analysis and Design Results (2012)
  • Author(s): J.F. Tregouet
  • Organizer: The 51th IEEE Conference on Decision and Control
  • Place of Presentation: Maui, Hawaii, USA
• [Presentation] Dual LMI Approach to Linear Positive System Analysis (2012)
  • Author(s): Y. Ebihara
  • Organizer: The 12th International Conference on Control, Automation and Systems
  • Place of Presentation: Jeju, Korea
• [Presentation] Optimal L1-Controller Synthesis for Positive Systems and Its Robustness Properties (2012)
  • Author(s): Y. Ebihara
  • Organizer: 2012 American Control Conference
  • Place of Presentation: Montreal, Quebec, Canada
• [Presentation] Robust Stability of Periodic Systems with Memory: New Formulations, Analysis and Design Results (2012)
  • Author(s): J.F. Tretouet
  • Organizer: The 7th IFAC Symposium on Robust Control Design
  • Place of Presentation: Aalborg, Denmark
• [Presentation] Periodic H2 Synthesis for Spacecraft Attitude Control with Magnetorquers and Reaction Wheels (2011)
  • Author(s): J.F. Tregouet, D. Arzelier, D. Peaucelle,Y. Ebihara, C. Pittet and A. Falcoz
  • Organizer: Proc. of the 50th IEEE Conference on Decision and Control
  • Place of Presentation: Orlando, Florida, USA
  • Year and Date: 2011-12-15
• [Presentation] Periodic H2 synthesis for spacecraft attitude control with magnetorquers and reaction wheels (2011)
  • Author(s): J.F.Tregouet, D.Arzelier, D.Peaucelle, Y.Ebihara, C.Pittet, A.Falcoz
  • Organizer: Decision and Control and European Control Conierence (CDC-ECC), 2011 50th IEEE Conference on
  • Place of Presentation: Orlando, USA
  • Year and Date: 2011-12-15
• [Presentation] L1 Gain Analysis of Linear Positive Systems and Its Application (2011)
  • Author(s): Y. Ebihara, D. Peaucelle and D. Arzelier
  • Organizer: Proc.of the 50th IEEE Conference on Decision and Control
  • Place of Presentation: Orlando, Florida, USA
  • Year and Date: 2011-12-13
• [Presentation] L1 gain analysis of linear positive systems and its application (2011)
  • Author(s): Y.Ebihara, D.Peaucelle, D.Arzelier
  • Organizer: Decision and Control and European Control Conlerence (CDC-ECC), 2011 50th IEEE Conference on
  • Place of Presentation: Orlando, USA
  • Year and Date: 2011-12-13
• [Presentation] Periodic FIR Controller Synthesis for Discrete-Time Uncertain Linear Systems (2011)
  • Author(s): J.F. Tregouet, D. Arzelier, D. Peaucelle,Y. Ebihara, C. Pittet and A. Falcoz
  • Organizer: Proc. of the 50th IEEE Conference on Decision and Control
  • Place of Presentation: Orlando, Florida, USA
  • Year and Date: 2011-12-12
• [Presentation] Periodic FIR controller synthesis for discrete-time uncertain linear systems (2011)
  • Author(s): J.F.Tregouet, D.Arzelier, D.Peacelle, Y.Ebihara, C.Pittet, A.Falcoz
  • Organizer: Decision and Control and European Control Conlerence (CDC-ECC), 2011 50th IEEE Conference on
  • Place of Presentation: Orlando, USA
  • Year and Date: 2011-12-12
• [Presentation] Some Conditions for Convexifying Static H-infinity Control Problems (2011)
  • Author(s): Y. Ebihara, D. Peaucelle and D. Arzelier
  • Organizer: Proc. of the 18th IFAC World Congress
  • Place of Presentation: Milano, Italy
  • Year and Date: 2011-08-31
• [Presentation] Some conditions for convexifying static H-infinity control problems (2011)
  • Author(s): Y.Ebihara, D.Peaucelle, D.Arzelier
  • Organizer: The 18th IFAC World Congress
  • Place of Presentation: Milano, Italy
  • Year and Date: 2011-08-31
• [Presentation] Asymptotic Exactness of Dual LMI Approach for Robust Performance Analysis of Uncertain LTI Systems (2010)
  • Author(s): Y. Ebihara, Y. Matsuda and T. Hagiwara
  • Organizer: Proc. of the 49th IEEE Conference on Decision and Control
  • Place of Presentation: Atlanta, Georgia, USA
  • Year and Date: 2010-12-15
• [Presentation] Asymptotic Exactness of Dual LMI Approach for Robust Performance Analysis of Uncertain LTI Systems (2010)
  • Author(s): Y.Ebihara
  • Organizer: The 49th IEEE Conference on Decision and Control
  • Place of Presentation: Atlanta, Georgia, USA
  • Year and Date: 2010-12-15
• [Presentation] Robust H2 Control of Uncertain Discrete-Time Linear Systemswith Periodically Time-Varying Memory State-Feedback (2010)
  • Author(s): Y. Ebihara
  • Organizer: Proc. of the IEEE Multi Conference on Systems and Control
  • Place of Presentation: Yokohama, Japan
  • Year and Date: 2010-09-08
• [Presentation] Robust H2 Control of Uncertain Discrete-Time Linear Systems with Periodically Time-Varying Memory State-Feedback (2010)
  • Author(s): Y.Ebihara
  • Organizer: IEEE Multi-conference on Systems and Control
  • Place of Presentation: Yokohama, Japan
  • Year and Date: 2010-09-08
• [Presentation] Periodically Time-Varying Controller Synthesis for Multiobjective H_2/H-infinity Control of Discrete-Time Systems and Analysis of Achievable Performance (2010)
  • Author(s): Y. Ebihara, J. Yamaguchi and T. Hagiwara
  • Organizer: Proc. of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010)
  • Place of Presentation: Budapest, Hungary
  • Year and Date: 2010-07-09
• [Presentation] Decentralized Control for Discrete-Time LTI Systems:Lower Bound Analysis of H-infinity Performance Achievable via LTI Controllers (2010)
  • Author(s): Y. Ebihara and N. Sebe
  • Organizer: Proc. of the American Control Conference
  • Place of Presentation: Baltimore, Maryland, USA
  • Year and Date: 2010-07-02
• [Presentation] 半正定値計画に基づく制御系のロバスト性解析・ロバスト設計 (2010)
  • Author(s): 蛯原義雄
  • Organizer: 第2回日本数式処理学会理論分科会研究会
  • Place of Presentation: クロスパル新潟
  • Year and Date: 2010-02-18
• [Presentation] Constructing a Sequence of Relaxation Problems for Robustness Analysis of Uncertain LTI Systems via Dual LMIs (2009)
  • Author(s): Y. Matsuda, Y. Ebihara and T. Hagiwara
  • Organizer: Proc.of the 48th IEEE Conference on Decision and Control
  • Place of Presentation: Shanghai, China
  • Year and Date: 2009-12-16
• [Presentation] Further Results on Periodically Time-Varying Dynamical State-Feedback Controller Synthesis for Discrete-Time Linear Systems (2009)
  • Author(s): Y. Ebihara, Y. Kuboyama, T. Hagiwara, D. Peaucelle and D. Arzelier
  • Organizer: Proc. of the 48th IEEE Conference on Decision and Control
  • Place of Presentation: Shanghai, China
  • Year and Date: 2009-12-16
• [Presentation] Constructing a Sequence of Relaxation Problems for Robustness Analysis of Uncertain LTI Systems via Dual LMIs (2009)
  • Author(s): Y.Ebihara
  • Organizer: The 48th IEEE Conference on Decision and Control
  • Place of Presentation: Shanghai, China
  • Year and Date: 2009-12-16
• [Presentation] Further Results on Periodically Time-Varying Dynamical State-Feedback Controller Synthesis for Discrete-Time Linear Systems (2009)
  • Author(s): Y.Ebihara
  • Organizer: The 48th IEEE Conference on Decision and Control
  • Place of Presentation: Shanghai, China
  • Year and Date: 2009-12-16
• [Presentation] Robustness Analysis of Uncertain Discrete-Time Linear Systemsbased on System Lifting and LMIs (2009)
  • Author(s): Y. Ebihara, D. Peaucelle and D. Arzelier
  • Organizer: Proc. of the ICROS-SICE International Joint Conference 2009
  • Place of Presentation: Fukuoka Japan
  • Year and Date: 2009-08-20
• [Presentation] An Elementary Proof for the Exactness of (D,G) Scaling (2009)
  • Author(s): Y. Ebihara
  • Organizer: Proc. of the 47th American Control Conference
  • Place of Presentation: St. Leouis, Missouri, USA
  • Year and Date: 2009-06-11
• [Book] LMI によるシステム制御 (2012)
  • Author(s): 蛯原義雄
  • Total Pages: 236
  • Publisher: 森北出版
• [Book] LMIによるシステム制御 (2012)
  • Author(s): 蛯原義雄
  • Total Pages: 236
  • Publisher: 森北出版