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Multi-objective Robust Control System Design Based on Finite Frequency KYP Lemma and Its Applications

Research Project

Project/Area Number 17360195
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Control engineering
Research InstitutionThe University of Tokyo

Principal Investigator

HARA Shinji  The University of Tokyo, Graduate School of Information Science and Technology, Professor (80134972)

Co-Investigator(Kenkyū-buntansha) TSUCHIYA Takashi  The Institure of Statistical Mathematics, Dept. of Mathematical Analysis and Statistical Inference, 教授 (00188575)
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥8,950,000 (Direct Cost: ¥8,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2006: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2005: ¥4,900,000 (Direct Cost: ¥4,900,000)
KeywordsControl system design / Robust control / Multi-objective control / KYP lemma / Frequency characteristics / Linear matrix inequality
Research Abstract

The purpose of this research project is to develop a unified theory of control synthesis based on the analytical results on generalized KYP lemma, which is a finite frequency version of the original KYP lemma Especially, our main focus are on a systematic design method considering the more practical situations and on the design algorithms.
The results on the synthesis theory are as follows:
(1) PID controller synthesis based on the generalized KYP lemma.
(2) A time-domain interpretation of the generalized KYP lemma, which includes an equivalence of positive-realness in frequency-domain and passivity in time-domain as a special case. It is a first step of the investigation for nonlinear systems.
(3) An SoS (Sum of Squares) decomposition characterization of the generalized KYP lemma The result is useful for plant design from the view point of control.
(4) A dual characterization of the generalized KYP lemma and its computational complexity analysis.
A analysis/synthesis tool box has been developed based on our theoretical results. We also implemented primal-dual algorithms for solving the generalized KYP based optimization problems and compared the computational costs. The comparison shows that the positive semi-definite optimization problems derived from the generalized KYP lemma are very hard to solve in general. This motivates us to develop a new algorithm considering the structure.

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (13 results)

All 2008 2007 2006 2005

All Journal Article (9 results) (of which Peer Reviewed: 4 results) Presentation (4 results)

  • [Journal Article] Sum-of-Square Decomposition via Generalized KYP Lemma2008

    • Author(s)
      S. Hara, T. Iwasaki
    • Journal Title

      Mathematical Engineering Technical Report METR 2008-25

      Pages: 1-13

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Sum-of-Square Decomposition via Generalized KYP Lemma2008

    • Author(s)
      S. Hara, T. Iwasaki
    • Journal Title

      Mathematical Engineering Technical Report, METR 2008-25

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Feedback Control Synthesis of Multiple Frequency Domain Specifications via Generalized KYP Lemma2007

    • Author(s)
      T. Iwasaki, S. Hara
    • Journal Title

      International Journal of Robust and Nonlinear Control 17・5-6

      Pages: 415-434

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Feedback Control Synthesis of Multiple Frequency Domain Specifications via Generalized KYP Lemma2007

    • Author(s)
      T. Iwasaki, S. Hara
    • Journal Title

      Int. J. of Robust and Nonlinear Control 17

      Pages: 415-434

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Feedback Control Synthesis of Multiple Frequency Domain Specifications via Generalized KYP Lemma2007

    • Author(s)
      T.Iwasaki, S.Hara
    • Journal Title

      International Journal of Robust and Nonlinear Control 17・5-6

      Pages: 415-434

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Robust PID Using Generalized KYP Synthesis: Direct open-loop shaping in multiple frequency ranges2006

    • Author(s)
      S. Hara, T. Iwasaki, D. Shiokata
    • Journal Title

      Control System Magazine 26・1

      Pages: 80-91

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Robust PID Using Generalized KYP Synthesis : Direct open-loop shaping in multiple frequency ranges2006

    • Author(s)
      S. Hara, T. Iwasaki, D. Shiokata
    • Journal Title

      IEEE Control System Magazine 26[1]

      Pages: 80-91

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Robust PID Using Generalized KYP Synthesis : Direct open-loop shaping in multiple frequency ranges2006

    • Author(s)
      Shinji Hara, Tetsuya Iwasaki, Daisuke Shiokata
    • Journal Title

      Control System Magazine 26・1

      Pages: 80-91

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Time domain interpretation of frequency domain inequalities on (semi) finite ranges2005

    • Author(s)
      T. Iwasaki, S. Hara, A. L. Fradkov
    • Journal Title

      Systems & Control Letters 54

      Pages: 681-691

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Presentation] 双対一般化KYP補題と最適化アルゴリズム2008

    • Author(s)
      山口健, 土谷隆, 原辰次
    • Organizer
      第8回計測自動制御学会制御部門大会
    • Place of Presentation
      京都大学
    • Year and Date
      2008-03-07
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Dual GKYP Lemma and Optimization Algorithms2008

    • Author(s)
      K. Yamaguchi, T. Tsuchiya, S. Hara
    • Organizer
      SICE 8th CCS
    • Place of Presentation
      Kyoto University
    • Year and Date
      2008-03-07
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A Unification of Analytical Expressions for Control Performance Limitations via Reciprocal Transform2007

    • Author(s)
      S. Hara
    • Organizer
      IFAC Workshop SSSC07
    • Place of Presentation
      Foz do Iguassu, Brazil
    • Year and Date
      2007-10-19
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] A Unification of Analytieal Expressions for Control Performance Limitations via Reciprocal Transfbrm2007

    • Author(s)
      S.Hara
    • Organizer
      IFAC Workshop SSSC07
    • Place of Presentation
      Foz do Iguassu,Brazil
    • Related Report
      2007 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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