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Computer Aided Design of Robust Control Systems Computational Geometry Approach

Research Project

Project/Area Number 11650448
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Control engineering
Research InstitutionKOBE UNIVERSITY

Principal Investigator

OHTA Yuzo  Kobe University Faculty of Engineering Professor, 工学部, 教授 (80111772)

Co-Investigator(Kenkyū-buntansha) MASUBUCHI Izumi  Kobe University Faculty of Engineering Research Associate, 工学部, 助手 (90283150)
藤崎 泰正  神戸大学, 工学部, 助教授 (30238555)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2000: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
KeywordsComputational geometry / Operations on sets / Robust control / Nonlinear Control / Switched systems / Polygon interval arithmetic / Piecewise linear Lvapunov functions / Linear matrix inequalities
Research Abstract

The main results obtained through the research are summarized as follows.
1. Development of CAD system for robust controllers design of linear systems.
We developed a CAD system for robust controllers design of linear systems using value sets. For systems which has completely decomposable transfer functions and/or characteristic equations, the method using polygon interval arithmetic is very useful to compute value sets. We proposed and implemented a method computing value sets of multi-polynomial functions, which need not be completely decomposable.
2. Generation of piecewise linear Lyapunov functions.
We proposed a new class of piecewise linear Lyapunov functions (PWLLFs) and derived stability results. A candidate of PWLLF has parameters corresponding to hyperplanes intersecting stability region. The set of stability conditions are formulated as Linear Programming Problem (LP) in terms of parameters inserted by the hyperplanes. If the computed optimal value is negative, we construct a PWLLF using the solution. When the optimal value of the LP is nonnegative, we modify the PWLLF candidate by adding appropriate hyperplanes to introduce more freedom in the LP formulation and arrive at the desired result. The optimal value of the resulting new LP is always less than or equal to that of the old LP.We also proposed a scheme to generate hyperplanes such that the optimal value of the new LPs is less than that of the old LP.Moreover, a fast method to compute the optimal solutoion of the new LP.
3. Data structure for Euclidean cell complex.
We proposed and implemented data structure for Euclidean cell complex. We used this data structure in programs for generation of PWLLFs and will be used for controller design using PWLLFs.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (28 results)

All Other

All Publications (28 results)

  • [Publications] I.Masubuchi: "Numerical Solution to a Class of Parameter-Dependent Convex Differential Inequalities"計測自動制御学会論文集. 36・3. 248-254 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohta: "Non-convex Polygon Interval Arithmetic as a Tool for the Analysis and Design of Robust Control Systems"J.of Reliable Computing. 6・3. 247-279 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohta: "Stability Analysis of Nonlinear Systems via Piecewise Linear Lyapunov Functions"Proceedings of ISCAS 2000, Pt.II. 208-211 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 太田有三: "PIA:パラメトリックアプローチのためのツールボックス"システム/制御/情報. 44・6. 325-330 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Wada: "Parametric Absolute Stability of Multivariable Lur's Systems"Automatica. 30. 1365-1372 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 太田有三: "区分的線形リヤプノフ関数の構成とその高速算法"システム制御情報学会論文誌. 45・8(掲載予定). (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohta: "Stability Analysis of Discontinuous Nonlinear Systems via Piecewise Linear Lyapunov Functions"Proc.of 2001 American Contorol Conference. WP09-4(掲載予定). (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] I.Masubuchi: "Numerical Solutions to a Class of Parameter-Dependent Convex Differential Inequalities"Trans.of Society of Instrument and Control Engineers. Vol.36, No.3. 248-254 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohta: "Non-convex Polygon Interval Arithmetic as a Tool for the Analysis and Design of Robust Control Systems"J.of Reliable Computing. Vol.6, No.3. 247-279 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohta: "Stability Analysis of Nonlinear Systems via Piecewise Linear Lyapunov Functions"Proceedings of ISCAS 2000, Pt.II. 208-211 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohta: "PIA : A Toolbox for Parametric Approach"Systems, Control and Information. Vol.44, No.6. 325-330 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Wada: "Parametric Absolute Stability of Multivariable Lur'e Systems"Automatica. Vol.30. 1365-1372 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohta: "Construction of Piecewise Linear Lyapunov Functions and Its Fast Method"Trans.of Institute of Systems, Control and Information Engineers. Vol.45, No.6 (to appear). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Ohta: "Stability Analysis of Discontinuous Nonlinear Systems via Piecewise Linear Lyapunov Functions"Proceedings of 2001 American Control Conference, WP09-4. (to appear). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] I.Masubuchi: "Numerical Solution to a Class of Parameter-Dependent Convex Differential Inequalities"計測自動制御学会論文集. 36・3. 248-254 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ohta: "Non-convex Polygon Interval Arithmetic as a Tool for the Analysis and Design of Robust Control Systems"J.of Reliable Computing. 6・3. 247-279 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ohta: "Stability Analysis of Nonlinear Systems via Piecewise Linear Lyapunov Functions"Proceedings of ISCAS 2000,Pt.II. 208-211 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 太田有三: "PIA:パラメトリックアプローチのためのツールボックス"システム/制御/情報. 44・6. 325-330 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Wada: "Parametric Absolute Stability of Multivariable Lur's Systems"Automatica. 30. 1365-1372 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 太田有三: "区分的線形リヤプノフ関数の構成とその高速算法"システム制御情報学会論文誌. 45・8(掲載予定). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ohta: "Stability Analysis of Discontinuous Nonlinear Systems via Piecewise Linear Lyapunov Functions"Proc.of 2001 American Contorol Conference. WP09-4(掲載予定). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Ohta: "Stability Analysis by Using Piecewise Linear Lyapunov Functions"Proceedings of 14th IFAC World Congress. Vol.D. 515-520 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 太田有三: "LMIを用いた非線形積分型ロバストサーボ系の設計"システム制御情報学会論文誌. 12・11. 671-679 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] I.Masubuchi: "On Numerical Solution to Parameter-Dependent Convex Differential Inequalities"Rroceedings of 38th IEEE Conference on Decision and Control. 305-309 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 増淵泉: "フィードフォワード項をもつロバスト安定サーボ系の設計について"システム制御情報学会論文誌. 12・12. 757-759 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Ohta: "Non-Convex Polygon Interval Arithmetic as a Tool for the Analysis and Design of Robust Control System"J.of Reliable Computing. 6・3(掲載予定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Ohta: "Stability Analysis of Nonlinear Systems via Piecewise Linear Lyapunov Functions"Proceedings of ISCAS 2000. (掲載予定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 太田有三: "PIA:パラメトリックアプローチのためのツールボックス"システム制御情報学会誌. 44・6(掲載予定). (2000)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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