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Control system design using non-smooth feedback

Research Project

Project/Area Number 15560378
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Control engineering
Research InstitutionHOKKAIDO UNIVERSITY (2004)
Nara Institute of Science and Technology (2003)

Principal Investigator

YAMASHITA Yuh  Hokkaido University, Graduate School of Information Science and Technology, Professor, 大学院・情報科学研究科, 教授 (90210426)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Hisakazu  Nara Institute of Science and Technology, Graduate School of Information Science, Assistant Professor, 情報科学研究科, 助手 (70362837)
Project Period (FY) 2003 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2003: ¥1,900,000 (Direct Cost: ¥1,900,000)
Keywordsnon-smooth feedback / converse Lyapunov theorem / finite-time convergence / nonholonomic system / homogeneous system / exact differentiator / non-smooth Lyapunov function / parking control / 不連続フィードバック / 非線形制御 / 連続時間有限整定制御 / 非ホロノミック系の制御 / 高次chained system / 同次システム
Research Abstract

1.We obtained a simple expression of the converse Lyapunov theorem for discontinuous systems. Also, the converse Lyapunov theorem for discontinuous homogeneous systems with dilations was developed, which shows that each discontinuous homogeneous strongly stable system with dilation has a homogeneous Lyapunov function. It was shown that the degree of homogeneity indicates the speed of the convergence, i.e. a homogeneous strongly stable system with a negative degree of homogeneity has a finite-time convergence property. The proof of the finite time convergence of high-order sliding mode control system follows the obtained theorem.
2.We obtained a new homogeneous discontinuous control law for chained system, a typical nonholonomic control system, by using a concept of finite-time convergence. The control law is locally bounded, and its controlled system is locally exponentially stable and globally asymptotically stable. We showed a method for setting the speed of convergence by multiplying the homogeneous norm to the control law to avoid a chattering phenomenon. This method was extended to the high-order chained system control so that the state converges to a final sliding hyper-surface in finite time. Moreover, we proposed another finite-time stabilizing control method for nonholonomic system, which is a control-Lyapunov-function approach with non-smooth Lyapunov function.
3.The control law mentioned above was applied to a car parking problem. We experimented on the parking problem with a small mobile robot, and showed the effectiveness of the proposed method.
4.We proposed a new angular-velocity estimation method for robot manipulators using an exact differentiator that has discontinuous dynamics. Experimental results on a real robot manipulator showed that the proposed method has a good noise-reduction performance. Moreover, we constructed an adaptive control system for a real robot manipulator with the proposed estimator.

Report

(3 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • Research Products

    (40 results)

All 2005 2004 2003 Other

All Journal Article (34 results) Publications (6 results)

  • [Journal Article] 入力制約付き非線形システムに対する制御則設計2005

    • Author(s)
      喜種 奈美
    • Journal Title

      計測自動制御学会論文集 41・3

      Pages: 250-258

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Controller design for a nonlinear system with an input constraints2005

    • Author(s)
      N.Kidane
    • Journal Title

      Trans.of SICE 41-3

      Pages: 250-258

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 入力制約付き非線形システムに対する制御則設計2005

    • Author(s)
      喜種 奈美
    • Journal Title

      計測自動制御学会論文集 41・3(掲載決定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Observer Design for Nonlinear Systems Described by Differential-Algebraic Equations2004

    • Author(s)
      Yuh Yamashita
    • Journal Title

      Process System Engineering 2003, Computer-Aided Chemical Engineering 15 (Elsevier)

      Pages: 1100-1105

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Inverse optimization for a nonlinear system with an input constraint2004

    • Author(s)
      Nami Kidane
    • Journal Title

      SICE Annual Conference 2004

      Pages: 1874-1897

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Lyapunov functions for homogeneous differential inclusions2004

    • Author(s)
      Hisakazu Nakamura
    • Journal Title

      6th IFAC Symposium on Nonlinear Control Systems

      Pages: 1000-1005

    • NAID

      80015912895

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Stabilization of a cascade-connected nonlinear system with an input constraint2004

    • Author(s)
      Hisakazu Nakamura
    • Journal Title

      6th IFAC Symposium on Nonlinear Control Systems

      Pages: 341-346

    • NAID

      130005441339

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 非線形オブザーバを用いた人工衛星の大域的漸近安定な姿勢制御系設計2004

    • Author(s)
      山下 裕
    • Journal Title

      計測自動制御学会論文集 40・11

      Pages: 1071-1077

    • NAID

      10014124767

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Controller design for a nonlinear system with inputs restricted to a direct product of Minkowski balls2004

    • Author(s)
      Nami Kidane
    • Journal Title

      43rd IEEE Conference on Decision and Control Proceedings

      Pages: 4069-4074

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Globally asymptotically stable attitude control system of satellite using nonlinear observer2004

    • Author(s)
      Y.Yamashita
    • Journal Title

      Trans.of SICE 40-11

      Pages: 1071-1077

    • NAID

      10014124767

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Observer design for nonlinear systems described by differential-algebraic equations2004

    • Author(s)
      Y.Yamashita
    • Journal Title

      Proceedings of PSE2003, Kunming Jan.5-10

      Pages: 1100-1105

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Control of two-wheeled mobile robot using a homogeneous finite-time control method2004

    • Author(s)
      T.Kaji
    • Journal Title

      SICE 4th Annual Conf.on Control Systems Kitakyushu May.26-28

      Pages: 555-560

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Lyapunov functions for homogeneous differential inclusions2004

    • Author(s)
      H.Nakamura
    • Journal Title

      6th IFAC Symposium on Nonlinear Control Systems, Stuttgart Sep.1-3

      Pages: 1001-1005

    • NAID

      80015912895

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Stabilization of a cascade-connected nonlinear system with an input constraint2004

    • Author(s)
      H.Nakamura
    • Journal Title

      6th IFAC Symposium on Nonlinear Control Systems, Stuttgart Sep.1-3

      Pages: 341-346

    • NAID

      130005441339

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Inverse optimization for a nonlinear system with an input Constraint2004

    • Author(s)
      N.Kidane
    • Journal Title

      SICE Annual Conf.2004, Sapporo Aug.4-6

      Pages: 1874-1879

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Stabilization of a cascade-connected nonlinear system with an input constraint2004

    • Author(s)
      H.Nakamura
    • Journal Title

      SICE Annual Conf.2004, Sapporo Aug.4-6

      Pages: 1210-1213

    • NAID

      130005441339

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Controller design for a nonlinear system with inputs restricted to a direct product of Minkowski balls2004

    • Author(s)
      N.Kidane
    • Journal Title

      43rd IEEE Conf.on Decision and Control, Bahamas Dec.14-17

      Pages: 4069-4074

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 非線形high-index DAE系に対する制御系設計2004

    • Author(s)
      喜種 奈美
    • Journal Title

      計測自動制御学会論文集 40・7

      Pages: 721-728

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Inverse optimization for a nonlinear system with an input constraint2004

    • Author(s)
      Nami Kidane
    • Journal Title

      SICE Annual Conference 2004, Sapporo

      Pages: 1874-1897

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Lyapunov functions for homogeneous differential inclusions2004

    • Author(s)
      Hisakazu Nakamura
    • Journal Title

      6th IFAC Symposium on Nonlinear Control Systems, Stuttgart

      Pages: 1000-1005

    • NAID

      80015912895

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stabilization of a cascade-connected nonlinear system with an input constraint2004

    • Author(s)
      Hisakazu Nakamura
    • Journal Title

      6th IFAC Symposium on Nonlinear Control Systems, Stuttgart

      Pages: 341-346

    • NAID

      130005441339

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 同次ディファレンシャル・インクルージョンに対するLyapunov関数2003

    • Author(s)
      中村 文一
    • Journal Title

      計測自動制御学会論文集 39・4

      Pages: 365-374

    • NAID

      80015912895

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] チェインドシステムに対する同次有限時間整定制御2003

    • Author(s)
      中村 文一
    • Journal Title

      計測自動制御学会論文集 39・8

      Pages: 717-725

    • NAID

      10011444298

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Finite-time Stabilization of The High-order Chained System2003

    • Author(s)
      Hisakazu Nakamura
    • Journal Title

      Proceedings of American Control Conference 2003

      Pages: 4137-4142

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Discontinuous Control of Nonholonomic Systems Using Non-differentiable Lyapunov Functions2003

    • Author(s)
      Hisakazu Nakamura
    • Journal Title

      Proceedings of SICE Annual Control Conference 2003

      Pages: 1967-1970

    • NAID

      130005440752

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Stabilizability Analysis and Controller Design for a Nonlinear System with an Input Constraint2003

    • Author(s)
      Nami Kidane
    • Journal Title

      Proceedings of SICE Annual Control Conference 2003

      Pages: 2320-2323

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 厳密微分器を用いたロボットアームの摩擦補償出力適応制御2003

    • Author(s)
      中村 文一
    • Journal Title

      第21回日本ロボット学会学術講演会

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Lyapunov functions for homogeneous differential inclusions2003

    • Author(s)
      H.Nakamura
    • Journal Title

      Trans.of SICE 39-4

      Pages: 365-374

    • NAID

      80015912895

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Homogeneous finite-time control of chained system2003

    • Author(s)
      H.Nakamura
    • Journal Title

      Trans.of SICE 39-8

      Pages: 717-725

    • NAID

      10011444298

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Finite-time stabilization of the high-order chained system2003

    • Author(s)
      H.Nakamura
    • Journal Title

      Proceedings of AOC03 June 4-6

      Pages: 4137-4142

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Discontinuous control of nonholonomic systems using non-differentiable Lyapunov functions2003

    • Author(s)
      H.Nakamura
    • Journal Title

      SICE Annual Conf.2003, Fukui Aug.4-6

      Pages: 1967-1970

    • NAID

      130005440752

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Stabilizability analysis and controller design for a nonlinear system with an input constraint2003

    • Author(s)
      N.Kidane
    • Journal Title

      SICE Annual Conf.2003, Fukui Aug.4-6

      Pages: 2320-2323

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Output adaptive control of a robot arm with joint friction compensation2003

    • Author(s)
      H.Nakamura
    • Journal Title

      21st Annual Conf.of RSJ, Tokyo Sep.20-22

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Globally convergent observer design for satellite2003

    • Author(s)
      Y.Yamashita
    • Journal Title

      32nd SICE Symp.on Control Theory, Hamamatsu Nov.5-7

      Pages: 375-378

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] 中村 文一: "同次ディファレンシャル・インクルージョンに対するLyapunov関数"計測自動制御学会論文集. 39・4. 365-364 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 中村 文一: "チェインドシステムに対する同次有限時間整定制御"計測自動制御学会論文集. 39・8. 717-725 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hisakazu Nakamura: "Finite-time Stabilization of The High-order Chained System"Proceedings of American Control Conference 2003. 4137-4142 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hisakazu Nakamura: "Discontinuous Control of Nonholonomic Systems Using Non-differentiable Lyapunov Functions"Proceedings of SICE Annual Conference 2003. 1967-1970 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Nami Kidane: "Stabilizability Analysis and Controller Design for a Nonlinear System with an Input Constraint"Proceedings of SICE Annual Conference 2003. 2320-2323 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 中村 文一: "厳密微分器を用いたロボットアームの摩擦補償出力適応制御"第21回日本ロボット学会学術講演会. (CD-ROM). (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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