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Study on the construction of control theory by the notion of invariance and the development of its introductory course

Research Project

Project/Area Number 13650479
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Control engineering
Research InstitutionHokkaido University

Principal Investigator

SHIMA Masasuke  Hokkaido Univ., Graduate School of Eng., Prof., 大学院・工学研究科, 教授 (10029457)

Co-Investigator(Kenkyū-buntansha) YOKOMICHI Masahiro  Miyazaki Univ., Faculty of Eng., Asso.Prof., 工学部, 助教授 (30274773)
KAWAMURA Takeshi  Kitami Inst.of Tech., Dep.of Electrical and Electronic Eng., Asso.Prof., 電気電子工学科, 助教授 (80234128)
ISURUGI Yoshihisa  Hokkaido Univ., Graduate School of Eng., Asso.Prof., 大学院・工学研究科, 助教授 (00109480)
YAMASHITA Yuu  Nara Inst.of Science and Tech., Graduate School of Inf.Sciences, Asso.Prof., 情報科学研究科, 助教授 (90210426)
ENOMOTO Ryuji  Toba National College of Maritime Tech., Control and Information Tech Dept., Asso.Prof., 制御情報工学科, 助教授 (90203645)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsinvariance / robust stability / monotonicity / Lie algebra / constrained system / singular optimal control / canonical equation / variational expression / 変分表現公式 / 可観測性と可制御性 / 制御理論入門教程 / 最適制御 / 不変性 / 区間システムの安定性 / 劣駆動機械系の追従特性 / 最適特異軌道 / Singular Optimal Controller / 区画システムの安定性 / 単調性の条件 / Frazer-Duncanの定理 / ドリフトレスシステム / フィードバック安定化 / 最適特異制御 / 一般化ルジャンドル・クレプシュの条件 / 局所強可到達分布 / 入門教程 / 電子テキスト / 大域的理論 / ロバスト安定性
Research Abstract

Firstly, the role of invariance in the control theory is studied [1]Invariance with respect to the variation of parameters : Using Frazer-Duncan theorem and monotonicity conditions, we derived a necessary and sufficient condition for the stability of linear systems without regard to the variation of interval parameters, and presented a monotonization method for the system which is not monotone. [2]Feedback design considering structures of Lie algebra : Feedback stabilization and improvement of tracking properties ties are studied for the under actuated mechanical systems such as axi-symmetric underactuated aircraft and PVTOL aircraft [3]Invriant formulation of design theory using invariance condition : Modem trends of studies of analytical dynamics with constraints are surveyed with focus to Poisson geometry, Lie algebroid and applications to control theory [4]Invariance optimality and Lie algebra : The existence region of optimal singular trajectories is classified by the dimensions of accessibility algebra, state space and input space A condition of optimality of Bang-bang control, conditions for the existence of optimal singular controllers and an approximation method of time optimal control are presented. Secondly, considering the shove results, we looked for the possibility of unified theory [5]Structure of control theory and development of an introductory course : Using the canonical equations and variations of inputs and initial conditions, we derived a variational expression of performance criterion or output and found that the expression is very convenient to survey the whole structure of control theory and has the possibility of constructing an introductory course to control theory. This is the main objective of this study attained in the last stage, though the whole contents are not prepared yet.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (28 results)

All Other

All Publications (28 results)

  • [Publications] T.Kawamura: "Stability analysis of the characteristic polynomials whose coefficients are polynomials of interval parameters using monotonicity"計測自動制御学会論文集. 38・6. 557-566 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Yokomichi: "Feedback stabilization of driftless systems by norm-bounded inputs"Proceedings of the 4^<th> Asian Control Conference. 1085-1088 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hitaka: "Regular trajectory generation for axi-symmetric underactuated spacecraft"Proceedings of the 5^<th> International Conference on Motion and Vibration Control. 289-294 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Kawamura: "Stability analysis for the linear system with structured uncertainties using pseudo-remainder sequences"Dynamics of Continuous, Discrete and Impulsive Systems : Series B : Application and Algorithms. 137-149 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 川村 武: "区間多項式の安定判別-多重線形と単調性"システム/制御/情報. 47・12. 571-76 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 榎本 隆二: "バコノミック力学系およびホロノミック力学系とその周辺"計測と制御. 42・10. 833-840 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hitaka: "Trajectory tuning for the tracking problem of the underactuated mechanical systems ; applications to PVTOL aircraft"Int.J.Artificial Life and Robotics. No.7. 69-77 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Kawamura, M.Shima: "Stability analysis of the characteristic polynomials whose coefficients are polynomials of interval parameters using monotonicity"Trans.of SICE. 38-6. 557-566 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Yokomichi: "Feedback stabilization of driftless Systems by norm-bounded inputs"Proceedings of the 4^<th> Asian Control Conference. 1085-1088 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hitaka, Y.Yokomichi: "Regular trajectory gene-Ration for axisymmetric underactuated spacecraft"Proceedings of the 6^<th> International Conference on Motion and Vibration Control. 289-294 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Kawamura, M.Shima: "Stability analysis for the linear system with structured uncertainties using pseudo-remainder sequences"Dynamics of Continuous, Discrete and Impulsive Systems ; Series B : Application and Algorithms. 10-1. 137-149 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Kawamura, M.Shima: "Stability criterion of interval polynomials-multilinearity and monotonicity (in Japanese)"Systems, Control and Information. 47-12. 571-576 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] R.Enomoto, M.Shima: "Vakonomic dynamical systems and nonholonomic dynamical systems (in Japanese)"Journal of SICE. 42-10. 833-840 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Hitaka, Y.Yokomichi, M.Kono: "Trajectory Tuning for the tracking problem of the underactuated Mechanical systems ; applications to the PVTOL aircraft"IntJ.Artificial Life and Robotics. 7. 69-77 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 島 公脩: "アファイン非線形系の最短時間制御の近似解法"第32回制御理論シンポジウム資料. 105-108 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 小平光夫: "ある最短時間制御問題に現われるBang-bang制御と特異制御"第19回計測自動制御学会北海道支部シンポジウム「ディジタル信号処理と数値解析」論文集. 35-36 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Kawamura: "Stability analysis for the linear system with structured uncertainties using pseudo-remainder sequences"Dynamics of Continuous, Discrete and Impulsive Systems ; Series B : Application and algorithm. 10・1. 137-149 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Kawamura: "Analysis of controllability and observability of linear system with structured uncertainties using monotonization methods"Proceedings of the 3^<rd> International DCDIS Conference. 76-81 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 川村 武: "区間多項式の安定性判別-多重線形と単調性"システム/制御/情報. 47・12. 571-576 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 榎本隆二: "バコノミック力学系および非ホロノミック力学系とその周辺"計測と制御. 42・10. 833-840 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Hitaka: "Trajectory tuning for the tracking problem of the underactuated mechanical systems applications to the PVTOL aircraft"Int.J.Artificial Life and Robotics. 7. 69-77 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 島 公脩: "最適特異制御、不変性、および可到達分布の関係について"第46回システム制御情報学会研究発表講演会講演論文集. 103-104 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 島 公脩: "最適特異軌道の存在について"第31回制御理論シンポジウム資料. 69-74 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 堂上悠介: "Singular Optimal Controllersが生成する軌道について"第35回計測自動制御学会北海道支部学術講演会論文集. 55-58 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Kawamura: "Stability analysis of the characteristic polynomials whose coefficients are polynomials of interval parameters using monotonicity"計測自動制御学会論文集. 38巻・6号. 557-566 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Kawamura: "Stability analysis for the linear system with structured uncertainties using pseudo-remainder sequences"Dynamics of Continuous, Discrete and impulsive Systems, Series B : Application and algorithms. Vol.10,No.1. 137-149 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Yokomichi: "Feedback stabilization of driftless systems by norm-bounded inputs"Proceedings of 4^<th> Asian Control Conference. 1085-1088 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Hitaka: "Regular trajectory generation for axisymmetric underactuated spacecraft"Proceedings of the sixth International Conference on Motion and Vibration Control. 289-294 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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