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Establishment of nonlinear control theory taking into account global structure of manifold

Research Project

Project/Area Number 19560435
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

YAMASHITA Yuh  Hokkaido University, 大学院・情報科学研究科, 教授 (90210426)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Hisakazu  奈良先端科学技術大学院大学, 情報科学研究科, 助教 (70362837)
NISHIDA Gou  独立行政法人理化学研究所, 基幹研究所, 基幹研究所研究員 (80435669)
NISHIMURA Yuki  山口大学, 大学院・理工研究科, 助教 (20549018)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords非線形制御理論 / 多様体 / 漸近安定化 / 制御リアプノフ関数 / 可縮 / 被覆 / 確率制御リアプノフ関数 / 弱リアプノフ関数 / 大域的漸近安定化 / ファイバー束 / モース関数 / 多重被覆
Research Abstract

This study presents a general framework for controlling nonlinear systems on general manifolds including non-Euclidean spaces which precedent control theories cannot handle. Global attitude control of satellites, obstacle avoidance of vehicles, and control of acrobots are examples of our problem. This framework provides design procedures generating control laws automatically with discontinuity, logic, or randomness, of which properties are necessary to stabilize such systems on non-Euclidean spaces.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (54 results)

All 2009 2008 2007

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (40 results)

  • [Journal Article] Global asymptotical stabilization of Morse-Smale systems using weak control-Lyapunov functions2009

    • Author(s)
      G. Nishida, T. Tsuzuki, H. Nakamura, Y. Yamashita
    • Journal Title

      SICE Journal of Control, Measurement, and System Integration Vol. 2

      Pages: 43-49

    • NAID

      10031152620

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Markov 過程の量子化を用いた確率的 Lyapunov 関数の近似構築2009

    • Author(s)
      西村悠樹, 山下裕
    • Journal Title

      システム制御情報学会論文誌 22巻

      Pages: 295-302

    • NAID

      10026193857

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Minimum Projection Method for Nonsmooth Control Lyapunov Function Design on General Manifolds2009

    • Author(s)
      H. Nakamura, Y. Yamashita, H. Nishitani
    • Journal Title

      Systems & Control Letters Vol. 58

      Pages: 716-723

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Minimum Projection Method for Nonsmooth Control Lyapunov Function Design on General Manifolds2009

    • Author(s)
      Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
    • Journal Title

      Systems & Control Letters 58

      Pages: 716-723

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global Asymptotical Stabilization of Morse-Smale Systems Using Weak Control-Lyapunov Functions2009

    • Author(s)
      G. Nishida, T. Tsuzuki, H. Nakamura, Y. Yamashita
    • Journal Title

      SICE Journal of Control, Measurement, and System Integration 2-1

      Pages: 43-49

    • NAID

      10031152620

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov過程の量子化を用いた確率的Lyapunov関数の近似設計2009

    • Author(s)
      西村悠樹・山下裕
    • Journal Title

      システム制御情報学会論文誌 22-8(掲載確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov 過程の量子化を用いた Lyapunov 関数の構築2008

    • Author(s)
      西村悠樹, 山下裕
    • Journal Title

      計測自動制御学会論文集 44巻

      Pages: 26-35

    • NAID

      10020126901

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 不連続制御系の解と大域漸近安定化問題2008

    • Author(s)
      都築卓有規, 山下裕
    • Journal Title

      システム/制御/情報 52巻

      Pages: 84-89

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] ブローアップを用いた同時ベクトル場の解析2008

    • Author(s)
      中村文一
    • Journal Title

      システム/制御/情報 52巻

      Pages: 90-95

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 無限時限ハミルトンおよびラグランジュ系におけるディラック構造2008

    • Author(s)
      西田豪・B. Mascheke
    • Journal Title

      システム/制御/情報 52巻

      Pages: 96-102

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Markov過程の量子化を用いたLyapunov関数の構築2008

    • Author(s)
      西村悠樹・山下裕
    • Journal Title

      計測自動制御学会論文集 44

      Pages: 26-35

    • NAID

      10020126901

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 不連続制御系の解と大域漸近安定化問題2008

    • Author(s)
      都築卓有規・山下裕
    • Journal Title

      システム/制御/情報 52

      Pages: 84-89

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ブローアップを用いた同時ベクトル場の解析2008

    • Author(s)
      中村文一
    • Journal Title

      システム/制御/情報 52

      Pages: 90-85

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 無限時限ハミルトンおよびラグランジュ系におけるディラック構造2008

    • Author(s)
      西田豪・B. Mascheke
    • Journal Title

      システム/制御/情報 52

      Pages: 96-102

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Stabilization problems of nonlinear systems using feedback laws with Wiener processes2009

    • Author(s)
      Y.Nishimura, K.Takehara, Y.Yamashita, K.Tanaka, Y.Wakasa
    • Organizer
      The 48th IEEE Conf.on Decision and Control
    • Place of Presentation
      上海(中国)
    • Year and Date
      2009-12-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] V Boundary Detection of Variational Symmetry Breaking using Port-Representati on of Conservation Laws2009

    • Author(s)
      G.Nishida, M.Sugiura, M.Yamakita, B.Maschke, R.Ikeura
    • Organizer
      The 48th IEEE Conf.on Decision and Control
    • Place of Presentation
      上海(中国)
    • Year and Date
      2009-12-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] Asymptotic stabilization of nonlinear systems on general manifolds via minimum protection method2009

    • Author(s)
      Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
    • Organizer
      European Control Conference 2009
    • Place of Presentation
      ブダペスト(ハンガリー)
    • Year and Date
      2009-08-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Variational structure of infinite-dimensional homogeneous systems with dilations2009

    • Author(s)
      G.Nisnida, H.Nakamura
    • Organizer
      European Control Conference 2009
    • Place of Presentation
      ブダペスト(ハンガリー)
    • Year and Date
      2009-08-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Scaling reduction of port-Hamiltonian systems for numerical calculation2009

    • Author(s)
      G.Nishida, D.Ichishima, K.Kashima, K.Fujimoto, M.Yamakita, R.Ikeura
    • Organizer
      ICROS-SICE International Joint Conference 2009
    • Place of Presentation
      福岡
    • Year and Date
      2009-08-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] Scaling reduction of port-Hamiltonian systems for numerical calculation2009

    • Author(s)
      G. Nishida, D. Ichishima, K. Kashima, K. Fujimoto, M. Yamakita, R. Ikeura
    • Organizer
      ICROS-SICE International Joint Conference 2009
    • Place of Presentation
      Fukuoka, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] Variational structure of infinite-dimensional homogeneous systems with dilations2009

    • Author(s)
      G. Nishida, H. Nakamura
    • Organizer
      European Control Conference 2009
    • Place of Presentation
      Budapest, Hungary
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic Stabilization of Nonlinear Systems on General Manifolds via Minimum Projection Method2009

    • Author(s)
      H. Nakamura, Y. Yamashita, H. Nishitani
    • Organizer
      European Control Conference 2009
    • Place of Presentation
      Budapest, Hungary
    • Related Report
      2009 Final Research Report
  • [Presentation] Boundary Detection of Variational Symmetry Breaking using Port-Representation of Conservation Laws2009

    • Author(s)
      G. Nishida, M. Sugiura, M. Yamakita, B. Maschke, R. Ikeura
    • Organizer
      The 48th IEEE Conf. on Decision and Control
    • Place of Presentation
      Shanghai, China
    • Related Report
      2009 Final Research Report
  • [Presentation] Stabilization problems of nonlinear systems using feedback laws with Wiener processes2009

    • Author(s)
      Y. Nishimura, K. Takehara, Y. Yamashita, K. Tanaka, Y. Wakasa
    • Organizer
      The 48th IEEE Conf. on Decision and Control
    • Place of Presentation
      Shanghai, China
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic Stabilization of Nonlinear Systems on General Manifolds via Minimum Projection Method2009

    • Author(s)
      H. Nakamura, Y. Yamashita, H. Nishitan
    • Organizer
      2009 European Control Conference
    • Place of Presentation
      Budapest, Hungary
    • Related Report
      2008 Annual Research Report
  • [Presentation] Global asymptotic stabilization for a nonlinear system on a manifold via a dynamic compensator2008

    • Author(s)
      T. Tsuzuki, Y. Yamashita
    • Organizer
      17th IFAC World Congress
    • Place of Presentation
      Seoul, Korea
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] Stabilization of Nonlinear Systems using Weak-Control-Lyapunov Functions2008

    • Author(s)
      G. Nishida, T. Tsuzuki, H. Nakamura, Y. Yamashita
    • Organizer
      17th IFAC World Congress
    • Place of Presentation
      Seoul, Korea
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] Stochastic Lyapunov Function Design using Quantization of Markov Process2008

    • Author(s)
      Y. Nishimura, Y. Yamashita
    • Organizer
      47th IEEE Conference on Decision and Control
    • Place of Presentation
      Cancun, Mexico
    • Related Report
      2009 Final Research Report
  • [Presentation] Port-representation of bi-Hamiltonian structure for infinite-dimensional symmetry2007

    • Author(s)
      G. Nisluda, M. Yamakita, Z. Luo
    • Organizer
      46th IEEE Conference on Decision and Control
    • Place of Presentation
      Hilton New Orleans Riverside, New Orleans, USA
    • Year and Date
      2007-12-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] Field port-Lagrangian systems with degenerate Lagrangian and external forces2007

    • Author(s)
      G. Nishida, M. Yamakita, Z. Luo
    • Organizer
      46th IEEE Conference on Decision and Control
    • Place of Presentation
      Hilton New Orleans Riverside, New Orleans, USA
    • Year and Date
      2007-12-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] Homogeneous stabilization for input-affine homogeneous systems2007

    • Author(s)
      N. Nakamura, H. Nakamura, Y. Yamashita, H. Nishitani
    • Organizer
      46th IEEE Conference on Decision and Control
    • Place of Presentation
      Hilton New Orleans Riverside, New Orleans, USA
    • Year and Date
      2007-12-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems of degree(l, l)2007

    • Author(s)
      N. Nakamura, H. Nakamura, Y. Yamashita, H. Nishitani
    • Organizer
      SICE Annual Conference 2007
    • Place of Presentation
      Kagawa University, Takamatsu, Japan
    • Year and Date
      2007-09-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] Semi-Global Output Regulation of Nonminimum-phase Nonlinear Systems via Error Feedback2007

    • Author(s)
      Y. Hirose, Y. Yamashita
    • Organizer
      SICE Annual Conference 2007
    • Place of Presentation
      Kagawa University, Takamatsu, Japan
    • Year and Date
      2007-09-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] Global asymptotic stabilization of nonlinear system with multiple singular pointsusing changeover of control Lyapunov-Morse function2007

    • Author(s)
      K. Takehara, T. Tsuzuki, Y. Yamashita
    • Organizer
      SICE Annual Conference 2007
    • Place of Presentation
      Kagawa University, Takamatsu, Japan
    • Year and Date
      2007-09-18
    • Related Report
      2007 Annual Research Report
  • [Presentation] 同次システムの解と楕円関数2007

    • Author(s)
      中村奈美, 中村文一
    • Organizer
      第36回制御理論シンポジウム
    • Place of Presentation
      ホテルライフォート札幌(札幌)
    • Year and Date
      2007-09-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] 被弱制御Lyapunov関数を用いた非線形系の安定化2007

    • Author(s)
      西田豪, 都築卓有規, 中村文一, 山下裕
    • Organizer
      第36回制御理論シンポジウム
    • Place of Presentation
      ホテルライフォート札幌(札幌)
    • Year and Date
      2007-09-05
    • Related Report
      2007 Annual Research Report
  • [Presentation] 被覆写像を用いた非線形システムの連続安定化2007

    • Author(s)
      中村文一, 中村奈美, 西田豪, 山下裕
    • Organizer
      第36回制御理論シンポジウム
    • Place of Presentation
      ホテルライフォート札幌(札幌)
    • Year and Date
      2007-09-05
    • Related Report
      2007 Annual Research Report
  • [Presentation] 制御Lyapunov関数と大域漸近可制御性について2007

    • Author(s)
      都築卓有規, 山下裕
    • Organizer
      第36回制御理論シンポジウム
    • Place of Presentation
      ホテルライフォート札幌(札幌)
    • Year and Date
      2007-09-05
    • Related Report
      2007 Annual Research Report
  • [Presentation] Stabilization of homogeneous systems using implicit control Lyapunov functions2007

    • Author(s)
      H. Nakamura, N. Nakamura, H. Nishitani
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems
    • Place of Presentation
      CSIR International Convention Centre, Pretoria, South Africa
    • Year and Date
      2007-08-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] Port-based energy balance on compact manifolds2007

    • Author(s)
      G. Nishida, R. Enomoto, M. Yamakita, Z. Luo
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems
    • Place of Presentation
      CSIR International Convention Centre, Pretoria, South Africa
    • Year and Date
      2007-08-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems2007

    • Author(s)
      N. Nakamura, H. Nakamura, Y. Yamashita, H. Nishitani
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems
    • Place of Presentation
      CSIR International Convention Centre, Pretoria, South Africa
    • Year and Date
      2007-08-22
    • Related Report
      2007 Annual Research Report
  • [Presentation] Time-varying port-representation of dissipative structures with gauge transformations2007

    • Author(s)
      G. Nishida, M. Yamakita, Z. Luo
    • Organizer
      European Control Conference 2007
    • Place of Presentation
      Kos International Convention Centre, Kos, Greece
    • Year and Date
      2007-07-05
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotic stability of gradient homogeneous systems2007

    • Author(s)
      H. Nakamura, C. Nishida, H. Nishitani
    • Organizer
      European Control Conference 2007
    • Place of Presentation
      Kos International Convention Centre, Kos, Greece
    • Year and Date
      2007-07-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotic stability of gradient homogeneous systems2007

    • Author(s)
      H. Nakamura, G. Nishida, H. Nishitani
    • Organizer
      European Control Conference 2007
    • Place of Presentation
      Kos, Greece
    • Related Report
      2009 Final Research Report
  • [Presentation] Time-varying port-representation of dissipative structures with gauge transformations2007

    • Author(s)
      G. Nishida, M. Yamakita, Z. Luo
    • Organizer
      European Control Conference 2007
    • Place of Presentation
      Kos, Greece
    • Related Report
      2009 Final Research Report
  • [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems2007

    • Author(s)
      N. Nakamura, H. Nakamura, Y. Yamashita, H. Nishitani
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems
    • Place of Presentation
      Pretoria, South Africa
    • Related Report
      2009 Final Research Report
  • [Presentation] Port-based energy balance on compact manifolds2007

    • Author(s)
      G. Nishida, R. Enomoto, M. Yamakita, Z. Luo
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems
    • Place of Presentation
      Pretoria, South Africa
    • Related Report
      2009 Final Research Report
  • [Presentation] Stabilization of homogeneous systems using implicit control Lyapunov functions2007

    • Author(s)
      H. Nakamura, N. Nakamura, H. Nishitani
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems
    • Place of Presentation
      Pretoria, South Africa
    • Related Report
      2009 Final Research Report
  • [Presentation] Global asymptotic stabilization of nonlinear system with multiple singular points using changeover of control Lyapunov-Morse function2007

    • Author(s)
      K. Takehara, T. Tsuzuki, Y. Yamashita
    • Organizer
      SICE Annual Conference 2007
    • Place of Presentation
      Takamatsu, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems of degree (l, l)2007

    • Author(s)
      N. Nakamura, H. Nakamura, Y. Yamashita, H. Nishitani
    • Organizer
      SICE Annual Conference 2007
    • Place of Presentation
      Takamatsu, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] Semi-Global Output Regulation of Nonminimum-phase Nonlinear Systems via Error Feedback2007

    • Author(s)
      Y. Hirose, Y. Yamashita
    • Organizer
      SICE Annual Conference 2007
    • Place of Presentation
      Takamatsu, Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] Homogeneous stabilization for input-affine homogeneous systems2007

    • Author(s)
      N. Nakamura, H. Nakamura, Y. Yamashita, H. Nishitani
    • Organizer
      46th IEEE Conference on Decision and Control
    • Place of Presentation
      New Orleans, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] Port-representation of bi-Hamiltonian structure for infinite-dimensional symmetry2007

    • Author(s)
      G. Nishida, M. Yamakita, Z. Luo
    • Organizer
      46th IEEE Conference on Decision and Control
    • Place of Presentation
      New Orleans, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] Field port-Lagrangian systems with degenerate Lagrangian and external forces2007

    • Author(s)
      G. Nishida, M. Yamakita, Z. Luo
    • Place of Presentation
      New Orleans, USA
    • Related Report
      2009 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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