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Stability Analysis of Homogeneous Systems via Homogeneous Eigenvalues

Research Project

Project/Area Number 19760288
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Control engineering
Research InstitutionNara Institute of Science and Technology

Principal Investigator

NAKAMURA Hisakazu  Nara Institute of Science and Technology, 情報科学研究科, 助教授 (70362837)

Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywords同次システム / 安定性 / 固有値 / 複素システム / 非線形制御理論 / 制御工学 / 制御理論 / システム理論 / 固有値解析 / 非線形システム / 非線形制御 / 安定性解析 / 複素非線形システム / 同次固有値 / トポロジー / 被覆空間
Research Abstract

本研究では、ベクトル場が同次かつ勾配である勾配同次システムが漸近安定となるための必要十分条件は同次固有値がすべて負であることを明らかにした。また、複素同次システムを定義することに成功し、(1,0)および(1,1)という2つの同次化手法を提案した。
さらに、得られた知見を用いて、同次制御Lyapunov関数を用いた同次制御系に対する同次安定化制御則と同次制御Lyapunov陰関数の設計法を開発し、異空間解釈に基づく制御法として最小射影法の開発に成功した。

Report

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

    (41 results)

All 2009 2008 2007 Other

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (37 results) Remarks (1 results)

  • [Journal Article] Homogeneous stabilization for input affine homogeneous systems2009

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

      IEEE Transactions on Automatic Control (掲載決定)

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

    • Author(s)
      中村文一
    • Journal Title

      ステム/制御/情報 Vol.52, No.3

      Pages: 90-95

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

    • Author(s)
      中村 文一
    • Journal Title

      システム/制御/情報 52

      Pages: 9095-9095

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] 入力アファインな非線形システムに対する収束速度保証付き大域的逆最適制御則2009

    • Author(s)
      中村・奈美
    • Organizer
      計測自動制御学会第9回制御部門大会
    • Place of Presentation
      広島
    • Year and Date
      2009-03-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] 被覆空間における最適性を利用した非可縮多様体上の最適制御2009

    • Author(s)
      中村文一
    • Organizer
      計測自動制御学会第9回制御部門大会
    • Place of Presentation
      広島
    • Year and Date
      2009-03-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] 最小射影法を用いた非可縮多様体上の制御Lyapunov関数設計2009

    • Author(s)
      中村文一
    • Organizer
      計測自動制御学会第9回制御部門大会
    • Place of Presentation
      広島
    • Year and Date
      2009-03-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] 最小射影法を使った二輪車両の障害物回避2009

    • Author(s)
      福井善朗
    • Organizer
      計測自動制御学会第9回制御部門大会
    • Place of Presentation
      広島
    • Year and Date
      2009-03-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] 特異値・特異ベクトルの修正型計算法を用いた特異値分解による非線形Receding Horizon制御2009

    • Author(s)
      的場俊亮
    • Organizer
      計測自動制御学会第9回制御部門大会
    • Place of Presentation
      広島
    • Year and Date
      2009-03-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] Asymptotic stabilization of nonlinear systems on general manifolds via minimum projection method2009

    • Author(s)
      Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
    • Organizer
      European Control Conference 2009 (ECC '09)
    • Place of Presentation
      Budapest
    • Related Report
      2008 Final Research Report
  • [Presentation] Universal control formula for feedack linearizab systems wh local LQ performance2009

    • Author(s)
      Hisakazu Nakamura, Yasuyuki Satoh, Nami Nakamura, Hitoshi Katayama, Hirokazu Nishitani
    • Organizer
      European Control Conference 2009 (ECC'09)
    • Place of Presentation
      Budapest
    • Related Report
      2008 Final Research Report
  • [Presentation] Comparison of mdLVs based methods for Nonlinear Receding Horizon Control2009

    • Author(s)
      Shunsuke Matoba, Hisakazu Nakamura, Hirokazu Nishitani
    • Organizer
      ICCAS-SICE 2009
    • Place of Presentation
      Fukuoka (掲載決定)
    • Related Report
      2008 Final Research Report
  • [Presentation] 入力アファインな非線形システムに対する収束速度保証付き大域的逆最適制御則2009

    • Author(s)
      中村奈美, 中村文一
    • Organizer
      第9回計測自動制御学会制御部門大会
    • Place of Presentation
      東広島
    • Related Report
      2008 Final Research Report
  • [Presentation] :被覆空間における最適性を利用した非可縮多様体上の最適制御2009

    • Author(s)
      中村文一, 山下裕
    • Organizer
      第9回計測自動制御学会制御部門大会
    • Place of Presentation
      東広島
    • Related Report
      2008 Final Research Report
  • [Presentation] 最小射影法を使った二輪車両の障害物回避2009

    • Author(s)
      福井善朗, 中村文一, 西谷絋一
    • Organizer
      第9回計測自動制御学会制御部門大会
    • Place of Presentation
      東広島
    • Related Report
      2008 Final Research Report
  • [Presentation] 最小射影法を用いた非可縮多様体上の制御Lyapunov関数設計2009

    • Author(s)
      中村文一, 山下裕
    • Organizer
      第9回計測自動制御学会制御部門大会
    • Place of Presentation
      東広島
    • Related Report
      2008 Final Research Report
  • [Presentation] 特異値・特異ベクトルの修正型計算法を用いた特異値分解による非線形Receding Horizon制御2009

    • Author(s)
      的場俊亮, 中村文一, 西谷絋一
    • Organizer
      第9回計測自動制御学会制御部門大会
    • Place of Presentation
      東広島
    • Related Report
      2008 Final Research Report
  • [Presentation] Universal control formula for feedback linearizable systems with local LQ performance2009

    • Author(s)
      Hisakazu Nakamura
    • Organizer
      European Control Conference 2009 (ECC '09)
    • Place of Presentation
      Budapest, Hungary(to appear)
    • Related Report
      2008 Annual Research Report
  • [Presentation] Asymptotic stabilization_of nonlinear systems on general manifolds via minimum projection method2009

    • Author(s)
      Hisakazu Nakamura
    • Organizer
      European Control Conference 2009 (ECC '09)
    • Place of Presentation
      Budapest, Hungary(to appear)
    • Related Report
      2008 Annual Research Report
  • [Presentation] Global inverse optimal controller with guaranteed convergence rate for input-affine nonlinear systems2008

    • Author(s)
      Hisakazu Nakamura
    • Organizer
      47th IEEE Conference on Decision and Control (CDC '08)
    • Place of Presentation
      Cancun, Mexico
    • Year and Date
      2008-12-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] Minimum projection method for nonsmooth control Lyapunov function design on general manifolds2008

    • Author(s)
      Hisakazu Nakamura
    • Organizer
      DYS CO Study Day
    • Place of Presentation
      Brussels, Belgium
    • Year and Date
      2008-11-14
    • Related Report
      2008 Annual Research Report
  • [Presentation] フィードバック線形化可能な非綿形シスデムに対する局所LQ性を有する大域的逆最適制御2008

    • Author(s)
      佐藤康之
    • Organizer
      第37回制御理論シンポジウム
    • Place of Presentation
      霧島
    • Year and Date
      2008-09-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] mdLVsアルゴリズムによる特異分解を用いたRH制御2008

    • Author(s)
      的場俊亮
    • Organizer
      第37回制御理論シンボシウム
    • Place of Presentation
      霧島
    • Year and Date
      2008-09-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] Transformation from real homogeneous systems of degree 1 to complex homogeneous systems of degree (1,0)2008

    • Author(s)
      Nami Nakamura
    • Organizer
      IFAC World Congress
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2008-07-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] Global invee optimal corollerith guaranteed convergence rate for input-affine nonlinear systems2008

    • Author(s)
      Nami Nakamura, Hisakazu Nakamura
    • Organizer
      47th IEEE Conference on Decision and Control (CDC 2008)
    • Place of Presentation
      Cancun
    • Related Report
      2008 Final Research Report
  • [Presentation] mdLVsアルゴリズムによる特異値分解を用いたRH制御2008

    • Author(s)
      的場俊亮, 中村文一, 西谷紘一
    • Organizer
      第37回制御理論シンポジウム
    • Place of Presentation
      霧島
    • Related Report
      2008 Final Research Report
  • [Presentation] フィードバック線形化可能な非線形システムに対する局所LQ性を有する大域的逆最適制御2008

    • Author(s)
      中村文一, 佐藤康之, 中村奈美
    • Organizer
      第37回制御理論シンポジウム
    • Place of Presentation
      霧島
    • Related Report
      2008 Final Research Report
  • [Presentation] Transformation from real homogeneous systems of degree l to complex homogeneous systems of degree (1,0)}2008

    • Author(s)
      Nami Nakamura, Hisakazu Nakamura, Hirokazu Nishitani
    • Organizer
      17th IFAC World Congress
    • Place of Presentation
      Seoul
    • Related Report
      2008 Final Research Report
  • [Presentation] 被覆理論を用いた非線形システムの連続状態フィードバック安定化2008

    • Author(s)
      中村文一, 山下裕
    • Organizer
      第8回計測自動制御学会制御部門大会
    • Place of Presentation
      京都
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Homogeneous stabilization for input-affine homogeneous systems2007

    • Author(s)
      Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
    • Organizer
      46th IEEE Conference on Decision and Control (CDC '07)
    • Place of Presentation
      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 (1,1)2007

    • Author(s)
      Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
    • Organizer
      SICE Annual Conference 2007
    • Place of Presentation
      高松
    • Year and Date
      2007-09-19
    • 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
      札幌
    • Year and Date
      2007-09-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] Stabilization of homogeneous systems using implicit control Lyapunov functions2007

    • Author(s)
      Hisakazu Nakamura, Nami Nakamura, Hirokazu Nishitani
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007)
    • Place of Presentation
      Pretoria, South Africa
    • Year and Date
      2007-08-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems2007

    • Author(s)
      Nami Nakamura, Hisakazu Nakamura
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007)
    • Place of Presentation
      Pretoria, South Africa
    • Year and Date
      2007-08-22
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotic stability of gradient homogeneous systems2007

    • Author(s)
      Hisakazu Nakamura, Gou Nishida, Hirokazu Nishitani
    • Organizer
      European Control Conference 2007 (ECC07)
    • Place of Presentation
      Kos, Greece
    • Year and Date
      2007-07-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] Homogeneous stabilization for input-affine homogeneous systems2007

    • Author(s)
      Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
    • Organizer
      46th IEEE Conference on Decision and Control (CDC '07)
    • Place of Presentation
      New Orleans
    • Related Report
      2008 Final 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
      札幌
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems2007

    • Author(s)
      Nami Nakamura, Hisakazu Nakamura
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007)
    • Place of Presentation
      Pretoria
    • Related Report
      2008 Final Research Report
  • [Presentation] Stabiliztion of homogeneous systems using implicit control Lyapunov functions2007

    • Author(s)
      Hisakazu Nakamura, Nami Nakamura, Hirokazu Nisitani
    • Organizer
      7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007)
    • Place of Presentation
      Pretoria
    • Related Report
      2008 Final Research Report
  • [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems of degree (1,1)2007

    • Author(s)
      Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
    • Organizer
      SICE Annual Conference 2007
    • Place of Presentation
      Takamatsu
    • Related Report
      2008 Final Research Report
  • [Presentation] Asymptotictability of gradient homogeneous systems2007

    • Author(s)
      Hisakazu Nakamura, Gou Nishida, Hiroazu Nishiti
    • Organizer
      European Control Conference 2007 (ECC '07)
    • Place of Presentation
      Kos
    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://sclab.naist.robotcontrol.html

    • Related Report
      2008 Final Research Report

URL: 

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

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