Nonlinear controller design based on control Lyapunov functions

• Project/Area Number: 19569004
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Control engineering
• Research Institution: Nara Institute of Science and Technology
• Principal Investigator: NAKAMURA Nami Nara Institute of Science and Technology, 情報科学研究科, 助教 (30452527)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,800,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥600,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 非線形制御理論 / 制御Lyapunov関数 / 入力制約 / 逆最適制御 / 同次システム / 座標変換 / 収束速度 / セクタ余裕 / 制御工学 / 非線形制御 / 非線形システム / 小入力特性 / 制御則設計

Research Abstract

We have proposed an asymptotically stabilizing controller and an adaptive controller for input affine nonlinear systems with convex input constraints by using given control Lyapunov functions. We have designed a global inverse optimal controller with local homogeneity for locally homogeneous input affine nonlinear systems by using locally homogeneous control Lyapunov functions. The proposed controller guarantees the local convergence rates and sector margins. We have clarified that local convergence rates and sector margins are invariant under coordinate transformations. We have proposed a global inverse optimal controller that is LQ optimal in a small neighborhood of the origin.

Research Products

• [Journal Article] Homogeneous stabilization for input affine homogeneous systems (2009)
  • Author(s): Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
  • Journal Title: IEEE Transactions on Automatic Control Vol.54,No.9 Pages: 2271-2275
  • Peer Reviewed
• [Journal Article] Homogeneous stabilization for input affine homogeneous systems (2009)
  • Author(s): Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
  • Journal Title: IEEE Transactions on Automatic Control Vol.54, No.9 Pages: 2271-2275
  • Peer Reviewed
• [Journal Article] 入力制約を有する不連続な非線形システムに対する制御Lyapunov関数を用いた制御則の設計と制御検証実験 (2007)
  • Author(s): 中村文一, 加藤健一, 中村奈美, 西谷紘一
  • Journal Title: 計測自動制御学会論文集 Vol.43,No.6 Pages: 506-513
  • NAID: 130003971651
  • Peer Reviewed
• [Journal Article] Global inverse optimal control with guaranteed convergence rates of input affine nonlinear systems
  • Author(s): Nami Nakamura, Hisakazu Nakamura, Hirokazu Nishitani
  • Journal Title: IEEE Transactions on Automatic Control (採録決定)
  • Peer Reviewed
• [Presentation] 座標変換による制御性能の不変性 (2009)
  • Author(s): 中村奈美, 中村文一
  • Organizer: 第38回制御理論シンポジウム
  • Place of Presentation: 大阪
  • Year and Date: 2009-09-14
• [Presentation] 多層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, 福井善朗, 中村奈美
  • Organizer: 第38回制御理論シンポジウム
  • Place of Presentation: 大阪
  • Year and Date: 2009-09-14
• [Presentation] 座標変換による制御性能の不変性 (2009)
  • Author(s): 中村奈美, 中村文一
  • Organizer: 第38回制御理論シンポジウム
  • Place of Presentation: ホテルコスモスクエア国際交流センター(大阪府)
  • Year and Date: 2009-09-14
• [Presentation] 多層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, 福井善朗, 中村奈美
  • Organizer: 第38回制御理論シンポジウム
  • Place of Presentation: ホテルコスモスクエア国際交流センター(大阪府)
  • Year and Date: 2009-09-14
• [Presentation] Universal control formula for feedback linearizable systems with local LQ performance (2009)
  • Author(s): Hisakazu Nakamura, Yasuyuki Satoh, Nami Nakamura, Hitoshi Katayama, Hirokazu Nishitani
  • Organizer: European Control Conference 2009
  • Place of Presentation: Budapest, Hungary
  • Year and Date: 2009-08-24
• [Presentation] Robust adaptive control of nonlinear systems with convex input constraints: case study on the magnetic levitation systems (2009)
  • Author(s): Yasuyuki Satoh, Hisakazu Nakamura, Nami Nakamura, Hitoshi Katayama, Hirokazu Nishitani
  • Organizer: ICCAS-SICE 2009
  • Place of Presentation: Fukuoka, Japan
  • Year and Date: 2009-08-21
• [Presentation] Robust adaptive control of nonlinear systems with convex input constraints : case study on the magnetic levitation systems (2009)
  • Author(s): Yasuyuki Satoh, Hisakazu Nakamura, Nami Nakamura, Hitoshi Katayama, Hirokazu Nishitani
  • Organizer: ICCAS-SICE 2009
  • Place of Presentation: Fukuoka International Congress Center (Fukuoka, Japan)
  • Year and Date: 2009-08-21
• [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回制御部門大会
  • Place of Presentation: 東広島
  • Year and Date: 2009-03-04
• [Presentation] Control formula for nonlinear systems subject to convex input constraints using control Lyapunov functions (2008)
  • Author(s): Yasuyuki Satoh, Hisakazu Nakamura, Nami Nakamura, Hitoshi Katayama, Hirokazu Nishitani
  • Organizer: 47th IEEE Conference on Decision and Control
  • Place of Presentation: Cancun, Mexico
  • Year and Date: 2008-12-10
• [Presentation] Global inverse optimal controller with guaranteed convergence rate for input-affine nonlinear systems (2008)
  • Author(s): Nami Nakamura, Hisakazu Nakamura
  • Organizer: 47th IEEE Conference on Decision and Control
  • Place of Presentation: Cancun, Mexico
  • Year and Date: 2008-12-10
• [Presentation] Control formula for nonlinear systems subject to convexinput constraints using control Lyapunov functions. (2008)
  • Author(s): Yasuyuki Satoh
  • Organizer: 47th IEEE Conference on Decision and Control
  • Place of Presentation: Cancun, Mexico
  • Year and Date: 2008-12-10
• [Presentation] Global inverse optimal controller with guaranteed convergence rate for input-affine nonlinear systerms (2008)
  • Author(s): Nami Nakamura
  • Organizer: 47th IEEE Conference on Decision and Control
  • Place of Presentation: Cancun, Mexico
  • Year and Date: 2008-12-10
• [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
  • Year and Date: 2008-09-19
• [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L Q性を有する大域的逆最適制御 (2008)
  • Author(s): 中村 文一
  • Organizer: 第37回制御理論シンポジウム
  • Place of Presentation: 鹿児島県霧島市
  • Year and Date: 2008-09-19
• [Presentation] Explicit formulas for ISS stabilization of nonlinear systems subject to bounded inputs and disturbances (2008)
  • Author(s): Hisakazu Nakamura, Nami Nakamura, Hirokazu Nishitani
  • Organizer: 17th IFAC World Congress
  • Place of Presentation: Seoul, Korea
  • Year and Date: 2008-07-11
• [Presentation] Explicit formulas for ISS stabilization of nonlinear systems subiect to bounded inputs and disturbances (2008)
  • Author(s): Hisakazu Nakamura
  • Organizer: 17th IFAC World Congress
  • Place of Presentation: Seoul, Korea
  • Year and Date: 2008-07-11
• [Presentation] Transformation from real homogeneous systems of degree l to complex homogeneous systems of degree (l, 0) (2008)
  • Author(s): Nami Nakamura, Hisakazu Nakamura
  • Organizer: 17th IFAC World Congress
  • Place of Presentation: Seoul, Korea
  • Year and Date: 2008-07-07
• [Presentation] Homogeneous stabilization for input-affine homogeneous systems (2007)
  • Author(s): Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita
  • Organizer: 46th IEEE Conference on Decision and Control
  • Place of Presentation: New Orleans, USA
  • Year and Date: 2007-12-12
• [Presentation] Homogeneous stabilization for input-affine homogeneous systems (2007)
  • Author(s): Nami Nakamura
  • Organizer: 46th IEEE Conference on Decision and Control
  • Place of Presentation: New Orleans, Louisian a USA
  • Year and Date: 2007-12-12
• [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems of degree (l, l) (2007)
  • Author(s): Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
  • Organizer: SICE Annual Conference 2007
  • Place of Presentation: Kagawa, Japan
  • Year and Date: 2007-09-19
• [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
• [Presentation] Stabilization of homogeneous systems using implicit control Lyapunov functions (2007)
  • Author(s): Hisakazu Nakamura, Nami Nakamura, Hirokazu Nishitani
  • Organizer: 7th IFAC Symposium on Nonlinear Control Systems
  • Place of Presentation: Pretoria, South Africa
  • Year and Date: 2007-08-24
• [Presentation] Homogeneous eigenvalue analysis for complex homogeneous systems (2007)
  • Author(s): Nami Nakamura, Hisakazu Nakamura
  • Organizer: 7th IFAC Symposium on Nonlinear Control Systems
  • Place of Presentation: Pretoria, South Africa
  • Year and Date: 2007-08-22
• [Presentation] Inverse optimal control for nonlinear systems with input constraints (2007)
  • Author(s): Nami Nakamura, Hisakazu Nakamura, Yuh Yamashita, Hirokazu Nishitani
  • Organizer: European Control Conference 2007
  • Place of Presentation: Kos, Greece
  • Year and Date: 2007-07-05
• [Remarks]
  • URL: http://sclab.naist.jp/Staff/namiff/home-ja.html