中国物理B ›› 2006, Vol. 15 ›› Issue (11): 2529-2534.doi: 10.1088/1009-1963/15/11/012

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LMI-based output feedback fuzzy control of chaotic system with uncertainties

谭文1, 王耀南1, 段峰1, 李晓辉2   

  1. (1)College of Electrical and Information Engineering, Hunan University, Changsha 410082, China; (2)School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
  • 收稿日期:2005-07-02 修回日期:2006-01-20 出版日期:2006-11-20 发布日期:2006-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60375001), the Hunan Province Natural\linebreak \makebox[1.6mm]{}Science Foundation, China (Grant No 03JJY3107) and the Scientific Research Funds of Hunan Provincial Education Department,\linebreak \makebox[1.6mm]{}China (Grant No 05B016).

LMI-based output feedback fuzzy control of chaotic system with uncertainties

Tan Wen(谭文)a), Wang Yao-Nan(王耀南)a), Duan Feng(段峰)a), and Li Xiao-Hui(李晓辉)b)   

  1. a College of Electrical and Information Engineering, Hunan University, Changsha 410082, China; b School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
  • Received:2005-07-02 Revised:2006-01-20 Online:2006-11-20 Published:2006-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60375001), the Hunan Province Natural\linebreak \makebox[1.6mm]{}Science Foundation, China (Grant No 03JJY3107) and the Scientific Research Funds of Hunan Provincial Education Department,\linebreak \makebox[1.6mm]{}China (Grant No 05B016).

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摘要： This paper studies the robust fuzzy control for nonlinear chaotic system in the presence of parametric uncertainties. An uncertain Takagi--Sugeno (T--S) fuzzy model is employed for fuzzy modelling of an unknown chaotic system. A sufficient condition formulated in terms of linear matrix inequality (LMI) for the existence of fuzzy controller is obtained. Then the output feedback fuzzy-model-based regulator derived from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system. The T--S fuzzy model ofthe chaotic Chen system is developed as an example for illustration. The effectiveness of the proposed controller design methodology is finally demonstrated through computer simulations on the uncertain Chen chaotic system.

关键词: chaos, output-feedback controller, T--S fuzzy model, linear matrix inequality

Abstract: This paper studies the robust fuzzy control for nonlinear chaotic system in the presence of parametric uncertainties. An uncertain Takagi--Sugeno (T--S) fuzzy model is employed for fuzzy modelling of an unknown chaotic system. A sufficient condition formulated in terms of linear matrix inequality (LMI) for the existence of fuzzy controller is obtained. Then the output feedback fuzzy-model-based regulator derived from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system. The T--S fuzzy model ofthe chaotic Chen system is developed as an example for illustration. The effectiveness of the proposed controller design methodology is finally demonstrated through computer simulations on the uncertain Chen chaotic system.

Key words: chaos, output-feedback controller, T--S fuzzy model, linear matrix inequality

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
05.45.Pq (Numerical simulations of chaotic systems)