中国物理B ›› 2006, Vol. 15 ›› Issue (1): 89-94.doi: 10.1088/1009-1963/15/1/014

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Robust fuzzy control for chaotic dynamics in Lorenz systems with uncertainties

王耀南1, 段峰1, 谭文2   

  1. (1)College of Electrical and Information Engineering, Hunan University, Changsha 410082, China; (2)College of Electrical and Information Engineering, Hunan University, Changsha 410082, China;School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
  • 收稿日期:2005-04-29 修回日期:2005-09-06 出版日期:2006-01-20 发布日期:2006-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China(Grant No 60375001), the HunanProvincial Natural Science Foundation, China(Grant No 03JJY3107) and the Scientific Research Funds of Hunan Provincial Education Department.

Robust fuzzy control for chaotic dynamics in Lorenz systems with uncertainties

Wang Yao-Nan (王耀南)a, Tan Wen (谭文)ab, Duan Feng (段峰)a   

  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:2005-04-29 Revised:2005-09-06 Online:2006-01-20 Published:2006-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China(Grant No 60375001), the HunanProvincial Natural Science Foundation, China(Grant No 03JJY3107) and the Scientific Research Funds of Hunan Provincial Education Department.

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摘要： This paper deals with the robust fuzzy control for chaotic systems in the presence of parametric uncertainties. An uncertain Takagi--Sugeno fuzzy model for a Lorenz chaotic system is first constructed. Then a robust fuzzy state feedback control scheme ensures the control for stable operations under bounded parametric uncertainties. For a chaotic system with known uncertainty bounds, a robust fuzzy regulator is designed by choosing the control parameters satisfying the linear matrix inequality. To verify the validity and effectiveness of the proposed controller design method, an analysis technique is suggested and applied to the control of an uncertain Lorenz chaotic system.

关键词: chaos, Takagi--Sugeno fuzzy model, robust control, linear matrixinequality

Abstract: This paper deals with the robust fuzzy control for chaotic systems in the presence of parametric uncertainties. An uncertain Takagi--Sugeno fuzzy model for a Lorenz chaotic system is first constructed. Then a robust fuzzy state feedback control scheme ensures the control for stable operations under bounded parametric uncertainties. For a chaotic system with known uncertainty bounds, a robust fuzzy regulator is designed by choosing the control parameters satisfying the linear matrix inequality. To verify the validity and effectiveness of the proposed controller design method, an analysis technique is suggested and applied to the control of an uncertain Lorenz chaotic system.

Key words: chaos, Takagi--Sugeno fuzzy model, robust control, linear matrixinequality

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

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