中国物理B ›› 2005, Vol. 14 ›› Issue (7): 1342-1346.doi: 10.1088/1009-1963/14/7/013

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Generating chaos in the sense of Devaney via decentralized feedback control from a stable Takagi-Sugeno fuzzy system

卢俊国   

  1. Department of Automation, Shanghai Jiaotong University, Shanghai　200030, China
  • 收稿日期:2004-11-25 修回日期:2005-01-24 出版日期:2005-06-20 发布日期:2005-06-20
  • 基金资助:
    Project supported by the National Postdoctoral Science Foundation of China and the National Natural Science Foundation of China (Grant No 60404005).

Generating chaos in the sense of Devaney via decentralized feedback control from a stable Takagi-Sugeno fuzzy system

Lu Jun-Guo (卢俊国)   

  1. Department of Automation, Shanghai Jiaotong University, Shanghai 200030, China
  • Received:2004-11-25 Revised:2005-01-24 Online:2005-06-20 Published:2005-06-20
  • Supported by:
    Project supported by the National Postdoctoral Science Foundation of China and the National Natural Science Foundation of China (Grant No 60404005).

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摘要： The problem of making a stable Takagi--Sugeno (TS) fuzzy system chaotic in the sense of Devaney by using decentralized state feedback control is studied. The proposed decentralized feedback controller is a decentralized linear feedback controller composed of the overflow nonlinear function of the 2's complement arithmetic. The overflow nonlinearity of the 2's complement arithmetic results in a rather complex dynamics. We apply the Shi--Chen theorem to mathematically prove that the controlled system is indeed chaotic in the sense of Devaney. In particular, an explicit formula for the computation of chaotification parameters is also obtained. A numerical example is used to visualize and illustrate the theoretical results.

关键词: chaotification, Devaney chaos, TS fuzzy system, two complement arithmetic

Abstract: The problem of making a stable Takagi--Sugeno (TS) fuzzy system chaotic in the sense of Devaney by using decentralized state feedback control is studied. The proposed decentralized feedback controller is a decentralized linear feedback controller composed of the overflow nonlinear function of the 2's complement arithmetic. The overflow nonlinearity of the 2's complement arithmetic results in a rather complex dynamics. We apply the Shi--Chen theorem to mathematically prove that the controlled system is indeed chaotic in the sense of Devaney. In particular, an explicit formula for the computation of chaotification parameters is also obtained. A numerical example is used to visualize and illustrate the theoretical results.

Key words: chaotification, Devaney chaos, TS fuzzy system, two complement arithmetic

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a