中国物理B ›› 2010, Vol. 19 ›› Issue (10): 100506-100506.doi: 10.1088/1674-1056/19/10/100506

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The stability control of fractional order unified chaotic system with sliding mode control theory

齐冬莲, 杨捷, 张建良   

  1. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
  • 收稿日期:2010-02-06 修回日期:2010-03-10 出版日期:2010-10-15 发布日期:2010-10-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 60702023), and the Key Scientific and Technological Project of Zhejiang Province of China (Grant No. 2007C11094).

The stability control of fractional order unified chaotic system with sliding mode control theory

Qi Dong-Lian(齐冬莲)†, Yang Jie(杨捷), and Zhang Jian-Liang(张建良)   

  1. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
  • Received:2010-02-06 Revised:2010-03-10 Online:2010-10-15 Published:2010-10-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 60702023), and the Key Scientific and Technological Project of Zhejiang Province of China (Grant No. 2007C11094).

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摘要： This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts: the continuous part and switching part. With Gronwall's inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method.

Abstract: This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts: the continuous part and switching part. With Gronwall's inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method.

Key words: fractional order unified chaotic system, sliding mode control, stability analysis

中图分类号:  (Control theory)

  • 02.30.Yy
05.45.Gg (Control of chaos, applications of chaos)