中国物理B ›› 2010, Vol. 19 ›› Issue (2): 20508-020508.doi: 10.1088/1674-1056/19/2/020508

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The feedback control of fractional order unified chaotic system

杨捷, 齐冬莲   

  1. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
  • 收稿日期:2009-04-03 修回日期:2009-06-11 出版日期:2010-02-15 发布日期:2010-02-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No.~60702023) and Natural Science Foundation of Zhejiang Province (Grant No.~Y107440).

The feedback control of fractional order unified chaotic system

Yang Jie(杨捷) and Qi Dong-Lian(齐冬莲)†   

  1. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
  • Received:2009-04-03 Revised:2009-06-11 Online:2010-02-15 Published:2010-02-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No.~60702023) and Natural Science Foundation of Zhejiang Province (Grant No.~Y107440).

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摘要： This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the ``equivalent passivity'' method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.

Abstract: This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the ``equivalent passivity'' method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.

Key words: state feedback control, fractional order, unified chaotic system, Lyapunov function

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

  • 05.45.Gg
02.30.Yy (Control theory) 02.30.Uu (Integral transforms)