中国物理B ›› 2008, Vol. 17 ›› Issue (2): 507-519.doi: 10.1088/1674-1056/17/2/028

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Controlling chaos based on an adaptive nonlinear compensator mechanism

李东海1, 田玲玲2, 孙先仿2   

  1. (1)Department of Thermal Engineering, Tsinghua University, Beijing 100084, China; (2)School of Automation Science and Electrical Engineering, Beijing University of Aeronautics & Astronautics, Beijing 100083, China
  • 收稿日期:2007-04-26 修回日期:2007-09-04 出版日期:2008-02-20 发布日期:2008-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 50376029).

Controlling chaos based on an adaptive nonlinear compensator mechanism

Tian Ling-Ling(田玲玲)a)†, Li Dong-Hai(李东海)b), and Sun Xian-Fang(孙先仿)a)   

  1. a School of Automation Science and Electrical Engineering, Beijing University of Aeronautics & Astronautics, Beijing 100083, China; b Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
  • Received:2007-04-26 Revised:2007-09-04 Online:2008-02-20 Published:2008-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 50376029).

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摘要： The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.

关键词: chaotic system, nonlinear compensator mechanism, Lorenz chaotic system

Abstract: The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.

Key words: chaotic system, nonlinear compensator mechanism, Lorenz chaotic system

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

  • 05.45.Gg
07.05.Dz (Control systems)