中国物理B ›› 2010, Vol. 19 ›› Issue (2): 20509-020509.doi: 10.1088/1674-1056/19/2/020509

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Controlling chaos to unstable periodic orbits and equilibrium state solutions for the coupled dynamos system

许海波1, 郝建红2, 吴淑花3   

  1. (1)Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; (2)School of Electric and Electronic Engineering, North China Electric Power University, Beijing 102206, China; (3)School of Electric and Electronic Engineering, North China Electric Power University, Beijing 102206, China;Department of Physics and Electrical Information Engineering, Shijiazhuang Normal College, Shijiazhuang 050035, China
  • 收稿日期:2009-06-03 修回日期:2009-07-28 出版日期:2010-02-15 发布日期:2010-02-15
  • 基金资助:
    Project supported by the Doctoral Foundation of North China Electric Power University (Grant No.~kH0433) and the International Science and Technology Cooperation Program (Grant No.~2007DFA71250).

Controlling chaos to unstable periodic orbits and equilibrium state solutions for the coupled dynamos system

Wu Shu-Hua(吴淑花)a)b)†, Hao Jian-Hong(郝建红) a), and Xu Hai-Bo(许海波)c)   

  1. a School of Electric and Electronic Engineering, North China Electric Power University, Beijing 102206, China; b Department of Physics and Electrical Information Engineering, Shijiazhuang Normal College, Shijiazhuang 050035, China; c Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2009-06-03 Revised:2009-07-28 Online:2010-02-15 Published:2010-02-15
  • Supported by:
    Project supported by the Doctoral Foundation of North China Electric Power University (Grant No.~kH0433) and the International Science and Technology Cooperation Program (Grant No.~2007DFA71250).

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摘要： In the case where the knowledge of goal states is not known, the controllers are constructed to stabilize unstable steady states for a coupled dynamos system. A delayed feedback control technique is used to suppress chaos to unstable focuses and unstable periodic orbits. To overcome the topological limitation that the saddle-type steady state cannot be stabilized, an adaptive control based on LaSalle's invariance principle is used to control chaos to unstable equilibrium (i.e. saddle point, focus, node, etc.). The control technique does not require any computer analysis of the system dynamics, and it operates without needing to know any explicit knowledge of the desired steady-state position.

Abstract: In the case where the knowledge of goal states is not known, the controllers are constructed to stabilize unstable steady states for a coupled dynamos system. A delayed feedback control technique is used to suppress chaos to unstable focuses and unstable periodic orbits. To overcome the topological limitation that the saddle-type steady state cannot be stabilized, an adaptive control based on LaSalle's invariance principle is used to control chaos to unstable equilibrium (i.e. saddle point, focus, node, etc.). The control technique does not require any computer analysis of the system dynamics, and it operates without needing to know any explicit knowledge of the desired steady-state position.

Key words: coupled dynamos system, delayed feedback control, adaptive control, controlling chaos

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

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