中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30508-030508.doi: 10.1088/1674-1056/22/3/030508

• GENERAL • 上一篇    下一篇

Adaptive control of bifurcation and chaos in a time-delayed system

李宁a, 袁惠群b, 孙海义c, 张庆灵a   

  1. a Institute of Systems Science, Northeastern University, Shenyang 110819, China;
    b Institute of Applied Mechanics, Northeastern University, Shenyang 110819, China;
    c College of Science, Shenyang JianZhu University, Shenyang 110168, China
  • 收稿日期:2012-07-11 修回日期:2012-08-18 出版日期:2013-02-01 发布日期:2013-02-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 10772043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090042110003), and the Science Research Project of Education Department of Liaoning Province, China (Grant No. L2012208).

Adaptive control of bifurcation and chaos in a time-delayed system

Li Ning (李宁)a, Yuan Hui-Qun (袁惠群)b, Sun Hai-Yi (孙海义)c, Zhang Qing-Ling (张庆灵)a   

  1. a Institute of Systems Science, Northeastern University, Shenyang 110819, China;
    b Institute of Applied Mechanics, Northeastern University, Shenyang 110819, China;
    c College of Science, Shenyang JianZhu University, Shenyang 110168, China
  • Received:2012-07-11 Revised:2012-08-18 Online:2013-02-01 Published:2013-02-01
  • Contact: Yuan Hui-Qun E-mail:yuan_hq@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 10772043), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090042110003), and the Science Research Project of Education Department of Liaoning Province, China (Grant No. L2012208).

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摘要： In this paper, the stabilization of a continuous time-delayed system is considered. To control the bifurcation and chaos in a time-delayed system, a parameter perturbation control and a hybrid control are proposed. Then, to ensure the asymptotic stability of the system in the presence of unexpected system parameter changes, the adaptive control idea is introduced, i.e., the perturbation control parameter and the hybrid control parameter are automatically tuned according to the adaptation laws, respectively. The adaptation algorithms are constructed based on the Lyapunov-Krasovskii stability theorem. The adaptive parameter perturbation control and the adaptive hybrid control methods improve the corresponding constant control methods. They have the advantages of increased stability, adaptability to the changes of the system parameters, control cost saving, and simplicity. Numerical simulations for a well-known chaotic time-delayed system are performed to demonstrate the feasibility and superiority of the proposed control methods. Besides, comparison of the two adaptive control methods are made in an experimental study.

关键词: delay, parameter perturbation control, hybrid control, adaptive control

Abstract: In this paper, the stabilization of a continuous time-delayed system is considered. To control the bifurcation and chaos in a time-delayed system, a parameter perturbation control and a hybrid control are proposed. Then, to ensure the asymptotic stability of the system in the presence of unexpected system parameter changes, the adaptive control idea is introduced, i.e., the perturbation control parameter and the hybrid control parameter are automatically tuned according to the adaptation laws, respectively. The adaptation algorithms are constructed based on the Lyapunov–Krasovskii stability theorem. The adaptive parameter perturbation control and the adaptive hybrid control methods improve the corresponding constant control methods. They have the advantages of increased stability, adaptability to the changes of the system parameters, control cost saving, and simplicity. Numerical simulations for a well-known chaotic time-delayed system are performed to demonstrate the feasibility and superiority of the proposed control methods. Besides, comparison of the two adaptive control methods are made in an experimental study.

Key words: delay, parameter perturbation control, hybrid control, adaptive control

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

  • 05.45.Gg
05.45.-a (Nonlinear dynamics and chaos)