中国物理B ›› 2008, Vol. 17 ›› Issue (7): 2412-2419.doi: 10.1088/1674-1056/17/7/014

• GENERAL • 上一篇    下一篇

Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system

蔡国梁, 郑松, 田立新   

  1. Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang 212013, China
  • 收稿日期:2007-11-22 修回日期:2008-01-03 出版日期:2008-07-09 发布日期:2008-07-09
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 70571030 and 90610031) and the Advanced Talent Foundation of Jiangsu University of China (Grant No 07JDG054).

Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system

Cai Guo-Liang(蔡国梁)†, Zheng Song(郑松), and Tian Li-Xin(田立新)   

  1. Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang 212013, China
  • Received:2007-11-22 Revised:2008-01-03 Online:2008-07-09 Published:2008-07-09
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 70571030 and 90610031) and the Advanced Talent Foundation of Jiangsu University of China (Grant No 07JDG054).

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摘要： This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.

Abstract: This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.

Key words: hyperchaotic Lorenz system, control, synchronization, Lyapunov stability theory

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
02.30.Yy (Control theory) 05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems)