中国物理B ›› 2006, Vol. 15 ›› Issue (10): 2266-2270.doi: 10.1088/1009-1963/15/10/014

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Passive control of chaotic system with multiple strange attractors

宋运忠1, 赵光宙2, 齐冬莲2   

  1. (1)College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China;College of Electrical Engineering, Zhejiang University,Hangzhou 310027, China; (2)College of Electrical Engineering, Zhejiang University,Hangzhou 310027, China
  • 收稿日期:2005-04-13 修回日期:2006-06-07 出版日期:2006-10-20 发布日期:2006-10-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60374013), the Natural Science Foundation of Zhejiang Province (Grant Nos M603217 and Y104414).

Passive control of chaotic system with multiple strange attractors

Song Yun-Zhong(宋运忠)a)b)†, Zhao Guang-Zhou(赵光宙)b), and Qi Dong-Lian(齐冬莲)b)   

  1. a College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China; b College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
  • Received:2005-04-13 Revised:2006-06-07 Online:2006-10-20 Published:2006-10-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60374013), the Natural Science Foundation of Zhejiang Province (Grant Nos M603217 and Y104414).

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摘要： In this paper we present a new simple controller for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form. Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.

关键词: chaos, passive control, the Newton--Leipnik equation attractor

Abstract: In this paper we present a new simple controller for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form. Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.

Key words: chaos, passive control, the Newton--Leipnik equation attractor

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

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