中国物理B ›› 2007, Vol. 16 ›› Issue (7): 1918-1922.doi: 10.1088/1009-1963/16/7/019

• GENERAL • 上一篇    下一篇

The open-plus-closed loop (OPCL) method for chaotic systems with multiple strange attractors

宋运忠   

  1. Complex Networks Laboratory, College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China
  • 收稿日期:2006-10-15 修回日期:2007-01-31 出版日期:2007-07-04 发布日期:2007-07-04
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60374013), the Doctorate Foundation of Henan Polytechnic University, China (Grant No 648606).

The open-plus-closed loop (OPCL) method for chaotic systems with multiple strange attractors

Song Yun-Zhong (宋运忠)†   

  1. Complex Networks Laboratory, College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China
  • Received:2006-10-15 Revised:2007-01-31 Online:2007-07-04 Published:2007-07-04
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60374013), the Doctorate Foundation of Henan Polytechnic University, China (Grant No 648606).

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摘要： Based on the open-plus-closed-loop (OPCL) control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, 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 proposed means.

Abstract: Based on the open-plus-closed-loop (OPCL) control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, 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 proposed means.

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

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

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