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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (1): 19-27 .doi: https://doi.org/10.1007/s10483-009-0103-z

• Articles • 上一篇    下一篇

混沌Mathieu_Duffing振子的开闭环控制

沈建和1,2;陈树辉1   

  1. 1.中山大学 应用力学与工程系, 广州 510275;
    2.福建师范大学 数学与计算机科学学院,福州 350007
  • 收稿日期:2008-07-19 修回日期:2008-11-05 出版日期:2009-01-01 发布日期:2009-01-01
  • 通讯作者: 陈树辉

An open-plus-closed-loop control for chaotic Mathieu-Duffing oscillator

Jian-he SHEN1,2;Shu-hui CHEN 1   

  1. 1. Department of Applied Mechanics and Engineering, Sun Yat-sen University,Guangzhou 510275, P. R. China; 2. School of Mathematics and Computer Science, Fujian Normal University,Fuzhou 350007, P. R. China
  • Received:2008-07-19 Revised:2008-11-05 Online:2009-01-01 Published:2009-01-01
  • Contact: Shu-hui CHEN

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摘要： 基于开闭环控制的思想,设计了一类由外激力与线性误差反馈组成的开闭环控制器,研究了Mathieu_Duffing振子混沌轨道至任意目标周期轨道的控制问题;同时,利用Liapunov稳定性理论与二阶常微分方程初值问题的一个比较定理,证明了上述开闭环控制夹带盆(basin of entrainment)的全局性.最后,利用数值模拟,验证了理论结果的正确性.

Abstract: By using the idea of open-plus-closed-loop(OPCL) control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to verify the theoretical results.

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