混沌Mathieu-Duffing振子的开闭环控制

沈建和; 陈树辉

混沌Mathieu-Duffing振子的开闭环控制

沈建和^1,2,
陈树辉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

基金项目: 国家自然科学基金资助项目(10672193)

详细信息

作者简介:
沈建和(1980- ),男,福建漳州人,博士(联系人.E-mail:jianheshen@sina.com

中图分类号: O322
计量
- 文章访问数: 2896
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- 被引次数: 0
出版历程
- 收稿日期: 2008-07-19
- 修回日期: 2008-11-17
- 刊出日期: 2009-01-15

Open-Plus-Closed-Loop Control for Chaotic Mathieu-Duffing Oscillator

SHEN Jian-he^1,2,
CHEN Shu-hui¹

1.
Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China;

摘要

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．
- Mathieu-Duffing振子 /
- 混沌控制 /
- 开闭环控制 /
- 全局夹带盆
Abstract: Utilizing the idea of the open-plus-closed-loop (OPCL) control, a controller which is composed of an external excitation and linear feedback was designed to entrain the chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of the open-plus-closed-loop control was proved by combining Liapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations were performed to demonstrate the theoretical results.
- Mathieu-Duffing oscillator /
- chaos control /
- OPCL control /
- global entrainment

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参考文献(18)

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