一维线性波动方程边界反馈的时空混沌反控制

华南理工大学学报（自然科学版） ›› 2005, Vol. 33 ›› Issue (7): 96-100.

一维线性波动方程边界反馈的时空混沌反控制

刘国刚赵怡

中山大学数学与计算科学学院，广东广州 510275

收稿日期:2004-02-26 出版日期:2005-07-25 发布日期:2005-07-25
通信作者: 刘国刚(1977-)，男，博士，主要从事动力系统与控制系统研究 E-mail:hnlgg@ 163.corn
作者简介:刘国刚(1977-)，男，博士，主要从事动力系统与控制系统研究
基金资助:
国家自然科学基金资助项目(10371136)

Boundary Feedback Anti-Control of Spatiotemporal Chaos for 1D Linear Wave Equation

Liu Guo-gang Zhao Yi

School of Mathematics&Computational Science,Sun Yat-sen Univ.,Guangzhou 510275,Guangdong,China

Received:2004-02-26 Online:2005-07-25 Published:2005-07-25
Contact: Liu Guo—gang(bom in 1977)，male，Ph．D．，mainly researches on dynamic system an d contro1 system． E-mail:hnlgg@ 163.corn
About author:Liu Guo—gang(bom in 1977)，male，Ph．D．，mainly researches on dynamic system an d contro1 system．
Supported by:
Supported by the National Natural Sc ience Foundation of China(10371136)

摘要/Abstract

摘要： 考虑具有线性或非线性边界条件的一维线性波动方程，在边界上用一个正弦函数驱动作为控制器去控制一个原本不混沌的线性系统，使它混沌，并通过特征线法把控制系统的解解析地表示出来．运用全变差和符号动力系统的理论证明了系统是混沌的，并进行了数值模拟，结果表明所提出的控制方法是有效的．

关键词: 混沌控制, 反馈反控制, 波动方程, 全变差

Abstract:

In this paper,a 1 D linear wave equation with linear or nonlinear boundary conditions is taken into account.A bo undary feedback controller is designed with a sine function,and is then used to drive an originally non-chaotic linear system chaotic.Moreover,the solution of the controlled system is an alytically expressed by the method of characteristic line.By the theory of total variation and symbol dynamic system,it is proved that the system is chaotic.Numerical simulations are finally carried out to verify the correctness of the proposed con-trolled method .

Key words: chaos control, feed back anti-control, wave equation, total variation

刘国刚赵怡. 一维线性波动方程边界反馈的时空混沌反控制[J]. 华南理工大学学报（自然科学版）, 2005, 33(7): 96-100.

Liu Guo-gang Zhao Yi. Boundary Feedback Anti-Control of Spatiotemporal Chaos for 1D Linear Wave Equation[J]. Journal of South China University of Technology (Natural Science Edition), 2005, 33(7): 96-100.