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基于线性状态反馈的混沌系统全局控制
Global control of chaotic systems based on linear state feedback
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摘要: 针对一类混沌系统,通过分析其非线性向量场的结构特征,提出了一种全局快速控制混沌的新方法.利用线性状态反馈,分离出一个稳定的独立状态变量方程,使受控的混沌系统逐渐退化为稳定的线性系统,进而完全消除非线性抖振现象.此方法可应用到Lorenz系统族或具有类似结构的新混沌系统的控制中,相应设计出一种结构简单的控制器,保证闭环系统在原点全局渐近稳定.数值算例验证了所提出方法的快捷性和正确有效性.Abstract: By analyzing structural characteristics of nonlinear vector field for a class of chaotic systems,a new approach to controlling chaos globally and rapidly is put forward.Based on linear state feedback,an independent stable equation of some state variables is separated.Controlled chaotic systems degenerate gradually into stable linear systems.Nonlinear quivering phenomenon is eliminated completely further.The approach can be used to control Lorenz system families or new chaotic systems with similar structures.A class of simple controllers is designed to guarantee that closed-loop systems are globally asymptotically stable at the origin.Numerical examples illustrate the shortcut and the validity of the presented approach in this paper.
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