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中国物理学会期刊

精确配置离散动力系统的所有Lyapunov指数

CSTR: 32037.14.aps.59.7630

Precise planement of all Lyapunov exponents for discrete-time dynamical systems

CSTR: 32037.14.aps.59.7630
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  • 针对给定的确定性离散时间动力学系统, 提出一种可以精确配置受控系统所有Lyapunov指数的混沌控制与反控制新方法. 本文不限制给定系统的具体形式,仅利用取模运算和预设的一组Lyapunov指数,设计出一种新的状态反馈控制器. 在控制器的作用下,受控系统的Lyapunov指数与预设的Lyapunov指数一致. 控制器的形式简单,可以用于解决混沌控制和混沌反控制两种问题. 给出了数学证明和两个实例, 仿真结果显示了算法的有效性.

     

    In this paper, a new algorithm for all Lyapunov Exponents precisely configuraling a discrete-time dynamical system is proposed. A given deterministic discrete-time dynamical system can be chaotified by the algorithm. A new feed-back controller is designed via moduling operation. All Lyapunov Exponents of the controlled system are equal to a given set of ones. The new controller is simple and can be used to control or anti-control a chaotic system . The corresponding proof as well as two illustrative examples are presented. The simulation results show the effectiveness of the algorithm.

     

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