精确配置离散动力系统的所有Lyapunov指数

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

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.