Intermittent Control and Synchronization of Fractional Order Chaotic System

DOI：

 作者 单位 王娴， 李东 重庆大学 数学与统计学院，重庆 401331

针对传统分数阶混沌系统连续控制同步方法存在的不足，提出了一种不连续的控制方法—间歇控制法；由于分数阶微分方程稳定性理论的发展不成熟，通过对控制器的改进构造了新的响应系统，将分数阶同步误差系统转化为整数阶同步误差系统，基于Lyapunov稳定性理论构造〖WTBX〗V〖WTBZ〗函数，得出分数阶混沌系统的间歇控制同步渐近稳定的充分条件，实现了分数阶混沌系统的间歇同步；特别地，当施加周期间歇控制时，可获得更为简单和实用的同步判据；并以分数阶Chen混沌系统为例进行数值模拟，实验结果表明间歇方法能够较好的对分数阶混沌系统进行控制同步。

In this paper， a discontinuous control method， intermittent control method， is proposed according to the insufficiency of traditional continuous control and synchronization of the fractional order chaotic system. Because of imperfect development of fractional order differential equation stability theory， by improving the controller， a new response system is constructed， the fractional order synchronous error system is converted into an integer order synchronous error system. Lyapunov stability theory is used to construct the V function， the sufficient condition is received for asymptotic stability of a fractional order chaotic system of intermittent control and synchronization， and the intermittent synchronization of the fractional order chaotic system is realized. In particular， a more simple and practical synchronization criterion can be obtained when periodic interval control is applied. Finally， numerical simulations are processed by taking fractional order Chen chaotic system as an example and the experimental results show that the intermittent control method can better realize the control and synchronization of fractional order chaotic system.