一类混沌系统的同步脉冲控制

Control of Pulse Synchronization for a Class of Chaotic Systems

基于脉冲微分方程的稳定理论,针对一类混沌系统,提出了一种脉冲控制同步的方法·该方法仅采用驱动系统与响应系统状态变量的线性误差反馈作为脉冲控制信号,实现了两个混沌系统的全局渐近同步·给出了两个混沌系统实现全局渐近同步的判据·当采用相同的脉冲控制矩阵和相等的脉冲间隔时,两个混沌系统实现全局渐近同步的判据可以被简化·该方法适用于一大类混沌系统的同步控制·以Lorenz混沌系统为例,进行了控制器的设计·所设计的控制器结构简单,易于实现,收敛速度快·理论分析和数值仿真结果证明了该方法的有效性·

Based on the stability theory of impulsive differential equation, a pulse synchronization control method for a class of chaotic systems is proposed. The global asymptotical synchronization of two chaotic systems is realized simply by using the linear error feedback from the state variables of drive and response systems as pulse control signal. Two criterions are thus given to guarantee the global asymptotical synchronization of the two chaotic systems, which could be simplified in case their pulse control matrices and pulse intervals are the same. The method is applicable to a large class of chaotic systems. A controller is therefore designed with Lorenz chaotic system as an example, which is simple and easy to implement with high convergence rate. The theoretic analysis and numerical simulation verified the effectiveness of the method.