Lü混沌系统自适应同步控制

Self-Adaptive Synchronization Control for Lü Chaotic System

基于Lyapunov稳定性理论,采用自适应控制方法,通过设计自适应控制器和参数调节律,实现2个不同参数的Lü混沌系统同步。无论是控制律还是参数调节律,都是使标量正定函数成为关于状态和参数误差动态方程的Lyapunov函数的基础上得到的。由于Lyapunov函数沿着误差动态方程的微分相对于状态误差和参数为半负定,利用Barbalat引理可保证混沌同步。数字仿真结果验证该方法有效。

Based on Lyapunov stability theory, Lü chaotic system of two different parameters synchronization is realized by using a self-adaptive control method and through designing a self-adaptive controller and the parametric adaptation laws. Both controller and parametric adaptation laws are derived from the Lyapunov function, which make scalar positive definite function become state and parametric error dynamic equations. Because derivative of the Lyapunov function along error dynamic equation for state error and parameter is negative semi-definite, using Barbalat lemma can guaranty chaotic synchronization. Numerical simulations results illustrate the effectiveness of the proposed scheme.