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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 the Lyapunov stability theory, an adaptive control method is used to synchronize Lü chaotic system with two different parameters by designing adaptive controller and parameter regulation law. Both the control law and the parametric tuning law are based on the Lyapunov function that makes the scalar positive definite function a dynamic equation of state and parameter errors. Since the derivative of Lyapunov function along the error dynamic equation is semi-negative definite relative to the state error and the parameters, the chaotic synchronization can be guaranteed by using the Barbalat lemma. The numerical simulation results show that the method is effective.