Adaptive Synchronization of Chaotic Systems with known Response System Parameters

A kind of adaptive synchronous control method was proposed to solve a special synchronization problem between two chaotic systems, where the response system is totally known without uncertainty but the driven system contains both unknown parameters and uncertain nonlinear functions. An update law of estimation of unknown parameters of driven system by constructing a proper Lyapunov energy function and the stability of the whole system was guaranteed by Lyapunov stability theorem. What is worthy pointing out is that the chaotic systems are not required to satisfy the Lipscitz condition. At last, detailed numerical situation was done to show the rightness and effectiveness of the proposed method.