Synchronization of Uncertain Chaotic Systems with Unknown Response Systems

Considering the situation with the same dimension but different structure in driven system and response system, a new kind of robust adaptive synchronization controller is designed based on the Lyapunov stability theorem . Both the unknown parameters and uncertain functions are considered and an adaptive turning law is constructed to handle the unknown parameters and a robust control law is adopted to deal with the uncertain functions in the system. At last, a four dimension chaotic system is taken as an example to testify the rightness of the proposed method. And numerical simulation result shows that the proposed method can realize the synchronization between driven chaotic system and response system with unknown parameters and uncertain nonlinear functions.