On Tracking Control and Synchronization Design for Chaotic Systems

The idea of controlling and synchronizing chaotic systems refers to a process where in two or many chaotic systems starting from different initial conditions adjust a given property of their motion to a common behaviors. In this paper, the stable tracking control of continuous chaotic systems are studied and a new control method is proposed. Based on Lyapunov stability theory, an adaptive controller is derived to achieve synchronization of Chen system and Rossler system. The controlled system can track reference signals in arbitrary form, including the output of other chaotic systems, and all variables are bounded, so the synchronization between different chaotic systems can be realized. Numerical simulations are used to show the effectiveness of the proposed technique.