Function Approximation Technique Based Adaptive Control for Chaos Synchronization between Different Systems with Unknown Dynamics

This paper presents a function approximation technique based immersion and invariance adaptive controller for chaos synchronization between nonidentical systems with unknown dynamics. In the proposed control scheme, the control system is reconstructed as the combination of a controllable linear system and a variation term from the original system. The variation term is treated as time-varying uncertainty and approximated by a group of weighted chosen basis functions. The immersion and invariance methodology is employed to design the adaptive control law such that both the synchronization error and uncertainty estimation error converge to zero. Two typical chaos synchronization problems are used in numerical simulations to verify the effectiveness and superiority of the proposed controller.