Sundarapandian Vaidyanathan
Vel Tech Dr. RR & Dr. SR Technical University, Tamil Nadu, INDIA

This paper derives new results for the adaptive control and synchronization design of the Cai system (2007), when the system parameters are unknown. Cai system is one of the paradigms of 3-D chaotic systems discovered by Cai and Tan (2007). In this paper, we first construct an adaptive controller to stabilize the Cai system to its unstable equilibrium at the origin. Then we build an adaptive synchronizer to achieve global chaos synchronization of the identical Cai systems with unknown parameters. The results derived for adaptive stabilization and adaptive synchronization for the Cai systems have been established using adaptive control theory and Lyapunov stability theory. Numerical simulations have been shown to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper for the Cai system.

Adaptive Control, Chaos, Chaotic Systems, Synchronization, Cai System.