Synchronization of Rossler chaotic systems via hybrid adaptive backstepping/sliding mode control

Abstract

In this paper, a hybrid control approach combining adaptive backstepping and fuzzy sliding mode control is proposed for the synchronization of two Rossler chaotic systems. The proposed approach provides fast, high accuracy chaos synchronization in presence of unknown system parameters and external disturbances. The adaptive backstepping control law is developed to stabilize the synchronization error dynamics arising from the mismatch between the drive and response systems. Both unknown system parameters and unknown external disturbance are estimated by the adaptive backstepping control approach in a way that the overall system with the controller becomes stable. As a result, the requirement to have a priori knowledge about the unknown parameters, e.g., disturbance bounds, is nullified. The fuzzy sliding mode controller is designed to accompany the adaptive backstepping to confine the synchronization error and enhance the synchronization speed between the two chaotic systems. Performance of the proposed approach is investigated for a numerical example and compared against commonly used chaos synchronization techniques including optimal control, active control, and adaptive backstepping control method. Simulation results indicate the superior performance of the hybrid control method over state-of-the-art for the synchronization of Rossler chaotic systems.