SMC-based Projective Synchronization of Lorenz System and Chen System with Fully Unknown Parameters

In this paper, an adaptive sliding mode controller (SMC) with a parameter update law is developed to realize projective synchronization of the Lorenz system and the Chen system with fully unknown parameters. The projective synchronization includes complete synchronization and anti-phase synchronization. Moreover, it is proven that the proposed adaptive SMC can maintain the existence of sliding mode in uncertain chaotic systems based on Lyapunov stability theory. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed control method.