Universal function projective lag synchronization of chaotic systems with uncertainty by using active sliding mode and fuzzy sliding mode control

In this paper, a novel synchronization scheme, universal function projective lag synchronization (UFPLS), is proposed. The synchronization scheme is a generalization of universal function projective synchronization and modified function projective lag synchronization. An active sliding mode controller is introduced for UFPLS of chaotic systems. By using the integral sliding surface, the determination of sliding parameters become easier than using the classical one. Furthermore, based on the consideration of reality, the systems with uncertainty and the system contaminated by noise are investigated. Theoretical proof is achieved with the Lyapunov stability theory. A fuzzy active sliding control method is presented by using a fuzzy system to adjust the coefficient of switch term so that the chattering can be weakened. Simulation results verify the effectiveness of the introduced schemes and illustrate that the application of fuzzy system eliminates the chattering effectively.