Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances

This paper investigates two classes of synchronization problems of multiple chaotic systems with unknown uncertainties and disturbances by employing sliding mode control. Modified projective synchronization and transmission synchronization are discussed here. For the modified projective synchronization problem, sliding mode controllers are designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances. For the transmission synchronization problem, based on adaptive sliding mode control, an integral sliding surface is selected and the adaptive laws are derived to tackle unknown uncertainties and disturbances for such systems. A class of nonlinear adaptive sliding mode controllers is developed to guarantee asymptotical stability of the error systems so that all chaotic systems can synchronize with each other. Simulation results are given to illustrate the effectiveness of the proposed schemes by comparing with the existing methods.