Chaos control and synchronization via a novel chatter free sliding mode control strategy

In this paper, we propose a novel chatter free sliding mode control (SMC) strategy for chaos control and synchronization to the nonlinear uncertain chaotic systems. A new sort of dynamical sliding mode surface with both integral and differential operators is introduced to divert the discontinuous sign function switch term into the first derivative of the control input; hence a chatter free control input is obtained for the chaotic systems with uncertainties. Based on the Lyapunov stability theory and SMC technique, stability analysis is performed and a theorem serving as designing the chatter free sliding mode control input is also proposed. In the simulation part, first, the results regarding chaos control and synchronization are given to show that the proposed strategy can control the states of the uncertain chaotic systems to desired states with fast speed. In order to show the advantage of eliminating chatter in control input of our method, we give the simulation results performed by traditional SMC and the method proposed recently. Simulation results indicate that this novel chatter free sliding mode control strategy is very effective to chaos control and synchronization.