Sliding mode control and synchronization of chaotic systems with parametric uncertainties

In this paper, we propose a result on controlling and synchronizing chaos. Our approach consists in using the sliding mode control theory. We first compare the OGY control method to the sliding mode control method. We next present a new sliding mode controller, we show that for the class of chaotic systems that can be stabilized using a smooth feedback controller, a sliding manifold can be easily constructed using a Lyapunov function. Moreover, we prove that if the states are confined to the sliding surface, then the originally chaotic trajectory will slide towards the equilibrium. We also prove that the proposed controller is robust to mismatched parametric uncertainties. To diminish the unwanted chattering phenomenon resulting from high sliding gains, an adaptive sliding controller is finally designed to present a robust model independent controller that achieves stabilization of the equilibrium points as well as synchronization of two systems. All these results will be confirmed through numerical simulations on a modified Chua’s system.