An adaptive scheme for chaotic synchronization in the presence of uncertain parameter and disturbances

Recently, several schemes have been proposed in the literature to synchronize chaotic systems. However, in most of these approaches, the presence of uncertain parameters and external disturbances were not considered. Motivated by the above consideration, this paper proposes an adaptive methodology to synchronize any chaotic system with unified chaotic systems, even if bounded disturbances are present. The proposed controller is composed of both variable proportional and adaptive control actions for guaranteeing the convergence of the residual synchronization error to zero in the presence of disturbances. Two possible modifications are considered: 1) only adaptive control action is implemented to overcome the well-known assumption of prior knowledge of upper bounds to compensate for the disturbances, and 2) the control gain of the proportional part is saturated, when the residual synchronization error has, practically, been removed. Lyapunov theory, in combination with Barbalat׳s Lemma, is used to design the proposed controller. Experimental simulations are provided to show the effectiveness of the proposed controller and its advantages, when compared with a recent work in the literature.