Adaptive synchronization of a class of chaotic systems via variable structure control

The synchronization problem under two cases is considered. One is that the bound on the uncertainty existing in the controller is known, the other is that the bound is unknown. In the latter case, the simple adaptation laws for upper bound on the norm of the uncertainty is proposed. Using this adaptive upper bound, a variable structure control is designed. The proposed method does not guarantee the convergence of the adaptive upper bound to the real one but makes the system asymptotically stable.