Design of adaptive sliding mode controller for chaos synchronization

A robust adaptive sliding control scheme is developed to achieve the synchronization problem for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without the requirement that the bounds of parameter and disturbance uncertainties should be known in advance. It is proved that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.