Synchronization of different chaotic systems via active radial basis functions sliding mode controller

This paper presents a new method to synchronize different chaoticsystems with disturbances via an active radial basis function (RBF)sliding controller. This method incorporates the advantages of activecontrol, neural network and sliding mode control. The main part ofthe controller is given based on the output of the RBF neuralnetworks and the weights of these single layer networks are tunedon-line based on the sliding mode reaching law. Only several radialbasis functions are required for this controller which takes thesliding mode variable as the only input. The proposed controller canmake the synchronization error converge to zero quickly and canovercome external disturbances. Analysis of the stability for thecontroller is carried out based on the Lyapunov stability theorem.Finally, five examples are given to illustrate the robustness andeffectiveness of the proposed synchronization control strategy.