Master-slave chaos synchronization using an adaptive dynamic sliding-mode neural control system

Since chaotic systems are important nonlinear deterministic systems that display complex, noisy-like and unpredictable behavior, synchronizing chaotic systems have become an important issue in the engineering community. This paper proposes an adaptive dynamic sliding-mode neural control (ADSMNC) system composed of a neural controller and a switching compensator. The neural controller uses a radial basis function (RBF) network to online approximate an ideal dynamic sliding-mode controller, and the switching compensator is designed to guarantee system stability in the Lyapunov stability sense. Moreover, the online adaptive laws with variable learning rate are derived to speed up the convergence rates of the tracking error and controller parameters. Finally, the synchronization problem between two chaotic gyros based on the mater-slave scheme is studied. It is shown by the simulation results that the chaotic behavior of two nonlinear identical chaotic gyros can be synchronized by the proposed ADSMNC scheme after learning of the controller parameters.