Generalized projective synchronization for chaotic systems via Gaussian Radial Basis Adaptive Backstepping Control

This paper proposes the generalized projective synchronization for chaotic systems via Gaussian Radial Basis Adaptive Backstepping Control. In the neural backstepping controller, a Gaussian radial basis function is utilized to on-line estimate the system dynamic function. The adaptation laws of the control system are derived in the sense of Lyapunov function, thus the system can be guaranteed to be asymptotically stable. The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is not necessary to calculate the Lyapunov exponents and the eigen values of the Jacobian matrix, which makes it simple and convenient. Also, it is a systematic procedure for generalized projective synchronization of chaotic systems and it can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. Note that it needs only one controller to realize generalized projective synchronization no matter how much dimensions the chaotic system contains and the controller is easy to be implemented. The proposed method is applied to three chaotic systems: Genesio system, Rössler system, and Duffing system.