Nonlinear Adaptive Synchronization for Rösseler System with Scalar Signal

Synchronization of two chaotic systems with unknown parameters via a scalar signal is both theoretically challenging and of practical importance. Synchronization of two Rosseler systems is achieved under the assumption that only one of the three state variables is available and the values of all parameters are unknown except ranges of the parameters. A novel adaptive observer is proposed to track the transmitted scalar signal, reconstruct the un-transmitted states, and estimate the unknown parameters. Lyapunov argument is applied to analyze and guarantee the stability of the error dynamics. Persistent excitation of the chaotic signal is checked to ensure that estimates of parameters converge to their true values. A real system is simulated to show the efficiency of the proposed adaptive observer