A stable adaptive synchronization scheme for uncertain chaotic systems via observer

A novel observer-based adaptive synchronization scheme is presented which is used in a chaos communication system. Also, a new nonlinear stochastic adaptive sliding mode observer is extended to reconstruct the states of the stochastic chaotic transmitter at the receiver. The observer is able to overcome the effect of model and parameters uncertainties as well as transmitter, channel and measurement noises. Moreover, a theorem is presented to prove the stability in probability of the proposed observer using stochastic Lyapunov stability criterion. The time-varying adaptation gains of the observer resulted from the proposed theorem ensure fast convergence of the estimated states. Adaptation gains are bounded and do not have any singularity problem especially when the mean value of the observer states’ error. In this paper, the parameters of the transmitter are unknown or are changed intermittently to increase the security of the message transmission. Performance of the message reconstruction in the receiver is enhanced using the scalar transmitted signal to estimate the parameters of the transmitter.