Stable chaos synchronisation scheme for non-linear uncertain systems

In this study, a novel non-linear stochastic adaptive sliding-mode observer is extended to reconstruct the states of a non-linear stochastic system with model uncertainties. Also, both process and measurement noises are considered in the system model. The outstanding feature of the proposed observer is its stability in probability which is proved through a theorem based on stochastic Lyapunov stability criterion. The time-varying adaptation gains obtained from the proposed theorem ensure high convergence rate of the observer. Another advantage of the observer is bounded adaptation gains which do not have any singularity problem especially when the mean value of the observer error converges to zero. The proposed observer is used in an observer-based chaos synchronisation scheme. Since both uncertainties and noises are considered in the observer model, it can effectively estimate the noisy states of a highly non-linear chaotic transmitter. Also the effect of the noises on the synchronisation is investigated through simulations.