Designing sliding mode observer for uncertain noisy chaotic systems

In this paper a novel stochastic adaptive sliding mode observer is developed which is able to estimate the states of an uncertain chaotic system with model and parametric uncertainties. The structure of the model uncertainty is unknown but its upper bound is estimated using adaptive methods. The unknown parameters are estimated using a proposed adaptation law. In addition, the effects of noise are considered and then using stochastic calculus and stability in probability concepts the stochastic stability of the states´ error system is proved. It is proved that the states of the proposed observer converge to the drive system states while the adaptation gains of the observer remain non-singular and bounded. Since the observer can suppress the effect of noise and uncertainties and states´ convergence is proved, the observer is used in a noisy chaos synchronization scheme in the simulations.