Stochastically stable robust observer for uncertain chaotic systems with system and measurement noises

This paper presents a new chaos synchronization scheme based on the proposed stochastic adaptive sliding mode observer. The observer overcomes the drive system model uncertainties and unknown parameters to recover the drive system chaotic states form a scalar noisy coupling signal. Using the appropriate adaptation low the unknown parameters of the drive system are estimated and used to boost the state estimations. In addition, drive system state noise, channel noise, and measurement noise, are considered and the system and observer are modeled via stochastic differential equations. Stochastic stability of the drive-response system is proved through several theorems. These theorems guarantee that the mean values of the state estimation errors converge to zero as time goes to infinity. In the observer the adaptive sliding mode gains are always nonsingular even when the estimation error goes to zero. Presented numerical simulations confirm the effectiveness of the proposed observer and chaos synchronization scheme.