%0 Journal Article
%A Ayati, Moosa
%A Khaloozadeh, Hamid
%T Designing a Stochastic Adaptive Stable in Probability Observer, for Noisy Uncertain Chaotic Systems
%J Journal of Control
%V 4
%N 3
%U http://joc.kntu.ac.ir/article-1-120-en.html
%R
%D 2010
%K Sliding mode observer, Stochastic Lyapunov stability, Chaotic systems synchronization, Stochastic differential equation.,
%X 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 type of the model uncertainty could be unknown and its upper bound is estimated by adaptive methods. The unknown parameters are estimated using a proposed adaptation law. In addition, the effects of noise are considered in the observer dynamics and then the response system is modeled via stochastic differential equations. Using stochastic calculus and stochastic Lyapunov stability, the stability in probability of the statesâ€™ error system is proved. Moreover, 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 the statesâ€™ convergence is proved, proposed observer is used in a noisy chaos synchronization system.
%> http://joc.kntu.ac.ir/article-1-120-en.pdf
%P 47-55
%& 47
%!
%9 Research paper
%L A-10-48-3
%+
%G eng
%@ 2008-8345
%[ 2010