Adaptive observer-based control for uncertain nonlinear stochastic systems with time-delay

This paper investigated the adaptive estimation and controller design for a class of stochastic time-delay systems with both deterministic disturbance and stochastic disturbance. A new design and analysis method to solve the problem of adaptive control is developed to guarantee that not only all the state vectors of the closed-loop system are asymptotically stable in the mean square sense, but also unknown parameters are finite in probability. The sufficient conditions for the existence of adaptive estimator are given. Moreover, the detailed systematic design algorithm of adaptive controller is presented particularly. A numerical example is given to indicate the feasibility of the proposed method.