Adaptive Stabilization of Time-Delay Feedforward Stochastic Nonlinear Systems

This paper discusses the problem of adaptive stabilization for stochastic feedforward nonlinear systems with time-delay. A universal-type adaptive update law is introduced into the observer and controller to deal with unknown growth rates. With the help of the appropriate Lyapunov-Krasovskii functional and stochastic Barbalat's lemma, it can be proved that the universal-type adaptive output feedback controller can regulate all the states of the closed-loop system almost surely. A simulation example is given to illustrate the effectiveness of the proposed method.