Adaptive Stabilization Control of a Class of Large-scale Stochastic Nonlinear Systems with Time-delays and Unknown Virtual Control Coefficients

Abstract

In this paper,the adaptive stabilization problem is investigated for a class of large-scale stochastic time-delay nonlinear systems with unknown virtual control coefficients and unknown noise covariances.First,corresponding to the unknown virtual control coefficients and unknown noise covariances,some parameters to be estimated are properly chosen. Then,in view of the effect of the time-varying delay on the stability of the closed-loop system,an suitable Lyapunov- Krasovskii functional is constructed,based on which and the well-known integrator backstepping method,a memoryless state-feedback control law is systematically designed.Under some mild conditions,it is shown that the equilibrium of the closed-loop system is globally stable in probability,and all the signals of the closed-loop system except for parameter estimates converge to zero almost surely.A simulation example is given to illustrate the effectiveness of the proposed approach.