Adaptive Asymptotic Stabilization for Stochastic Nonlinear Systems with Dynamic Uncertainties

In this paper, the problem of adaptive stabilization is investigated for stochastic nonlinear systems with three types of uncertainties: parametric uncertainties, uncertain nonlinearities and unmodeled dynamics. Under the assumption that the unmodeled dynamics are stochastic input-to-state stable, for the general smooth systems in which both drift and diffusion vector fields depend on not only the output but also the unmodeled dynamics, an adaptive output-feedback controller is constructively designed by the methods of adaptive backstepping with tuning function and changing the supply function. It is shown that under mild conditions, the closed-loop system is bounded in probability and moreover, the output can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin.