Adaptive Robust Control for a Class of Stochastic Nonlinear Uncertain Systems

This paper is concerned with the control design for a class of stochastic nonlinear systems. Three uncertainties are considered; that is, nonlinear parameter uncertainty, matched uncertainty and stochastic disturbance. The nonlinear uncertainty contains some uncertain parameter and satisfies bound condition. Neither the exact value of the matched uncertainty nor its possible bound is known; its upper bound function satisfies certain concave condition. The stochastic disturbance is a standard Wiener process. Based on stochastic Lyapunov stability theory, the adaptive robust controller is designed, which renders the state variables of the closed-loop system bounded in probability, regardless of all uncertainties. The desired controller is constructed by the upper bound function and the saturation function, in which the upper bound function represents the magnitude of the control, while the saturation function indicates the control direction. The design of the adaptive robust controller is based on the minimum information of uncertainty, which is simple and can be easily realized in practical systems. Finally, a two-tank water level control example is used to demonstrate the effectiveness of our control design.