Abstract
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.
Highlights
The stochastic disturbance often occurs in practical systems and causes instability
Remark 5: In (16) (17), the upper bound function represents the magnitude of the controller, and the saturation function shows its direction
The nonlinear uncertainty is bounded in probability
Summary
The stochastic disturbance often occurs in practical systems and causes instability. it is necessary and challenging to investigate control problems for stochastic systems. A neural network (NN) was employed in [19] to compensate for the unknown upper function of the nonlinear interconnections, where a decentralized adaptive output-feedback stabilization controller for a class of large-scale stochastic nonlinear strict-feedback systems was designed. Reference [26] constructed an observer to estimate the unknown state variables, and solved the observer-based adaptive fuzzy control problem for nonstrict-feedback stochastic nonlinear systems with input saturation and prescribed performance. An observer-based fuzzy adaptive output feedback controller was proposed for a class of switched stochastic nonlinear uncertain systems with quantized input signals in [27]. It is noted that there are few results on the adaptive robust control design for stochastic nonlinear systems embracing nonlinear parameter uncertainty, matched uncertainty and stochastic disturbance. The proposed control scheme is applicable to many systems and requires only the minimum structural information of the uncertainty
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