Anti-disturbance control of stochastic nonlinear systems based on extended state observer

In this paper, we study the controller design and stability analysis for a class of stochastic cascade nonlinear systems with external disturbances. The unmeasurable external disturbance is viewed as a extended state. In order to estimate the unmeasurable system states and the external disturbance, a new extended state observer (ESO) based on the Riccati differential equation is constructed. The stochastic inverse dynamics, the error dynamics of observer, and the ESO constitute a new stochastic nonlinear systems. Based on this new systems, an adaptive output feedback controller is proposed by combining stochastic input-to-state stability with backstepping design technique. The controller guaranteed that all the signals of the states are almost surely bounded and the states of the stochastic closed-loop system are globally asymptotically stable in probability. Finally, a simulation example is given to the validity of the proposed method.