Output feedback control based on augmented observer for random system

In this paper, for a class of nonlinear systems with stationary processes and modeling errors, an observer-based backstepping controller is designed. The main work consists of three aspects. First, an augmented observer is constructed to estimate the unmeasurable states and the modeling errors; Second, an output-feedback controller is designed by using the integrator backstepping approach; Third, it is proved that the output can be regulated to an arbitrarily small neighborhood of the origin and all the other signals in the closed-loop system are bounded in probability. A simulation example is presented to demonstrate reasonability and efficiency of the proposed method.