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 hounded in probability. A simulation example is presented to demonstrate reasonability and efficiency of the proposed method.