Observer-based backstepping dynamic surface control for stochastic nonlinear strict-feedback systems

An observer-based dynamic surface control approach is proposed for a class of stochastic nonlinear strict-feedback systems in order to solve the problem of ‘explosion of complexity’ in the backstepping design; that is, the dynamic surface control approach is extended to the stochastic setting. The circle criterion is applied to designing a nonlinear observer, and so no linear growth condition is imposed on nonlinear functions depending on system states. It is proved that the closed-loop system is semi-globally uniformly ultimately bounded in fourth moment, and the ultimate boundedness can be tuned arbitrarily small. Two examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.