Adaptive Dynamic Surface Control of Stochastic Strict Feedback Nonlinear Systems

Based on the integral-type Lyapunov function and the approximation capability of neural networks, an adaptive dynamic surface control scheme is proposed for a class of stochastic strict-feedback nonlinear systems in this paper. The design makes the approach of dynamic surface control be extended to the stochastic nonlinear systems, and relaxes the extent of application of the dynamic surface control approach. By introducing the first order filter, the explosion of complexity caused by the repeated differentiations of certain nonlinear functions such as virtual controls in traditional backstepping design is avoided. Compared with the existing literature, the proposed approach reduces the number of adjustable parameters effectively. By theoretical analysis, it is shown that all signals in the closed-loop system are bounded in probability.