Adaptive state feedback control for a class of stochastic nonlinear systems

In this paper, tracking problem is studied for a class of stochastic nonlinear systems, which is in strict-feedback form and with unknown parametric nonlinearities. Under the condition of all system states being available for feedback, by employing the stochastic Lyapunov-like theorem and the backstepping design technique, an adaptive state feedback control is developed. The output of the closed-loop system is proven to follow the desired trajectory asymptotically in probability.