Further results on adaptive stabilization for a class of uncertain stochastic nonlinear systems

This paper concerns the global adaptive stabilization for a class of uncertain stochastic nonlinear systems. Comparing with the existing literature, the systems under investigation are somewhat general, and allow more unknowns/uncertainties in the inverse dynamics and the system nonlinearities. Quite differently, with the help of skillfully selecting an unknown parameter, we develop an improved adaptive control design scheme to stabilize the system. The main feature of the design scheme is that the dimensional of dynamic compensator is remarkably reduced from n to 2, and hence this considerably allays the overparametrization in the existing literature. It is worthy of pointing out that, the new controller can guarantee all the resulting closed-loop system states are global bounded and the original system states converge to the origin, both with probability one.