Adaptive tracking control for a class of random nonlinear systems

Different with nonlinear systems described by Itó integral (or differential) equations, the model in form of RDSs with uncertain parameters is researched in this paper. Compared with the traditional methods of stochastic backstepping control, which focus the attentions on Hessian terms caused by Brown motions, an adaptive backstepping control scheme is designed to perform the task of output-tracking, by adopting separation technique. It is proved that the tracking error can be made arbitrarily small and all other signals are bounded in probability. A numerical simulation example is presented to explain the reasonability of the proposed method.