Prescribed-Time Output-Feedback Control of Stochastic Nonlinear Systems

We present prescribed-time output-feedback-stabilizing designs for stochastic nonlinear strict-feedback systems. We first propose a new nonscaling output-feedback control scheme to solve the prescribed-time mean-square stabilization problem for stochastic nonlinear systems without sensor uncertainty. In this case, compared with the existing results on stochastic nonlinear prescribed-time stabilization, an appealing feature in our design is that the order of the scaling function in the controller is dramatically reduced, which yields a simpler controller and with the control effort reduced. We then consider prescribed-time output-feedback control for stochastic nonlinear systems with sensor uncertainty. In this case, the new design ingredient is that a time-varying controller is designed to guarantee prescribed-time mean-square stabilization, different from the existing results where an adaptive controller is designed to ensure almost sure regulation (as time goes to infinity). Finally, two simulation examples are given to illustrate the stochastic nonlinear prescribed-time output-feedback designs.