Stochastic prescribed-time state feedback control under unknown growth rate

This paper investigates the problem of prescribed-time mean-square stabilization via state feedback control for stochastic nonlinear systems with the unknown linear growth rate. Specifically, a novel nonscaling backstepping scheme is proposed, not only to address system uncertainties but also to ensure stochastic prescribed-time convergence. The core design strategy is to decouple the dominant terms from the unknown components in the recursive process, allowing the linear growth rate to be incorporated into the coefficients of the upper bound estimate inequalities. Notably, these inequalities are dominated by a scaling function whose exponent includes an adjustable parameter. By tuning the parameter, the proposed control law guarantees that the closed-loop system has an almost surely unique solution, with the trivial solution being prescribed-time mean-square stable and the control input remaining uniformly mean-square bounded. Finally, a simulation example is provided to demonstrate the effectiveness of the control design.