Prescribed-Time Control for Stochastic High-Order Nonlinear Systems With Parameter Uncertainty

This brief focuses on the problem of prescribed-time mean-square control for uncertain stochastic high-order
$(p$
-normal) nonlinear systems. Compared to existing results, a more general model is considered. First, a prescribed-time mean-square stable controller is constructed with the assistance of the power integrator technique, the time-varying prescribed-time function and a non-scaling framework. Then, based on the stability theorem of stochastic systems and the useful proposition of the selected Lyapunov function, the prescribed-time mean-square stability of all signals is analyzed. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed control strategy.