Stochastic Nonlinear Prescribed-Time Stabilization and Inverse Optimality

We solve the prescribed-time mean-square stabilization and inverse optimality control problems for stochastic strict-feedback nonlinear systems by developing a new nonscaling backstepping design scheme. A key novel design ingredient is that the time-varying function is not used to scale the coordinate transformations and is only suitably introduced into the virtual controllers. The advantage of this approach is that a simpler controller results and the control effort is reduced. By using this method, we design a new controller to guarantee that the equilibrium at the origin of the closed-loop system is prescribed-time mean-square stable. Then, we redesign the controller and solve the prescribed-time inverse optimal mean-square stabilization problem, with an infinite gain margin. Specifically, the designed controller is not only optimal with respect to a meaningful cost functional but also globally stabilizes the closed-loop system in the prescribed-time. Finally, two simulation examples are given to illustrate the stochastic nonlinear prescribed-time control design.