State‐feedback stabilization and inverse optimal control for stochastic high‐order nonlinear systems with time‐varying powers

Abstract This paper considers the stability and optimality problems associated with stochastic high‐order nonlinear systems with time‐varying powers. This research extends previous studies on the plant with constant powers. In this paper, we firstly construct a state‐feedback controller to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable (GAS) in probability. Then we redesign a new optimal controller with infinite gain margin to solve the inverse optimal stabilization (IOS) problem. Specifically, the optimal controller is not only optimal with respect to a meaningful cost functional but also globally asymptotically stabilizes the closed‐loop system. The efficiency of the designed controllers is demonstrated by a simulation example.