Finite‐Time Inverse Optimal Control for Low‐Order Stochastic Nonlinear Systems With Time‐Varying Orders

This study investigates the finite‐time inverse optimal control problem for low‐order stochastic nonlinear systems with time‐varying orders. By designing a state feedback controller to ensure the finite‐time stabilization of the system, and subsequently applying the finite‐time inverse optimal control principle, we redesign an optimal controller. This paper combines inverse optimal control with finite‐time stability and introduces it for the first time to low‐order stochastic nonlinear systems. It ensures that the designed controller is not only optimal in terms of meaningful cost functions but also capable of globally stabilizing the closed‐loop system within a finite time. Two examples are given to validate the feasibility of the proposed scheme.