A varying terminal time structure for stochastic optimal control under constrained condition

TL;DR

This paper introduces a new stochastic maximum principle for optimal control problems with state constraints, where the terminal time varies with the control, providing a novel approach to constrained stochastic control.

Contribution

It proposes a varying terminal time structure and a corresponding stochastic maximum principle for constrained stochastic optimal control problems, advancing the theoretical framework.

Findings

Developed a new stochastic maximum principle for variable terminal time control.

Verified the optimal control pair using the proposed maximum principle.

Extended the theory of stochastic control under state constraints.

Abstract

In this study, we propose a varying terminal time structure for the optimal control problem under state constraints, in which the terminal time follows the varying of the control via the constrained condition. Focusing on this new optimal control problem, we investigate a novel stochastic maximum principle, which differs from the traditional optimal control problem under state constraints. The optimal pair of the optimal control model can be verified via this new stochastic maximum principle.