The Pontryagin's maximum principle for stochastic differential systems under state constraints

TL;DR

This paper develops a stochastic maximum principle for optimal control problems with path-dependent state constraints, extending classical results to more complex constrained stochastic systems.

Contribution

It introduces a new near optimal control problem and establishes the maximum principle under multi-time state constraints, with a practical production planning example.

Findings

Established stochastic maximum principle under multi-time state constraints

Validated results with a production planning example

Extended control theory to path-constrained stochastic systems

Abstract

In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for the optimal control problem under state constraints, we investigate a new near optimal control problem. In the following, we establish the stochastic maximum principle for the new optimal control problem under multi-time state constraints. In the end, we give a production planning example to verify the main results of this study.