Stochastic Linear Quadratic Optimal Control with General Control Domain

TL;DR

This paper develops a new maximum principle for stochastic linear quadratic control problems with nonconvex control domains, expanding the theoretical framework for such complex control systems.

Contribution

It introduces a novel maximum principle for stochastic LQ problems with nonconvex control domains using functional analysis and convex perturbation methods.

Findings

Established a maximum principle for nonconvex control domains

Demonstrated the principle with a practical example

Extended the theoretical understanding of stochastic control

Abstract

This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of the proposed maximum principle is illustrated through a work-out example.