Stochastic maximum principle for optimal control of SPDEs

TL;DR

This paper establishes a stochastic maximum principle for optimal control of stochastic partial differential equations, accommodating non-convex control domains and control-dependent diffusion coefficients.

Contribution

It extends the stochastic maximum principle to more general SPDE control problems with non-convex controls and control-dependent diffusions.

Findings

Derived the maximum principle for general SPDEs with non-convex controls.

Included control-dependent diffusion coefficients in the framework.

Provided theoretical conditions for optimality in complex SPDE control problems.

Abstract

In this note, we give the stochastic maximum principle for optimal control of stochastic PDEs in the general case (when the control domain need not be convex and the diffusion coefficient can contain a control variable).