On the existence of optimal controls for SPDEs with boundary-noise and boundary-control

TL;DR

This paper proves the existence of optimal boundary controls for a stochastic heat equation with boundary noise, using stochastic Hamiltonian systems under certain assumptions.

Contribution

It establishes the existence of strong optimal controls for SPDEs with boundary noise and control, advancing the theoretical understanding of such systems.

Findings

Existence of optimal controls proven under specific conditions.

Solution of the stochastic Hamiltonian system is key.

Results applicable to boundary-controlled stochastic heat equations.

Abstract

We consider a stochastic optimal control problem for an heat equation with boundary noise and boundary controls. Under suitable assumptions on the coefficients, we prove existence of optimal controls in strong sense by solving the stochastic hamiltonian system related.