# Optimal control of stochastic differential equations with dynamical boundary conditions

## TL;DR

This paper studies the optimal control of complex stochastic systems with dynamic boundary conditions, combining infinite and finite-dimensional dynamics, to address non-standard boundary control challenges.

## Contribution

It introduces a novel framework for controlling stochastic systems with boundary conditions governed by separate stochastic differential equations.

## Key findings

- Developed a mathematical model for stochastic systems with dynamic boundary conditions.
- Provided existence and uniqueness results for the control problem.
- Outlined potential applications in systems with coupled internal and boundary dynamics.

## Abstract

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are concerned with non standard boundary conditions, as the value at the boundary is governed by a different stochastic differential equation.