# Optimal control for the stochastic FitzHugh-Nagumo model with recovery variable

## TL;DR

This paper establishes the existence and uniqueness of solutions for an optimal control problem involving a stochastic FitzHugh-Nagumo model with a recovery variable, addressing challenges posed by non-linear drift coefficients.

## Contribution

It introduces a novel approach using Ekeland's variational principle to handle the non-linearities in the stochastic control of the FitzHugh-Nagumo model.

## Key findings

- Proves existence and uniqueness of solutions for the control problem.
- Develops a method to handle cubic non-linearity in stochastic models.
- Provides a framework for optimal control in complex neural models.

## Abstract

In the present paper we derive the existence and uniqueness of a solution for the optimal control problem determined by a stochastic FitzHugh-Nagumo equation with recovery variable. In particular due the cubic non-linearity in the drift coefficients, standard techniques cannot be applied so that the Ekeland's variational principle has to be exploited.