Optimal control of the FitzHugh-Nagumo stochastic model with nonlinear diffusion

TL;DR

This paper investigates the optimal control of a stochastic FitzHugh-Nagumo model with nonlinear diffusion, introducing a rescaling method to simplify the problem and derive first-order optimality conditions.

Contribution

It presents a novel application of the rescaling method to a stochastic nonlinear diffusion control problem inspired by the FitzHugh-Nagumo model.

Findings

Established existence of optimal controls.

Derived first-order optimality conditions.

Reduced the stochastic control problem to a simpler form.

Abstract

We consider the existence and first order conditions of optimality for a stochastic optimal control problem inspired by the celebrated FitzHugh-Nagumo model, with nonlinear diffusion term, perturbed by a linear multiplicative Brownian-type noise. The main novelty of the present paper relies on the application of the {\it rescaling method} which allows us to reduce the original problem to a random optimal one.