# American Institute of Mathematical Sciences

December  2018, 7(4): 571-585. doi: 10.3934/eect.2018027

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

 University of Verona - Department of Computer Science, Strada le Grazie 15, 37134, Verona, Italy

* Corresponding author: Luca Di Persio

Received  May 2018 Revised  July 2018 Published  September 2018

In the present paper we derive the existence and uniqueness of the solution for the optimal control problem governed by the stochastic FitzHugh-Nagumo equation with recovery variable. Since the drift coefficient is characterized by a cubic non-linearity, standard techniques cannot be applied, instead we exploit the Ekeland's variational principle.

Citation: Francesco Cordoni, Luca Di Persio. Optimal control for the stochastic FitzHugh-Nagumo model with recovery variable. Evolution Equations & Control Theory, 2018, 7 (4) : 571-585. doi: 10.3934/eect.2018027
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