Brandão, Adilson José VieiraFernandez Cara, EnriqueMagalhães, Paulo Marcelo Dias deRojas Medar, Marko Antonio2015-03-122015-03-122008BRANDÃO, A. J. V. et al. Theoretical analysis and control results for the FitzHugh-Nagumo equation. Electronic Journal of Differential Equations, v. 2008, n. 164, p. 1-20, 2008. Disponível em: <http://ejde.math.txstate.edu/Volumes/2008/164/brandao.pdf>. Acesso em: 09 mar. 2015.1072-6691http://www.repositorio.ufop.br/handle/123456789/4601In this paper we are concerned with some theoretical questions for the FitzHugh-Nagumo equation. First, we recall the system, we briefly explain the meaning of the variables and we present a simple proof of the existence and uniqueness of strong solution. We also consider an optimal control problem for this system. In this context, the goal is to determine how can we act on the system in order to get good properties. We prove the existence of optimal state-control pairs and, as an application of the Dubovitski-Milyoutin formalism, we deduce the corresponding optimality system. We also connect the optimal control problem with a controllability question and we construct a sequence of controls that produce solutions that converge strongly to desired states. This provides a strategy to make the system behave as desired. Finally, we present some open questions related to the control of this equation.en-USArtigo publicado em periodicoO periódico Electronic Journal of Differential Equations permite o arquivamento da versão PDF do editor no Repositório Institucional. Fonte: Sherpa/Romeo <http://www.sherpa.ac.uk/romeo/search.php?issn=1072-6691>. Acesso em: 08 nov. 2016.