In the present paper, an optimal control problem
constrained by the tridomain equations in
electrocardiology is investigated. The state equations
consisting in a coupled reaction-diffusion system
modelling the propagation of the intracellular and
extracellular electrical potentials, and ionic currents,
are extended to further consider the effect of an
external bathing medium. The existence and uniqueness of
solution for the tridomain problem and the related
control problem is assessed, and the primal and dual
problems are discretized using a finite volume method
which is proved to converge to the corresponding weak
solution. In order to illustrate the control of the
electrophysiological dynamics, we present some
preliminary numerical experiments using an efficient
implementation of the proposed scheme.