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This work deals with an inverse electrocardiological problem considering the reconstruction of where one has to reconstruct the heart transmembrane potential from thorax's high density measurements. The problem will be solved as an optimal control one for a partial differential system with incomplete data. The electrical activity on the heart is here modelled by a system of FitzHugh–Nagumo's type where the initial conditions corresponding to the transmembrane potential and to the gating variables are unknown. We use the low-regret optimal control method by J.-L. Lions to tackle this problem. We prove the existence and uniqueness of a low-regret control that we characterise by a singular optimality system.

Low-regret optimal control for an inverse electrocardiological problem with incomplete data