Key result
Virtual control regularization enables rigorous optimal control analysis for the monodomain model in cardiac electrophysiology.
The study presents a virtual control regularization approach for optimal control of the monodomain model in cardiac electrophysiology, enabling rigorous analysis and numerical optimization.
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Virtual control regularization enables analysis of constrained optimal control in cardiac models; leaves open clinical translation to electrophysiology.
This study explores an optimal control problem of the monodomain model, a coupled system of a reaction-diffusion partial differential equation and an ordinary differential equation, employing the concept of virtual control to effectively handle both control and state constraints. The state constraints are addressed through a regularization technique based on virtual control, enabling a rigorous analysis of the existence of optimal control and the derivation of the first-order optimality system for the regularized problem. We provide a detailed estimation of the regularization error in terms of the regularization parameter, facilitating the analysis of the convergence of the optimal solution of the regularized problem to that of the original problem. Finally, numerical results are presented using the semi-smooth Newton method for optimization and the finite element method for discretization.
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Robert et al. (2026) studied Cardiac electrophysiology (computational model). Virtual control regularization approach was evaluated. A virtual control regularization approach for the monodomain model in cardiac electrophysiology enabled rigorous analysis of optimal control and derivation of the first-order optimality system.
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