Motivated by the termination of undesirable arrhythmia, a time optimal control formulation for the monodomain equations is proposed. It is shown that, under certain conditions, the optimal solutions of this problem steer the system into an appropriate stable neighborhood of the resting state. Towards this goal, some new regularity results and asymptotic properties for the monodomain equations with the Rogers−McCulloch ionic model are obtained. For the numerical realization, a monolithic approach, which simultaneously optimizes for the optimal times and optimal controls, is presented and analyzed. Its practical realization is based on a semismooth Newton method. Numerical examples and comparisons are included.
DOI : 10.1051/m2an/2015048
Mots clés : Time optimal control, monodomain equations, semismooth Newton method, reaction diffusion system, asymptotic behavior
@article{M2AN_2016__50_2_381_0, author = {Kunisch, Karl and Pieper, Konstantin and Rund, Armin}, title = {Time optimal control for a reaction diffusion system arising in cardiac electrophysiology {\textendash} a monolithic approach}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {381--414}, publisher = {EDP-Sciences}, volume = {50}, number = {2}, year = {2016}, doi = {10.1051/m2an/2015048}, mrnumber = {3482548}, zbl = {1341.35174}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015048/} }
TY - JOUR AU - Kunisch, Karl AU - Pieper, Konstantin AU - Rund, Armin TI - Time optimal control for a reaction diffusion system arising in cardiac electrophysiology – a monolithic approach JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 381 EP - 414 VL - 50 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015048/ DO - 10.1051/m2an/2015048 LA - en ID - M2AN_2016__50_2_381_0 ER -
%0 Journal Article %A Kunisch, Karl %A Pieper, Konstantin %A Rund, Armin %T Time optimal control for a reaction diffusion system arising in cardiac electrophysiology – a monolithic approach %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 381-414 %V 50 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015048/ %R 10.1051/m2an/2015048 %G en %F M2AN_2016__50_2_381_0
Kunisch, Karl; Pieper, Konstantin; Rund, Armin. Time optimal control for a reaction diffusion system arising in cardiac electrophysiology – a monolithic approach. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 2, pp. 381-414. doi : 10.1051/m2an/2015048. http://www.numdam.org/articles/10.1051/m2an/2015048/
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