Geodesic
Time optimal control for a reaction diffusion system arising in cardiac electrophysiology – a monolithic approach
Kunisch, Karl1, 2  ; Pieper, Konstantin3 ; Rund, Armin1
1 Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria
2 Radon Institute, Austrian Academy of Sciences, Austria
3 Chair of Optimal Control, Technische Universität München, Boltzmannstraße 3, 85748 Garching bei München, Germany
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 2, pp. 381-414

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
DOI : 10.1051/m2an/2015048
Classification : 35M30, 49K20, 49J52, 90C46
Keywords: Time optimal control, monodomain equations, semismooth Newton method, reaction diffusion system, asymptotic behavior

Kunisch, Karl 1, 2 ; Pieper, Konstantin 3 ; Rund, Armin 1

1 Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 Graz, Austria
2 Radon Institute, Austrian Academy of Sciences, Austria
3 Chair of Optimal Control, Technische Universität München, Boltzmannstraße 3, 85748 Garching bei München, Germany 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :