Geodesic
Compensator design for the monodomain equations with the FitzHugh−Nagumo model
Breiten, Tobias1  ; Kunisch, Karl1, 2 
1 Institute for Mathematics and Scientic Computing, Karl-Franzens-Universität, Heinrichstr. 36, 8010 Graz, Austria.
2 Altenberger Straße 69, 4040 Linz, Austria.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 241-262

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The problem of finite-dimensional compensator design for the monodomain equations with the FitzHugh−Nagumo model is investigated. Exponential stabilizability and detectability of the linearized infinite-dimensional control system is studied. It is shown that the system is not exactly null-controllable but still can be exponentially stabilized by finite-rank input and output operators provided the desired stability margin is small enough. Based on existing results on model order reduction of infinite-dimensional systems, a finite-dimensional compensator is obtained by LQG-balanced truncation. Using partial measurements, the compensator produces a feedback control that is shown to be locally stabilizing for the infinite-dimensional nonlinear control system. Examples motivated by cardiophysiology are used to illustrate these results in a numerical setup.

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Accepté le :
DOI : 10.1051/cocv/2015047
Classification : 35K57, 93B52, 93C20, 93D15
Keywords: Compensator design, LQG-balanced truncation, monodomain equations, FitzHugh−Nagumo model

Breiten, Tobias 1 ; Kunisch, Karl 1, 2

1 Institute for Mathematics and Scientic Computing, Karl-Franzens-Universität, Heinrichstr. 36, 8010 Graz, Austria.
2 Altenberger Straße 69, 4040 Linz, Austria. 
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     title = {Compensator design for the monodomain equations with the {FitzHugh\ensuremath{-}Nagumo} model},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Breiten, Tobias; Kunisch, Karl. Compensator design for the monodomain equations with the FitzHugh−Nagumo model. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 241-262. doi: 10.1051/cocv/2015047

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