Issue |
ESAIM: COCV
Volume 23, Number 1, January-March 2017
|
|
---|---|---|
Page(s) | 241 - 262 | |
DOI | https://doi.org/10.1051/cocv/2015047 | |
Published online | 02 December 2016 |
Compensator design for the monodomain equations with the FitzHugh−Nagumo model
1 Institute for Mathematics and
Scientic Computing, Karl-Franzens-Universität, Heinrichstr. 36,
8010
Graz,
Austria.
tobias.breiten@uni-graz.at
2 Altenberger Straße 69,
4040
Linz,
Austria.
karl.kunisch@uni-graz.at
Received:
16
December
2014
Revised:
7
May
2015
Accepted:
10
September
2015
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.
Mathematics Subject Classification: 35K57 / 93B52 / 93C20 / 93D15
Key words: Compensator design / LQG-balanced truncation / monodomain equations / FitzHugh−Nagumo model
© EDP Sciences, SMAI 2016
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