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.

Accepted:

DOI: 10.1051/cocv/2015047

Keywords: Compensator design, LQG-balanced truncation, monodomain equations, FitzHugh−Nagumo model

^{1}; Kunisch, Karl

^{1, 2}

@article{COCV_2017__23_1_241_0, author = {Breiten, Tobias and Kunisch, Karl}, title = {Compensator design for the monodomain equations with the {FitzHugh\ensuremath{-}Nagumo} model}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {241--262}, publisher = {EDP-Sciences}, volume = {23}, number = {1}, year = {2017}, doi = {10.1051/cocv/2015047}, mrnumber = {3601023}, zbl = {1371.35153}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2015047/} }

TY - JOUR AU - Breiten, Tobias AU - Kunisch, Karl TI - Compensator design for the monodomain equations with the FitzHugh−Nagumo model JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 241 EP - 262 VL - 23 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015047/ DO - 10.1051/cocv/2015047 LA - en ID - COCV_2017__23_1_241_0 ER -

%0 Journal Article %A Breiten, Tobias %A Kunisch, Karl %T Compensator design for the monodomain equations with the FitzHugh−Nagumo model %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 241-262 %V 23 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015047/ %R 10.1051/cocv/2015047 %G en %F COCV_2017__23_1_241_0

Breiten, Tobias; Kunisch, Karl. Compensator design for the monodomain equations with the FitzHugh−Nagumo model. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 1, pp. 241-262. doi : 10.1051/cocv/2015047. http://archive.numdam.org/articles/10.1051/cocv/2015047/

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