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.
2 Altenberger Straße 69, 4040 Linz, Austria.
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