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Title
Ricatti-based feedback control of the monodomain equations with the Fitzhugh-Nagumo model.
AuthorBreiten, Tobias ; Kunisch, Karl
Published in
SIAM Journal on Control and Optimization, 2014, Vol. 52, Issue 6, page 4057-4081
PublishedSociety for Industrial and Applied Mathematics, 2014
LanguageEnglish
Document typeJournal Article
Keywords (EN)feedback control / Riccati equation / monodomain equations / FitzHugh-Nagumo model
ISSN0363-0129
URNurn:nbn:at:at-ubg:3-3442 Persistent Identifier (URN)
DOI10.1137/140964552 
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 The work is publicly available
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Abstract (English)

Feedback control for the monodomain equations is studied. The dynamics of interest are governed by a coupled PDE-ODE reaction diffusion system with nonmonotone nonlinearity of FitzHugh--Nagumo type. A localized distributed control is used to locally stabilize the nonlinear system. This is achieved by a Riccati-based feedback law, determined by the linearized system. It is shown that the Riccati equation corresponding to the PDE variable suffices for exponential stabilization of the linearized PDE-ODE system. The theoretical findings are underlined by several numerical examples.

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