SIAM Journal on Control and Optimization / Ricatti-based feedback control of the monodomain equations with the Fitzhugh-Nagumo model

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.