# American Institute of Mathematical Sciences

June  2015, 4(2): 205-220. doi: 10.3934/eect.2015.4.205

## Finite rank distributed control for the resistive diffusion equation using damping assignment

 1 LCIS Laboratoire de Conception et d'Intégration des Systèmes, Grenoble Alpes University, F-26902, France, France

Received  May 2014 Revised  October 2014 Published  May 2015

A first extension of the IDA-PBC control synthesis to infinite dimensional port Hamiltonian systems is investigated, using the same idea as for the finite dimensional case, that is transform the original model into a closed loop target Hamiltonian model using feedback control. To achieve this goal both finite rank distributed control and boundary control are used. The proposed class of considered port Hamiltonian distributed parameters systems is first defined. Then the matching equation is derived for this class before considering the particular case of damping assignment on the resistive diffusion example, for the radial diffusion of the poloidal magnetic flux in tokamak reactors.
Citation: Ngoc Minh Trang Vu, Laurent Lefèvre. Finite rank distributed control for the resistive diffusion equation using damping assignment. Evolution Equations & Control Theory, 2015, 4 (2) : 205-220. doi: 10.3934/eect.2015.4.205
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