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

Ngoc Minh Trang  Vu; Laurent  Lefèvre

doi:10.3934/eect.2015.4.205

Article Contents

2015, Volume 4, Issue 2: 205-220. Doi: 10.3934/eect.2015.4.205

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

Ngoc Minh Trang Vu^1, and
Laurent Lefèvre^1,

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

Received: April 30, 2014

Revised: September 30, 2014

Published: May 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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