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Adaptive Observer for Parabolic PDEs with Uncertain Parameter in the Boundary Condition

Tarek Ahmed-Ali 1 Fouad Giri 1 M. Krstic 2 Laurent Burlion 3 Françoise Lamnabhi-Lagarrigue 4
1 Equipe Automatique - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
2 UCSD - Department of Mechanical and Aerospace Engineering [San Diego]
3 ONERA - The French Aerospace Lab [Toulouse]
4 L2S - Laboratoire des signaux et systèmes
Abstract : We are considering the problem of state observation for a class of infinite dimensional systems. The latter are modelled by a parabolic PDE and a boundary condition involving an unknown parameter. The problem is dealt with using an adaptive observer that provides online estimates of the system (spatially distributed) state and the unknown parameters. The observer is formally shown to be exponentially convergent under an ad-hoc persistent excitation condition.
Keywords : multidimensional systems observers parabolic equations partial differential equations uncertain systems adaptive systems Index Terms-parabolic PDE state observation parameter estimation adaptive observer
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Tarek Ahmed-Ali, Fouad Giri, M. Krstic, Laurent Burlion, Françoise Lamnabhi-Lagarrigue. Adaptive Observer for Parabolic PDEs with Uncertain Parameter in the Boundary Condition. 14th annual European Control Conference - ECC 2015, Jun 2015, Linz, Australia. ⟨10.1109/ECC.2015.7330725⟩. ⟨hal-01260473⟩

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