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
2 MAE - UC San Diego - Department of Mechanical and Aerospace Engineering [Univ California San Diego]
3 ONERA - The French Aerospace Lab [Toulouse]
4 L2S - Laboratoire des signaux et systèmes

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.

Mots clés: multidimensional systems; observers; parabolic equations; partial differential equations; uncertain systems; adaptive systems; Index Terms-parabolic PDE; state observation; parameter estimation; adaptive observer

Domaines: Automatique; Automatique / Robotique

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⟩