Adaptive boundary observer for parabolic PDEs subject to domain and boundary parameter uncertainties

Tarek Ahmed-Ali (1) , Fouad Giri (1) , Miroslav Krstic (2) , Laurent Burlion (3) , Francoise Lamnabhi-Lagarrigue (4)

1 UNICAEN - Université de Caen Normandie
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 modeled by parabolic type PDEs. The model is subject to parametric uncertainty entering in both the domain equation and the boundary condition. An adaptive boundary observer, providing online estimates of the system state and parameters, is designed using finite- and infinite-dimensional backstepping-like transformations. The observer is exponentially convergent under an ad hoc persistent excitation condition.

Mots clés: PARAMETER UNCERTAINTY; ADAPTIVE OBSERVER; BACKSTEPPING DESIGN; PARABOLIC PDE

Domaines: Physique de l'espace [physics.space-ph]

Tarek Ahmed-Ali, Fouad Giri, Miroslav Krstic, Laurent Burlion, Francoise Lamnabhi-Lagarrigue. Adaptive boundary observer for parabolic PDEs subject to domain and boundary parameter uncertainties. Automatica, 2016, 72, pp.115-122. ⟨10.1016/j.automatica.2016.06.006⟩. ⟨hal-01426551⟩