Adaptive Observer for a Class of Parabolic PDEs

Tarek Ahmed-Ali (1) , Fouad Giri (2) , Miroslav Krstic (3) , Françoise Lamnabhi-Lagarrigue (4) , Laurent Burlion (5)

1 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
2 Equipe Automatique - Laboratoire GREYC - UMR6072
3 UC San Diego - University of California [San Diego]
4 L2S - Laboratoire des signaux et systèmes
5 ONERA - The French Aerospace Lab [Toulouse]

The problem of state observation, based on spatially-sampled output measurements, is addressed for a class of infinite dimensional systems, modelled by a semi-linear heat equation augmented with a structured uncertain part involving a set of unknown parameters. An adaptive observer is designed that provides online estimates of the system (spatially distributed) state and unknown parameters based on sampled data (in space). Sufficient conditions for the observer to be exponentially convergent are established. These include an ad-hoc persistent excitation condition as well as a condition on how the observer gain must be selected in relation with the space sampling interval.

Keywords: Nonlinear system; observer design; PDE systems

Domains: Automatic

Tarek Ahmed-Ali, Fouad Giri, Miroslav Krstic, Françoise Lamnabhi-Lagarrigue, Laurent Burlion. Adaptive Observer for a Class of Parabolic PDEs. IEEE Transactions on Automatic Control, 2016, 61 (10), pp.3083-3090. ⟨10.1109/tac.2015.2500237⟩. ⟨hal-01260172⟩