Adaptive Observer for a Class of Parabolic PDEs

Abstract : 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.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01260172
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Submitted on : Thursday, January 21, 2016 - 4:03:02 PM
Last modification on : Tuesday, April 2, 2019 - 1:36:20 AM

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

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