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Reconstructing initial data using iterative observers for wave type systems

Haine, Ghislain Reconstructing initial data using iterative observers for wave type systems. (2013) In: 11th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2013), 03-07 Jun 2013, Gammarth, Tunisia .

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Official URL: http://www.lamsin.tn/waves13/

Abstract

An iterative algorithm for solving initial data inverse problems from partial observations has been proposed in 2010 by Ramdani, Tucsnak and Weiss (Automatica, 2010). In this work, we are concerned with the convergence of this algorithm when the inverse problem is ill-posed, i.e. when the observations are not sufficient to reconstruct any initial data. We prove that the state space can be decomposed as a direct sum, stable by the algorithm, corresponding to the observable and unobservable part of the initial data. We show that this result holds for both locally distributed and boundary observation.

Item Type:Conference or Workshop Item (Paper)
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Université de Lorraine (FRANCE)
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Deposited By: Ghislain Haine
Deposited On:28 Jun 2013 09:51

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