Observer-based data assimilation for barotropic gas transport using distributed measurements

  • We consider a state estimation problem for gas pipeline flow modeled by the one-dimensional barotropic Euler equations. In order to reconstruct the system state, we construct an observer system of Luenberger type based on distributed measurements of one state variable. First, we show the existence of Lipschitz-continuous semi-global solutions of the observer system and of the original system for initial and boundary data satisfying smallness and compatibility conditions for a single pipe and for general networks. Second, based on an extension of the relative energy method we prove that the state of the observer system converges exponentially in the long time limit towards the original system state. We show this for a single pipe and for star-shaped networks.

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Metadaten
Author:Jan Giesselmann, Martin Gugat, Teresa Kunkel
DOI:https://doi.org/10.4310/CMS.240918203214
Publisher:Communications in Mathematical Sciences
Document Type:Article
Language:English
Date of Publication (online):2024/09/18
Release Date:2023/03/10
Volume:22
First Page:2271
Last Page:2309
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Technische Universität Darmstadt
Subprojects:C05
Licence (German):License LogoCreative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International
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