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

Gugat M, Giesselmann J, Kunkel T (2024)

Publication Type: Journal article, Original article

Publication year: 2024

Journal

Communications in Mathematical Sciences International Press

Book Volume: 22

Pages Range: 2271-2309

Journal Issue: 8

DOI: 10.4310/CMS.240918203214

Abstract

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.

Authors with CRIS profile

Martin Gugat Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Technische Universität Darmstadt DE Germany (DE)

How to cite

APA:

Gugat, M., Giesselmann, J., & Kunkel, T. (2024). Observer-based data assimilation for barotropic gas transport using distributed measurements. Communications in Mathematical Sciences, 22(8), 2271-2309. https://doi.org/10.4310/CMS.240918203214

MLA:

Gugat, Martin, Jan Giesselmann, and Teresa Kunkel. "Observer-based data assimilation for barotropic gas transport using distributed measurements." Communications in Mathematical Sciences 22.8 (2024): 2271-2309.

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