TY - INPR A1 - Giesselmann, Jan A1 - Kunkel, Teresa T1 - Identification of minimal number of measurements allowing synchronization of a nodal observer for the wave equation N2 - We study a state estimation problem for a 2x2 linear hyperbolic system on networks with eigenvalues with opposite signs. The system can be seen as a simplified model for gas flow through gas networks. For this system we construct an observer system based on nodal measurements and investigate the convergence of the state of the observer system towards the original system state. We assume that measurements are available at the boundary nodes of the network and identify the minimal number of additional measurements in the network that are needed to guarantee synchronization of the observer state towards the original system state. It turns out that for tree-shaped networks boundary measurements suffice to guarantee exponential synchronization, while for networks that contain cycles synchronization can be guaranteed if and only if at least one measurement point is added in each cycle. This is shown for a system without source term and for a system with linear friction term. Y1 - 2024 ER - TY - JOUR A1 - Giesselmann, Jan A1 - Gugat, Martin A1 - Kunkel, Teresa T1 - Observer-based data assimilation for barotropic gas transport using distributed measurements N2 - 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. Y1 - 2023 U6 - https://doi.org/10.4310/CMS.240918203214 VL - 22 SP - 2271 EP - 2309 PB - Communications in Mathematical Sciences ER -