2024/09/30 by Jan Giesselmann, Giesselmann, Jan, Teresa Kunkel +1
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2409.20345
openalex publication_date 2024/09/30 · openalex created_date 2024/10/28 · openalex updated_date 2026/07/28
We study a state estimation problem for a 2× 2 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.