On a nodal observer for a semilinear model for the flow in gas networks

TL;DR

This paper introduces a nodal observer for gas flow networks modeled by hyperbolic PDEs, demonstrating exponential convergence of the observer to the true system state with supporting numerical validation.

Contribution

The paper develops and proves the effectiveness of a novel nodal observer for semilinear gas flow models, enabling accurate state estimation from limited measurements.

Findings

Observer system converges exponentially to the true state.

Numerical experiments validate theoretical convergence results.

Abstract

The flow of gas through networks of pipes can be modeled by coupling hyperbolic systems of partial differential equations that describe the flow through the pipes that form the edges of the graph of the network by algebraic node conditions that model the flow through the vertices of the graph. In the network, measurements of the state are available at certain points in space. Based upon these nodal observations, the complete system state can be approximated using an observer system. In this paper we present a nodal observer, and prove that the state of the observer system converges to the original state exponentially fast. Numerical experiments confirm the theoretical findings.