Exponential synchronization of a nodal observer for a semilinear model for the flow in gas networks

The flow of gas through networks of pipes can be modelled 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 for general graphs and prove that the state of the observer system converges to the original state exponentially fast. Numerical experiments confirm the theoretical findings.