System State Estimation for Gas Flows Using Observers Based on Density Measurements

We study how to estimate the system state in transient operations of pipe networks for gas transport. To this end we set up an observer system based on distributed measurements of the density. Using an extension of the relative energy method we show that the state of the observer system converges exponentially in the long time limit to the original system state, i.e., we reconstruct the complete system state from distributed measurements of only one of the state variables. This result can be shown for a single pipe as well as for star-shaped networks.