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.

翻译：我们考虑一维气压欧拉方程描述的天然气管道流动状态估计问题。为重构系统状态，基于单个状态变量的分布式测量，构建了Luenberger型观测器系统。首先，证明在单管道及一般网络中，当初始边界数据满足小性条件和相容性条件时，观测器系统与原系统存在Lipschitz连续半全局解。其次，基于相对能量方法的推广，证明在长时间极限下观测器系统状态指数收敛至原系统状态——该结论对单管道与星形网络均成立。