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：我们研究由一维正压欧拉方程建模的输气管道流动状态估计问题。为重构系统状态，我们基于单一状态变量的分布式测量构建了Luenberger型观测器系统。首先，我们证明了在满足小性和相容性条件的初始边界数据下，观测器系统与原系统在单管道及一般网络中存在Lipschitz连续半全局解。其次，基于相对能量方法的扩展，我们证明了观测器系统状态在长时间极限下以指数速率收敛于原系统状态。该结论在单管道及星形网络结构中均得到验证。