天然气网络中掺氢管道流动的观测器：指数同步
An Observer for pipeline flow with hydrogen blending in gas networks: exponential synchronization
AI总结：
本文研究掺氢天然气管网流动的状态估计问题，提出基于节点测量的观测器系统，并利用带指数权重的李雅普诺夫函数证明其在精确测量下指数收敛、在测量误差下有界逼近。
摘要：
我们考虑在天然气中掺入氢气的管网中气体流动的状态估计问题。该流动由图上的拟线性等温欧拉方程耦合一个平流方程来建模。管道连接处的顶点流动由代数节点条件控制。状态通过一个使用节点测量值的观测器系统来近似。我们证明，如果测量值是精确的，观测器系统的状态在 $L^2$ 范数下以指数速度收敛到原始系统状态。如果存在测量误差，我们证明观测器状态以与最大测量误差成比例的误差逼近原始系统状态。同步结果的证明使用了带指数权重的李雅普诺夫函数。
英文摘要：
We consider a state estimation problem for gas flows in pipeline networks where hydrogen is blended into the natural gas. The flow is modeled by the quasi-linear isothermal Euler equations coupled to an advection equation on a graph. The flow through the vertices where the pipes are connected is governed by algebraic node conditions. The state is approximated by an observer system that uses nodal measurements. We prove that the state of the observer system converges to the original system state exponentially fast in the $L^2$-norm if the measurements are exact. If measurement errors are present we show that the observer state approximates the original system state up to an error that is proportional to the maximal measurement error. The proof of the synchronization result uses Lyapunov functions with exponential weights.
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