An Observer for Pipeline Flow with Hydrogen Blending in Gas Networks: Exponential Synchronization

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-08-07 DOI:10.1137/23m1563840

Martin Gugat, Jan Giesselmann

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2273-2296, August 2024.
Abstract. 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 [math]-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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天然气网络中混有氢气的管道流量观测器：指数同步

SIAM 控制与优化期刊》第 62 卷第 4 期第 2273-2296 页，2024 年 8 月。摘要我们考虑了在天然气中掺入氢气的管网中天然气流的状态估计问题。气流模型是准线性等温欧拉方程和图上的平流方程。流经管道连接顶点的气流受代数节点条件支配。状态由使用节点测量的观测器系统近似表示。我们证明，如果测量精确，观察者系统的状态会以指数[math]-norm 的速度收敛到原始系统状态。如果存在测量误差，我们将证明观测器状态近似于原始系统状态，最大误差与最大测量误差成正比。同步结果的证明使用了具有指数权重的 Lyapunov 函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.