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2017 | OriginalPaper | Buchkapitel

5. Challenges in Optimal Control Problems for Gas and Fluid Flow in Networks of Pipes and Canals: From Modeling to Industrial Applications

verfasst von : Falk M. Hante, Günter Leugering, Alexander Martin, Lars Schewe, Martin Schmidt

Erschienen in: Industrial Mathematics and Complex Systems

Verlag: Springer Singapore

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Abstract

We consider optimal control problems for the flow of gas or fresh water in pipe networks as well as drainage or sewer systems in open canals. The equations of motion are taken to be represented by the nonlinear isothermal Euler gas equations, the water hammer equations, or the St. Venant equations for flow. We formulate model hierarchies and derive an abstract model for such network flow problems including pipes, junctions, and controllable elements such as valves, weirs, pumps, as well as compressors. We use the abstract model to give an overview of the known results and challenges concerning equilibria, well-posedness, controllability, and optimal control. A major challenge concerning the optimization is to deal with switching on–off states that are inherent to controllable devices in such applications combined with continuous simulation and optimization of the gas flow. We formulate the corresponding mixed-integer nonlinear optimal control problems and outline a decomposition approach as a solution technique.

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Titel: Challenges in Optimal Control Problems for Gas and Fluid Flow in Networks of Pipes and Canals: From Modeling to Industrial Applications
verfasst von: Falk M. Hante
Günter Leugering
Alexander Martin
Lars Schewe
Martin Schmidt
Verlag: Springer Singapore
Buch: Industrial Mathematics and Complex Systems
Print ISBN: 978-981-10-3757-3

Electronic ISBN: 978-981-10-3758-0

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-981-10-3758-0_5

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