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Challenges in optimal control problems for gas and fluid flow in networks of pipes and canals: From modeling to industrial applications

  • 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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Metadaten
Verfasserangaben:Falk Hante, Günter Leugering, Alexander Martin, Lars Schewe, Martin Schmidt
Dokumentart:Wissenschaftlicher Artikel
Sprache:Englisch
Datum der Veröffentlichung (online):09.12.2016
Datum der Erstveröffentlichung:09.12.2016
Datum der Freischaltung:09.12.2016
Freies Schlagwort / Tag:Euler and St. Venant equations; Networks; hierarchy of models; optimal control; pipes
Seitenzahl:40
Institute:Friedrich-Alexander-Universität Erlangen-Nürnberg
Teilprojekte:A03
A05
B07
B08