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

Falk Hante, Günter Leugering, Alexander Martin, Lars Schewe, Martin Schmidt

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract / Description of output

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.
Original languageEnglish
Title of host publicationIndustrial Mathematics and Complex Systems: Emerging Mathematical Models, Methods and Algorithms
EditorsPammy Manchanda, René Lozi, Abul Hasan Siddiqi
Place of PublicationSingapore
PublisherSpringer Singapore
Number of pages46
ISBN (Print)978-981-10-3758-0
Publication statusPublished - 2017

Publication series

NameIndustrial and Applied Mathematics
PublisherSpringer Singapore

Keywords / Materials (for Non-textual outputs)

  • Networks, pipes, canals, Euler and St. Venant equations, hierarchy of models, domain decomposition, controllability, optimal control.


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