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

  • Falk M. HanteEmail author
  • Günter Leugering
  • Alexander Martin
  • Lars Schewe
  • Martin Schmidt
Part of the Industrial and Applied Mathematics book series (INAMA)


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.


Networks Pipes Canals Euler and St. Venant equations Hierarchy of models Domain decomposition Controllability Optimal control 



The authors thank the Deutsche Forschungsgemeinschaft for their support within projects A03, A05, B07, and B08 in the Sonderforschungsbereich/Transregio 154 Mathematical Modeling, Simulation and Optimization using the Example of Gas Networks. In addition, parts of this research were performed as part of the Energie Campus Nürnberg and supported by funding through the “Aufbruch Bayern (Bavaria on the move)” initiative of the state of Bavaria.


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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  • Falk M. Hante
    • 1
    Email author
  • Günter Leugering
    • 1
  • Alexander Martin
    • 2
  • Lars Schewe
    • 2
  • Martin Schmidt
    • 2
    • 3
  1. 1.Lehrstuhl Angewandte Mathematik IIFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  2. 2.Discrete OptimizationFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  3. 3.Energie Campus NürnbergNürnbergGermany

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