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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

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Industrial Mathematics and Complex Systems

Part of the book series: Industrial and Applied Mathematics ((INAMA))

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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Acknowledgements

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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Authors and Affiliations

  1. Lehrstuhl Angewandte Mathematik II, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstr. 11, 91058, Erlangen, Germany

    Falk M. Hante & Günter Leugering

  2. Discrete Optimization, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstr. 11, 91058, Erlangen, Germany

    Alexander Martin, Lars Schewe & Martin Schmidt

  3. Energie Campus Nürnberg, Fürther Str. 250, 90429, Nürnberg, Germany

    Martin Schmidt

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  1. Falk M. Hante
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  2. Günter Leugering
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  4. Lars Schewe
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Correspondence to Falk M. Hante .

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Editors and Affiliations

  1. Department of Mathematics, Guru Nanak Dev University, Amritsar, Punjab, India

    Pammy Manchanda

  2. CNRS, Dieudonné Center of Mathematics, University Côte d’Azur, Nice, France

    René Lozi

  3. School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, India

    Abul Hasan Siddiqi

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Hante, F.M., Leugering, G., Martin, A., Schewe, L., Schmidt, M. (2017). Challenges in Optimal Control Problems for Gas and Fluid Flow in Networks of Pipes and Canals: From Modeling to Industrial Applications. In: Manchanda, P., Lozi, R., Siddiqi, A. (eds) Industrial Mathematics and Complex Systems. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3758-0_5

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