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Mixed-Integer Optimal Control for PDEs: Relaxation via Differential Inclusions and Applications to Gas Network Optimization

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Mathematical Modelling, Optimization, Analytic and Numerical Solutions

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

Abstract

We show that mixed-integer control problems for evolution type partial differential equations can be regarded as operator differential inclusions. This yields a relaxation result including a characterization of the optimal value for mixed-integer optimal control problems with control constraints. The theory is related to partial outer convexification and sum-up rounding methods. The results are applied to optimal valve switching control for gas pipeline operations. A numerical example illustrates the approach.

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Acknowledgements

This work was supported by the DFG grant CRC/Transregio 154, project A03.

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Authors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik 2, Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Falk M. Hante

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  1. Falk M. Hante
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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. Laboratory Math, J.A. Dieudonné, University Côte d’Azur, Nice, France

    René Pierre 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. (2020). Mixed-Integer Optimal Control for PDEs: Relaxation via Differential Inclusions and Applications to Gas Network Optimization. In: Manchanda, P., Lozi, R., Siddiqi, A. (eds) Mathematical Modelling, Optimization, Analytic and Numerical Solutions. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-0928-5_7

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