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

  • 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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Metadaten
Author:Falk Hante
Parent Title (German):Mathematical Modelling, Optimization, Analytic and Numerical Solutions, Springer Series on Industrial and Applied Mathematics, 2020
Document Type:Article
Language:English
Date of Publication (online):2018/09/14
Date of first Publication:2018/09/19
Release Date:2018/09/19
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:A03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International