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Euler discretization for a class of nonlinear optimal control problems with control appearing linearly

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Abstract

We investigate Euler discretization for a class of optimal control problems with a nonlinear cost functional of Mayer type, a nonlinear system equation with control appearing linearly and constraints defined by lower and upper bounds for the controls. Under the assumption that the cost functional satisfies a growth condition we prove for the discrete solutions Hölder type error estimates w.r.t. the mesh size of the discretization. If a stronger second-order optimality condition is satisfied the order of convergence can be improved. Numerical experiments confirm the theoretical findings.

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Acknowledgements

The authors would like to thank the anonymous referees for their careful reading of the manuscript and their constructive and valuable suggestions and comments.

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Authors and Affiliations

  1. Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07740, Jena, Germany

    Walter Alt

  2. Institut für Mathematik, Brandenburgische Technische Universität Cottbus-Senftenberg, 03013, Cottbus, Germany

    Ursula Felgenhauer

  3. Siemens AG, Research in Digitalization and Automation, 81739, Munich, Germany

    Martin Seydenschwanz

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  1. Walter Alt
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  2. Ursula Felgenhauer
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  3. Martin Seydenschwanz
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Correspondence to Walter Alt.

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Alt, W., Felgenhauer, U. & Seydenschwanz, M. Euler discretization for a class of nonlinear optimal control problems with control appearing linearly. Comput Optim Appl 69, 825–856 (2018). https://doi.org/10.1007/s10589-017-9969-7

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