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On Numerical Solution of Singularly Perturbed Optimal Control Problems

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Abstract

We study singularly perturbed optimal control problems in which optimal controls may take the form of rapidly oscillating functions. Such rapidly oscillating controls can be constructed on the basis of solutions of certain approximating averaged optimal control problems. We proposed an iterative algorithm for finding numerical solutions of the latter. The effectiveness of the algorithms is demonstrated with the help of numerical examples.

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Acknowledgements

The authors would like to thank Lars Grüne for his participation in the original discussion of the project.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Engineering, Macquarie University, Sydney, NSW, 2109, Australia

    Vladimir Gaitsgory

  2. Institut für Mathematik und Rechneranwendung, Fakultät für Luft- und Raumfahrttechnik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Matthias Gerdts

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  1. Vladimir Gaitsgory
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  2. Matthias Gerdts
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Correspondence to Matthias Gerdts.

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Communicated by Asen L. Dontchev.

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Gaitsgory, V., Gerdts, M. On Numerical Solution of Singularly Perturbed Optimal Control Problems. J Optim Theory Appl 174, 762–784 (2017). https://doi.org/10.1007/s10957-017-1138-8

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