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Robust error estimates for regularization and discretization of bang–bang control problems

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Abstract

We investigate the simultaneous regularization and discretization of an optimal control problem with pointwise control constraints. Typically such problems exhibit bang–bang solutions: the optimal control almost everywhere takes values at the control bounds. We derive discretization error estimates that are robust with respect to the regularization parameter. These estimates can be used to make an optimal choice of the regularization parameter with respect to discretization error estimates.

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Acknowledgments

This work was partially funded by Austrian Science Fund (FWF) Grant P23848.

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  1. Institut für Mathematik, Universität Würzburg, 97074 , Würzburg, Germany

    Daniel Wachsmuth

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  1. Daniel Wachsmuth
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Correspondence to Daniel Wachsmuth.

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Wachsmuth, D. Robust error estimates for regularization and discretization of bang–bang control problems. Comput Optim Appl 62, 271–289 (2015). https://doi.org/10.1007/s10589-014-9645-0

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  • DOI: https://doi.org/10.1007/s10589-014-9645-0

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