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arXiv · 2003.05298

A space-time relaxation for $L^1$ optimal control problems

Malte Kampschulte
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Abstract

We introduce a vertical type relaxation for optimal control problems which only have $L^1$-coercivity for their controls. Usually such problems feature both concentration and oscillation effects at the same time. We propose relaxing to an associated problem in space-time, where the controls can be considered bounded in $L^\infty$, greatly simplifying any analysis. In this relaxation, concentrations are transformed into vertical parts and oscillations can be dealt with using Young-measures. This technique can be extended to similar problems on infinite-dimensional spaces.

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Malte Kampschulte. 2020-03-11. A space-time relaxation for $L^1$ optimal control problems. https://arxiv.org/abs/2003.05298

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