Abstract
We prove continuity of certain cost functions arising from optimal control of affine control systems. We give sharp sufficient conditions for this continuity. As an application, we prove a version of weak KAM theorem and consider the Aubry–Mather problems corresponding to these systems.
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Acknowledgements
Andrei Agrachev was supported by PRIN and Paul W. Y. Lee was supported by the NSERC postdoctoral fellowship.
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Communicated by L. Ambrosio.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Agrachev, A., Lee, P.W.Y. Continuity of optimal control costs and its application to weak KAM theory. Calc. Var. 39, 213–232 (2010). https://doi.org/10.1007/s00526-010-0308-4
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DOI: https://doi.org/10.1007/s00526-010-0308-4