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Continuity of optimal control costs and its application to weak KAM theory
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https://doi.org/10.1007/s00526-010-0308-4Abstract
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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