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Continuity of optimal control costs and its application to weak KAM theory

  • Author(s): Agrachev, Andrei
  • Lee, Paul W.
  • et al.
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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