Continuity of Optimal Control Costs and its application to Weak KAM Theory

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.

arXiv comment23 pages, 1 figures, added explanations in the proofs of the main theorem and the example