Title: Continuity of optimal control costs and its application to weak KAM theory
Authors: A.A. Agrachev, P. Lee
Journal title: Calculus of Variations and Part. Dif. Eq.
Year: 2010
Volume: 39
Pages: 213-232
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.