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.

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