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

  • Andrei AgrachevEmail author
  • Paul W. Y. Lee
Open Access
Article

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.

Mathematics Subject Classification (2000)

35F21 49L25 

Notes

Acknowledgements

Andrei Agrachev was supported by PRIN and Paul W. Y. Lee was supported by the NSERC postdoctoral fellowship.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2010

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.International School for Advanced StudiesTriesteItaly
  2. 2.Steklov Mathematical InstituteMoscowRussia
  3. 3.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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