Reference

Marc Quincampoix, and Jérôme Renault, "On the existence of a limit value in some non expansive optimal control problems.", SIAM Journals, vol. 49, n. 5, 2011, pp. 2118–2132.

Abstract

We investigate the limit of the average value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state, as is usually done in the literature.