Convergence of Solutions of Optimal Control Problems with Discounting on Large Intervals in the Regions Close to the Endpoints

摘要

In the present paper we analyze the convergence of approximate solutions of a discrete-time optimal control system with discounting. The states of this system belong to a compact metric space and no convexity (concavity) assumption is assumed. Recently it was shown that approximate solutions are determined mainly by the objective function, except in regions close to the endpoints of the time interval. In this paper we show that approximate solutions on large intervals converge to solutions of corresponding infinite horizon problems in regions close to the endpoints of the time intervals.