Structure of approximate solutions of discrete time optimal control Bolza problems on large intervals

In this paper we study the structure of approximate solutions of an autonomous discrete-time optimal control system with a compact metric space of states. These optimal control systems are discrete-time analogs of Bolza problems in the calculus of variations. We obtain the full description of approximate solutions of these problems on large intervals. This description shows that on large intervals the approximate solutions are determined mainly by our optimality criterion and are essentially independent of the choice of time intervals and data.