LINEAR PROGRAMMING BASED OPTIMALITY CONDITIONS AND APPROXIMATE SOLUTION OF A DETERMINISTIC INFINITE HORIZON DISCOUNTED OPTIMAL CONTROL PROBLEM IN DISCRETE TIME

摘要

It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual, the latter taking the form of a certain max-min problem. In the present paper, we use these results to establish necessary and sufficient optimality conditions for this optimal control problem and to investigate a way how the latter can be used for the construction of a near optimal control.