Turnpike results for discrete-time optimal control systems arising in economic dynamics

Abstract

In this work we study the structure of approximate solutions of an autonomous discrete-time control system with a compact metric space of states X . This control system is described by a bounded upper semicontinuous function v : X × X → R 1 which determines an optimality criterion and by a nonempty closed set Ω ⊂ X × X which determines a class of admissible trajectories (programs). We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. For when X is a compact convex subset of a finite-dimensional Euclidean space, the set Ω is convex and the function v is strictly concave we obtain a full description of the structure of approximate solutions.