Optimal Control Problems with Singleton Turnpikes

Abstract

In this chapter we study the structure of solutions of a discrete-time control system with a compact metric space of states X which arises in economic dynamics. This control system is described by a nonempty closed set $\Omega \subset X \times X$ which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous objective function $v:X\times X \to R^1$ which determines an optimality criterion. We show the stability of the turnpike phenomenon under small perturbations of the objective function v and the set Ω.