Stability of a turnpike phenomenon for a class of optimal control systems in metric spaces

Abstract

We study a turnpike property of approximate solutions of a discrete-time control system with a compact metric space of states. In our recent work we prove this turnpike property and show that it is stable under perturbations of an objective function. In the present paper we improve this turnpike result by showing that it also holds for those solutions defined on a finite interval (domain) which are approximately optimal on all subintervals of the domain that have a fixed length which does not depend on the length of the whole domain.