Introduction

Abstract

The study of the existence and the structure of solutions of optimal control problems defined on infinite intervals and on sufficiently large intervals has recently been a rapidly growing area of research. See, for example, [3, 4, 7–11, 13, 14, 16, 18–22, 25, 27, 32–34, 36, 44, 45, 52, 55] and the references mentioned therein. These problems arise in engineering [1, 23, 57], in models of economic growth [2, 5, 12, 13, 17, 22, 26, 31, 35, 38, 39, 40, 45], in infinite discrete models of solid-state physics related to dislocations in one-dimensional crystals [6, 41] and in the theory of thermodynamical equilibrium for materials [15, 24, 28–30]. In this chapter we discuss the structure of solutions of a discrete-time optimal control system describing a general model of economic dynamics.