Infinite-Horizon Discrete-Time Optimal Control Problems

摘要: The study of optimal control problems defined on infinite intervals has recently been a rapidly growing area research. These arise in engineering [1,2], models economic growth [5,16,26–28,40], discrete solid-state physics related to dislocations one-dimensional crystals [3,31], and the theory thermodynamical equilibrium for materials [7,14,17–20,34,35,37]. In this survey, we consider discrete-time problems. Sections 2 3 are devoted autonomous discretetime systems compact metric spaces. Sec. 2, present two fundamental tools an horizon: reduction finite cost representation formula established [9]. 3, number results obtained [32,33] which establish existence weakly solutions horizon describe their structure. turnpike theorem infinite-dimensional system with convex function [39] is considered 4. 5, discuss generalization result class nonautonomous nonconvex [41]. Section 6 Lagrange multipliers periodic [15]. 7, finite-state Markov decision processes [11,13].