A survey of average cost problems in deterministic discrete-time control systems

被引：5

作者：

Hernandez-Lerma, Onesimo ^{[1
]}

Laura-Guarachi, Leonardo R. ^{[2
]}

Mendoza-Palacios, Saul ^{[3
]}

机构：

[1] CINVESTAV, Dept Math, Ave Politecn 2508, Mexico City 07360, DF, Mexico

[2] SEPI ESE IPN, Plan Agua Prieta 66, Mexico City 11340, DF, Mexico

[3] Ctr Invest & Docencia Econ, Carretera Mexico Toluca 3655, Mexico City 01210, DF, Mexico

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 522卷 / 01期

关键词：

Average cost; Markov decision processes; Dynamic programming; Discrete time systems; MARKOV DECISION-PROCESSES; STABILIZATION; FORMULATIONS; THEOREM; GROWTH;

D O I：

10.1016/j.jmaa.2022.126906

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns optimal control problems for infinite-horizon discrete-time deterministic systems with the long-run average cost (AC) criterion. This optimality criterion can be traced back to a paper by Bellman [6] for a class of Markov decision processes (MDPs). We present a survey of some of the main approaches to study the AC problem, namely, the AC optimality (or dynamic programming) equation, the steady state approach, and the vanishing discount approach, emphasizing the difference between the deterministic control problem and the corresponding (stochastic) MDP. Several examples illustrate these approaches and related results. We also state some open problems. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：24