TY - JOUR
T1 - A survey of average cost problems in deterministic discrete-time control systems
AU - Hernández-Lerma, Onésimo
AU - Laura-Guarachi, Leonardo R.
AU - Mendoza-Palacios, Saul
N1 - Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2023/6/1
Y1 - 2023/6/1
N2 - 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.
AB - 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.
KW - Average cost
KW - Discrete time systems
KW - Dynamic programming
KW - Markov decision processes
UR - http://www.scopus.com/inward/record.url?scp=85144760268&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2022.126906
DO - 10.1016/j.jmaa.2022.126906
M3 - Artículo
AN - SCOPUS:85144760268
SN - 0022-247X
VL - 522
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 126906
ER -