Towards the optimal control of Markov chains with constraints

被引：18

作者：

Miller, Boris ^{[1
,2
]}

Miller, Gregory ^{[3
]}

Siemenikhin, Konstantin ^{[4
]}

机构：

[1] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia

[2] Inst Informat Transmiss Problems, Moscow 127994, Russia

[3] RAS, Inst Informat Problems, Moscow 119333, Russia

[4] Moscow Inst Aviat Technol, Probabil Theory Dept, Moscow 125993, Russia

来源：

AUTOMATICA | 2010年 / 46卷 / 09期

基金：

澳大利亚研究理事会;

关键词：

Markov chains; Constraints; Optimal control; Maximum principle; DECISION-PROCESSES;

D O I：

10.1016/j.automatica.2010.06.003

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

An optimal control problem with constraints is considered on a finite interval fora non-stationary Markov chain with a finite state space. The constraints are given as a set of inequalities. The optimal solution existence is proved under a natural assumption that the set of admissible controls is non-empty. The stochastic control problem is reduced to a deterministic one and it is shown that the optimal solution satisfies the maximum principle, moreover it can be chosen within a class of Markov controls. On the basis of this result an approach to the numerical solution is proposed and its implementation is illustrated by examples. (c) 2010 Published by Elsevier Ltd

引用

页码：1495 / 1502

页数：8

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