Maximum principle for discrete-time stochastic optimal control problem and stochastic game

IF 0.9 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI:10.3934/mcrf.2021031

Zhen Wu, Feng Zhang

引用次数: 15

Abstract

This paper is first concerned with one kind of discrete-time stochastic optimal control problem with convex control domains, for which necessary condition in the form of Pontryagin's maximum principle and sufficient condition of optimality are derived. The results are then extended to two kinds of discrete-time stochastic games. Two illustrative examples are studied, for which the explicit optimal strategies are given. This paper establishes a rigorous version of discrete-time stochastic maximum principle in a clear and concise way and paves a road for further related topics.

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离散时间随机最优控制问题和随机对策的极大值原理

本文首先研究了一类具有凸控制域的离散时间随机最优控制问题，给出了该问题的庞特里亚金极大值原理形式的必要条件和最优性的充分条件。然后将结果推广到两类离散时间随机对策。研究了两个实例，给出了明确的最优策略。本文以清晰简洁的方式建立了离散时间随机极大值原理的严格版本，为进一步开展相关课题奠定了基础。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.