连续时间有限状态平均场对策的控制理论研究

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-03-12 DOI:10.3934/mcrf.2022029

Y. Averboukh

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引用次数: 1

摘要

本文研究了连续时间有限状态平均场对策的解与参与人初始分布的依赖关系。我们的方法依赖于平均场博弈的价值多功能概念，这是一个映射，分配给初始时间和初始分布，即与平均场博弈的解相对应的代表性参与者的一组预期结果。利用有限状态平均场对策作为混合约束控制问题的重新表述，利用生存理论给出了给定多函数是值多函数的充分条件。通过对某控制系统的后向可达性集刻画了最大多函数(即分配给平均场对策解的全部值的初始时间和初始分布的映射)。

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Control theory approach to continuous-time finite state mean field games

In the paper, we study the dependence of solutions of the continuous-time finite state mean field game on initial distribution of players. Our approach relies on the concept of value multifunction of the mean field game that is a mapping assigning to an initial time and an initial distribution a set of expected outcomes of the representative player corresponding to solutions of the mean field game. Using the reformulation of the finite state mean field game as a control problem with mixed constraints, we give the sufficient condition on a given multifunction to be a value multifunction in the terms of the viability theory. The maximal multifunction (i.e., the mapping assigning to an initial time and an initial distribution the whole set of values corresponding to solutions of the mean field game) is characterized via the backward attainability set for the certain control system.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.