Linear–quadratic mean-field game for stochastic systems with partial observation

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-09-21 DOI:10.1016/j.automatica.2024.111821

Min Li , Na Li , Zhen Wu

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Abstract

This paper is concerned with a class of linear–quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each agent follows a linear stochastic differential equation driven by the individual noise, and all agents are coupled together via the control average term. By studying the associated mean-field game and using the backward separation principle with a state decomposition technique, the decentralized optimal control can be obtained in the open-loop form through a forward–backward stochastic differential equation with the conditional expectation. The optimal filtering equation is also provided. Thanks to the decoupling method, the decentralized optimal control can also be further presented as the feedback of state filtering via the Riccati equation. The explicit solution of the control average limit is given, and the consistency condition system is discussed. Moreover, the related $ɛ$ -Nash equilibrium property is verified. To illustrate the good performance of theoretical results, an example in finance is studied.

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部分观测随机系统的线性-二次均场博弈

本文研究的是一类具有部分信息的线性-二次随机大群体问题，在这类问题中，个体代理只能获得与状态相关的噪声观测过程。每个代理的动态遵循由个体噪声驱动的线性随机微分方程，所有代理通过控制平均项耦合在一起。通过研究相关的均场博弈，并利用后向分离原理和状态分解技术，可以通过带条件期望的前向-后向随机微分方程得到开环形式的分散最优控制。同时还提供了最优滤波方程。由于采用了解耦方法，分散最优控制还可以通过里卡提方程进一步表示为状态滤波的反馈。给出了控制平均极限的显式解，并讨论了一致性条件系统。此外，还验证了相关的ɛ-纳什均衡特性。为了说明理论结果的良好性能，我们研究了一个金融方面的例子。

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

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.