Two system transformation data-driven algorithms for linear quadratic mean-field games

IF 2.5 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

European Journal of Control Pub Date : 2025-04-12 DOI:10.1016/j.ejcon.2025.101226

Xun Li , Guangchen Wang , Yu Wang , Jie Xiong , Heng Zhang

引用次数: 0

Abstract

This paper studies a class of continuous-time linear quadratic (LQ) mean-field game problems. We develop two system transformation data-driven algorithms to approximate the decentralized strategies of the LQ mean-field games. The main feature of the obtained data-driven algorithms is that they eliminate the requirement on all system matrices. First, we transform the original stochastic system into an ordinary differential equation (ODE). Subsequently, we construct some Kronecker product-based matrices by the input/state data of the ODE. By virtue of these matrices, we implement a model-based policy iteration (PI) algorithm and a model-based value iteration (VI) algorithm in data-driven fashions. In addition, we also demonstrate the convergence of these two data-driven algorithms under some mild conditions. Finally, we illustrate the practicality of our algorithms via two numerical examples.

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线性二次平均场对策的两种系统变换数据驱动算法

研究了一类连续时间线性二次（LQ）平均场对策问题。我们开发了两种系统转换数据驱动算法来近似LQ平均场博弈的分散策略。所获得的数据驱动算法的主要特点是它们消除了对所有系统矩阵的需求。首先，我们将原始随机系统转化为常微分方程。随后，我们利用ODE的输入/状态数据构造了一些基于Kronecker积的矩阵。利用这些矩阵，我们以数据驱动的方式实现了基于模型的策略迭代（PI）算法和基于模型的值迭代（VI）算法。此外，我们还证明了这两种数据驱动算法在一些温和条件下的收敛性。最后，我们通过两个数值例子说明了我们算法的实用性。

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

European Journal of Control 工程技术-自动化与控制系统

CiteScore

5.80

自引率

5.90%

发文量

131

审稿时长

1 months

期刊介绍： The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field. The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering. The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications. Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results. The design and implementation of a successful control system requires the use of a range of techniques: Modelling Robustness Analysis Identification Optimization Control Law Design Numerical analysis Fault Detection, and so on.