Mean-field social optimization for linear–quadratic Markov switching systems with Poisson jumps

IF 2.6 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

European Journal of Control Pub Date : 2025-08-30 DOI:10.1016/j.ejcon.2025.101356

Ruimin Xu , Jingyu Zhang , Kaiyue Dong , Haiyang Wang

引用次数: 0

Abstract

This paper investigates social optima for linear–quadratic-Gaussian (LQG) games of stochastic mean-field Markov regime-switching systems with jump diffusion processes, where the individual agents of the system are coupled via individual state dynamics and cost functionals. A verification theorem in the form of maximum principle is established, specifying the sufficient conditions for optimality. A set of decentralized strategies is designed according to the feedback representation of optimal control. The decentralized strategies are proved to be asymptotically social optimal. As an illustration, a numerical example is provided to show the consistency of the mean-field estimation and the influence of the population’s collective behaviors.

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带泊松跳变的线性二次马尔可夫切换系统的平均场社会优化

本文研究了具有跳跃扩散过程的随机平均场马尔可夫状态切换系统的线性二次高斯（LQG）对策的社会最优性，其中系统的各个agent通过个体状态动力学和代价函数耦合。建立了极大值原理形式的验证定理，给出了最优性的充分条件。根据最优控制的反馈表示，设计了一组分散策略。证明了分散策略是渐近社会最优的。作为说明，给出了一个数值例子来说明平均场估计的一致性和群体集体行为的影响。

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.