Systems, Control and Mean Field Games on Networks

网络上的系统、控制和平均场博弈

• 批准号: RGPIN-2019-05336
• 负责人: Caines, Peter
• 金额: $ 4.01万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=738204
• 关键词: Systems; Control; Mean; Field; Games

Mean Field Game (MFG) theory for large agent population systems has revolutionized both non-cooperative game theory and large scale systems control. The core of the MFG Nash equilibrium theory is the pair of PDEs consisting of (i) the Hamilton-Jacobi-Bellman (HJB) equation of optimal control for a generic agent, and (ii) the Fokker-Planck-Kolmogorov (FPK) equation (or the equivalent stochastic SDE) for the probability distribution of the state of such an agent, both linked by that distribution. In this program three new directions are proposed in the analysis and control of complex large scale systems: respectively, the new Graphon Network Control (GNC) theory, the newly introduced Graphon Mean Field Game (GMFG) theory, and their various New Application domains; their key common feature is the extension of MFG based methods to systems on networks. First, the advancement is planned for our newly introduced (MFG based) GNC theory of the control of complex network systems using infinite node graph limit (graphon) theory and infinite dimensional systems control theory. This methodology permits the design of controls for large complex finite network systems via their derivation for the simpler infinite limit systems. Research topics in GNC theory include advances in graphon system controllability, observability, and system identification. Second, we propose research in the new direction in MFG theory recently introduced by the proposer which greatly generalizes standard theory so that it applies to populations distributed on unbounded networks where the equilibria are given by the so-called Graphon MFG (GMFG) equations. Key areas of research in GMFG theory now include existence and uniqueness theory, epsilon - Nash approximation theory, and GMFG systems classification via graphon structures, together with major-minor agent system theory, systems with hybrid agents with distinct modes of behaviour and systems where the major agents are not completely observable. Third, new applications domains will be investigated, including: (i) GNC: Methodologies for data based GNC from real world networks, e.g. electricity grids, and neuronal and social networks. (ii) MFG: applications of state estimation (i.e. filtering) theory to finance with hybrid dynamical major agents and large population minor agents. (iii) GMFG: Modelling, estimation, dynamics and control will be employed in applications to instances of systems in finance, economics, transportation, epidemiology, neuronal systems, flocking, evolutionary games and to the formation and decay of coalitions.

大智能体种群系统的平均场博弈(MFG)理论对非合作博弈理论和大系统控制都具有革命性的意义。MFG Nash均衡理论的核心是由两个偏微分方程组成的：(I)仿制药的最优控制的Hamilton-Jacobi-Bellman(HJB)方程，和(Ii)这种药状态的概率分布的Fokker-Planck-Kolmogorov(FPK)方程(或等价的随机SDE)，两者都由该分布联系在一起。本课题提出了复杂大系统分析和控制的三个新方向：新的图形网络控制(GNC)理论、新引入的图形平均场博弈(GMFG)理论及其各种新的应用领域，它们的主要共同特点是将基于GMFG的方法扩展到网络系统。首先，利用无限结点图极限理论和无限维系统控制理论，对我们新引入的(基于制造流图的)复杂网络系统控制的GNC理论进行了改进。这种方法允许通过对更简单的无限极限系统的推导来设计大型复杂有限网络系统的控制。GNC理论的研究主题包括在图形系统能控性、可观性和系统辨识方面的进展。其次，我们建议在作者最近引入的MFG理论的新方向上进行研究，该方向极大地推广了标准理论，使其适用于分布在无界网络上的种群，其中均衡由所谓的Graphon MFG(GMFG)方程给出。目前GMFG理论的主要研究领域包括存在唯一性理论、epsilon-Nash逼近理论、基于石墨结构的GMFG系统分类、主-次智能体系统理论、具有不同行为模式的混合智能体系统和主智能体不完全可观测的系统。第三，将研究新的应用领域，包括：(I)GNC：来自真实世界网络(如电网、神经网络和社会网络)的基于数据的GNC方法。(Ii)MFG：状态估计(即过滤)理论在具有混合动态主要代理和大群体次要代理的金融中的应用。(3)GMFG：将在金融、经济、运输、流行病学、神经系统、集群、进化博弈以及联盟的形成和衰败的系统实例中应用建模、估计、动力学和控制。