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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=715472
• 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.

大智能体群体系统的平均场博弈理论对非合作博弈理论和大规模系统控制都产生了革命性的影响。MFG纳什均衡理论的核心是一对偏微分方程，由(i)通用代理的最优控制的Hamilton-Jacobi-Bellman （HJB）方程和（ii）这种代理状态的概率分布的Fokker-Planck-Kolmogorov （FPK）方程（或等效的随机SDE）组成，两者由该分布联系起来。本文提出了复杂大系统分析与控制的三个新方向：分别是新的石墨网络控制理论（GNC）和新引入的石墨平均场博弈理论（GMFG）及其各种新的应用领域；它们的主要共同特征是将基于MFG的方法扩展到网络上的系统。