Mean Field, Distributed and Hybrid Control Systems

平均场、分布式和混合控制系统

• 批准号: RGPIN-2014-04373
• 负责人: Caines, Peter
• 金额: $ 4.44万
• 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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=646684
• 关键词: Mean; Field; Distributed; Hybrid; Control

The overall objective of the proposed research program is to advance the fundamental analysis and design of control systems for (i) distributed large scale systems (i.e. systems without centralized control or information which are of high state cardinality) and (ii) systems with both continuous and discrete states and dynamics. Such systems are ubiquitous in the contemporary networked information and computation based environment and so their enhanced control and optimization would bring great benefits.** Mean Field Game (MFG) theory constitutes a fundamental new methodology for the analysis and design of distributed large scale systems which originated in NSERC supported work by the proposer together with his student Minyi Huang and the co-supervisor Roland Malhame' during 2003 - 2007, and, independently, by J.-M. Lasry and P.- L. Lions during 2006 - 2007. Since then the field has undergone vigorous development due to the continuing contributions of these and other researchers world wide; moreover, potential applications of MFG methodology and new, challenging problems are continually being discovered in a vast range of domains. * * MFG theory establishes the existence of approximate Nash equilibria generated solely by local feedback for stochastic dynamical system agents in games involving large numbers of agents. The equilibria and the feedback laws applied in the finite population case are obtained via the far simpler solutions to the fundamental infinite population MFG Hamilton-Jacobi-Bellman and (McKean-Vlasov)-Fokker-Planck-Kolmogorov PDEs which are linked by the state distribution of a generic agent, otherwise known as the system's mean field. As the number of agents goes to infinity the approximation error goes to zero.** This proposal maps a five year research program on the following themes: (a) Estimation in MF Systems: a central problem for MF system theory is that partially observed systems with major agents (i.e. non-asymptotically vanishing with population size) have stochastic mean fields which must be recursively estimated along with the major agents' partially observed states. A state estimation theory for non-linear partially observed MFG systems with major and minor agents, and hence stochastic mean fields, will be of great significance and will be exploited in the development of (b) Spatially Dynamic MF Systems, (c) Coalition Formation in MF Systems, (d) Locally Infinite and Large Scale Topology MF Systems, and (e) MF Market and Auction Models.**In large areas of systems and control engineering hybrid control systems are synonymous with advanced control methodology. Recent advances have generated both a sophisticated Hybrid Minimum Principle (HMP) theory and computational methods, and a parallel theory of Hybrid Dynamic Programming (HDP). Building on the proposer's work, it is planned to generate (i) a unified HMP - HDP theory, (ii) a theory and associated algorithms for the fundamental class of HDP problems where the systems are subject to state switching constraints, and (iii) an integrated HDP - Model Predictive Control methodology.**Success in the overall program will yield 8 PhDs and 4 MEng degrees, plus 4 PDFs, and will contribute to the emergence of new techniques enabling networks of distributed adaptive agents to control large scale systems evolving in random environments; prime examples (already initiated in Canada) include the integration of smart meters, electric vehicle charging systems and localized generation, where the vehicles and generators are themselves optimized using hybrid system control algorithms.

提出的研究计划的总体目标是推进控制系统的基本分析和设计：(i)分布式大规模系统（即没有集中控制或具有高状态基数的信息的系统）和（ii）具有连续和离散状态和动态的系统。这类系统在当今网络化的信息计算环境中无处不在，加强控制和优化将带来巨大的效益。**平均场博弈（MFG）理论构成了分布式大规模系统分析和设计的一种基本的新方法，它起源于2003年至2007年期间由提案人与他的学生Minyi Huang和共同导师Roland Malhame共同支持的NSERC工作，并独立由j.m。拉斯里和P. L.狮子在2006 - 2007年。从那时起，由于这些研究人员和世界各地其他研究人员的不断贡献，该领域得到了蓬勃发展；此外，MFG方法的潜在应用和新的、具有挑战性的问题在广泛的领域不断被发现。* * MFG理论建立了在涉及大量agent的博弈中随机动力系统agent仅由局部反馈产生的近似纳什均衡的存在性。有限种群情况下的平衡和反馈律是通过对基本无限种群MFG （Hamilton-Jacobi-Bellman）和(McKean-Vlasov)-Fokker-Planck-Kolmogorov偏微分方程的更简单的解得到的，这些偏微分方程由一般代理的状态分布连接起来，或者称为系统的平均场。当智能体的数量趋于无穷近似值误差趋于零。**本提案映射了以下主题的五年研究计划：(a) MF系统中的估计：MF系统理论的一个中心问题是具有主要代理的部分可观测系统（即随种群大小非渐近消失）具有随机平均场，必须与主要代理的部分可观测状态一起递归估计。具有主要和次要代理的非线性部分观测MFG系统的状态估计理论，以及随机平均场，将具有重要意义，并将在(b)空间动态MF系统，(c) MF系统中的联盟形成，(d)局部无限和大规模拓扑MF系统以及(e) MF市场和拍卖模型的发展中得到利用。**在大范围的系统和控制工程中，混合控制系统是先进控制方法的代名词。近年来，既有复杂的混合最小原理（HMP）理论和计算方法，也有并行的混合动态规划（HDP）理论。基于提案人的工作，计划生成(i)统一的HMP - HDP理论，（ii）系统受状态切换约束的HDP问题的基本类别的理论和相关算法，以及（iii）集成的HDP -模型预测控制方法。**整个项目的成功将产生8个博士学位和4个b孟学位，外加4个pdf文件，并将有助于新技术的出现，使分布式自适应代理网络能够控制随机环境中进化的大规模系统；典型的例子（已经在加拿大启动）包括智能电表、电动汽车充电系统和本地化发电的集成，其中车辆和发电机本身使用混合系统控制算法进行优化。