Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control

被引：105

作者：

Grammatico, Sergio ^{[1
]}

Parise, Francesca ^{[2
]}

Colombino, Marcello ^{[2
]}

Lygeros, John ^{[2
]}

机构：

[1] Eindhoven Univ Technol, Dept Elect Engn, Control Syst Grp, NL-5612 Eindhoven, Netherlands

[2] Swiss Fed Inst Technol, Automat Control Lab, CH-8092 Zurich, Switzerland

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 11期

基金：

瑞士国家科学基金会;

关键词：

Population control; mean field games; noncooperative agents; large-scale systems; POTENTIAL GAMES; LQG CONTROL; MANAGEMENT; PRINCIPLE;

D O I：

10.1109/TAC.2015.2513368

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion amean field Nash equilibriumin the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem.

引用

页码：3315 / 3329

页数：15

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