Crowd-averse robust mean-field games: approximation via state space extension
File(s)
Accepted version
Author(s)
Bauso, D
Mylvaganam, T
Astolfi, A
Type
Journal Article
Abstract
We consider a population of dynamic agents, also referred to as players. The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a cross-coupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowd-averse.” Motivations for this model are analyzed and discussed in three main contexts: a stock market application, a production engineering example, and a dynamic demand management problem in power systems. For the problem in its abstract formulation, we illustrate the paradigm of robust mean-field games. Main contributions involve first the formulation of the problem as a robust mean-field game; second, the development of a new approximate solution approach based on the extension of the state space; third, a relaxation method to minimize the approximation error. Further results are provided for the scalar case, for which we establish performance bounds, and analyze stochastic stability of both the microscopic and the macroscopic dynamics.
Date Issued
2016-07-01
Date Acceptance
2015-09-09
Citation
IEEE Transactions on Automatic Control, 2016, 61 (7), pp.1882-1894
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
1882
End Page
1894
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
61
Issue
7
Copyright Statement
© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://ieeexplore.ieee.org/document/7271023
Grant Number
EP/L014343/1
Subjects
Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
Closed loop systems
control design
control engineering
optimal control
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status
Published
Date Publish Online
2015-09-17