NDLI: A solution to the initial mean consensus problem via a continuum based Mean Field control approach

Content Provider	IEEE Xplore Digital Library
Author	Nourian, M. Caines, P.E. Malhame, R.P.
Copyright Year	2011
Description	Author affiliation: CIM and Department of Electrical & Computer Engineering, McGill University, 3480 University Street, Montreal, QC H3A 2A7, Canada (Nourian, M.; Caines, P.E.) \|\| GERAD and Department of Electrical Engineering, École Polytechnique de Montréal, QC H3C 3A7, Canada (Malhame, R.P.)
Abstract	This paper presents a continuum approach to the initial mean consensus problem via Mean Field (MF) stochastic control theory. In this problem formulation: (i) each agent has simple stochastic dynamics with inputs directly controlling its state's rate of change, and (ii) each agent seeks to minimize its individual cost function involving a mean field coupling to the states of all other agents. For this dynamic game problem, a set of coupled deterministic (Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov) equations is derived approximating the stochastic system of agents in the continuum (i.e., as the population size N goes to infinity). In a finite population system (analogous to the individual based approach): (i) the resulting MF control strategies possess an εN-Nash equilibrium property where εN goes to zero as the population size N approaches infinity, and (ii) these MF control strategies steer each individual's state toward the initial state population mean which is reached asymptotically as time goes to infinity. Hence, the system with decentralized MF control strategies reaches mean-consensus on the initial state population mean asymptotically (as time goes to infinity).
Starting Page	5708
Ending Page	5713
File Size	317358
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6161410
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Equations Mathematical model Optimal control Stochastic processes Gaussian distribution Biological system modeling Games
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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