NDLI: A Mean Field Game Synthesis of Initial Mean Consensus Problems: A Continuum Approach for Non-Gaussian Behavior<formula formulatype=inline> <tex Notation=TeX>$ $</tex> </formula>

Content Provider	IEEE Xplore Digital Library
Author	Nourian, M. Caines, P.E. Malhame, R.P.
Copyright Year	1963
Abstract	This technical note presents a continuum approach to a non-Gaussian 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 by continuous state feedback its individual discounted cost function involving the mean of 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 as the population size goes to infinity. In a finite population system (analogous to the MF LQG framework): (i) the resulting decentralized 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.
Sponsorship	IEEE Control Systems Society
Starting Page	449
Ending Page	455
Page Count	7
File Size	1765154
File Format	PDF
ISSN	00189286
Volume Number	59
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	stochastic optimal control Consensus problems continuum models decentralized control mean field control Nash equilibria
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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