Discrete-time decentralized control using the risk-sensitive performance criterion in the large population regime: A mean field approach

Jun Moon, Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper considers a discrete-time decentralized control problem using the risk-sensitive cost function when there is a large number of agents. We solve this problem via mean field control theory. We first obtain an individual robust decentralized controller that is a function of the local state information and a bias term that is related to the mean field term. We then construct an auxiliary system that characterizes the best approximation to the mean field term in the mean-square sense when the number of agents, say N, goes to infinity. We prove that the set of individual decentralized controllers is an ε-Nash equilibrium, where ε can be made arbitrarily close to zero when N → ∞. Finally, we show that in view of the relationship with risk-sensitive, H, and LQG control, the equilibrium features robustness, and converges to that of the LQG mean field game when the risk-sensitivity parameter goes to infinity.

Original languageEnglish (US)
Title of host publicationACC 2015 - 2015 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4779-4784
Number of pages6
ISBN (Electronic)9781479986842
DOIs
StatePublished - Jul 28 2015
Event2015 American Control Conference, ACC 2015 - Chicago, United States
Duration: Jul 1 2015Jul 3 2015

Publication series

NameProceedings of the American Control Conference
Volume2015-July
ISSN (Print)0743-1619

Other

Other2015 American Control Conference, ACC 2015
CountryUnited States
CityChicago
Period7/1/157/3/15

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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