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Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
Department of Industrial and Enterprise Systems Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Illinois, USA.
2012 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 57, no 4, 904-919 p.Article in journal (Refereed) Published
Abstract [en]

We consider the problem of distributed convergenceto a Nash equilibrium in a noncooperative game where the playersgenerate their actions based only on online measurements oftheir individual cost functions, corrupted with additive measurementnoise. Exact analytical forms and/or parameters ofthe cost functions, as well as the current actions of the playersmay be unknown. Additionally, the players’ actions are subjectto linear dynamic constraints. We propose an algorithm basedon discrete-time stochastic extremum seeking using sinusoidalperturbations and prove its almost sure convergence to a Nashequilibrium. We show how the proposed algorithm can be appliedto solving coordination problems in mobile sensor networks,where motion dynamics of the players can be modeled as: 1) singleintegrators (velocity-actuated vehicles), 2) double integrators(force-actuated vehicles), and 3) unicycles (a kinematic modelwith nonholonomic constraints). Examples are given in which thecost functions are selected such that the problems of connectivitycontrol, formation control, rendezvous and coverage control aresolved in an adaptive and distributed way. The methodology isillustrated through simulations.

Place, publisher, year, edition, pages
2012. Vol. 57, no 4, 904-919 p.
Keyword [en]
Convergence, extremum seeking, learning, mobile sensor networks, multi-agent control, Nash equilibrium, noncooperative games, stochastic optimization
National Category
Control Engineering
Research subject
URN: urn:nbn:se:kth:diva-72945DOI: 10.1109/TAC.2011.2174678ISI: 000302499500007ScopusID: 2-s2.0-84859722327OAI: diva2:488345
Knut and Alice Wallenberg FoundationSwedish Research CouncilICT - The Next Generation

QC 20120508

Available from: 2012-02-01 Created: 2012-02-01 Last updated: 2013-04-11Bibliographically approved

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Stankovic, Milos S.Johansson, Karl Henrik
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