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1、1AsynchronousConsensusProtocolsUsingNonlinearParacontractionsTheoryLeiFangandPanosJ.AntsaklisAbstractSeveralconsensusprotocolshavebeenproposedintheliteratureandtheirconvergencepropertiesstudiedviaavarietyofmethods.Inallthesemethods,thecommunicationtopologiesplayakeyrolein
2、theconvergenceofconsensusprocesses.Inthisnote,basedonasynchronousiterationmethodsfornonlinearparacontractions,weestablishanewresultwhichshowsthatconsensusisreachableunderdirectionalandtime-varyingtopologiesbyusingasynchronousnonlinearprotocols.Ourresultmakesuseoftheconflue
3、ntiterationgraphwhichunifiesvariouscommunicationassumptionsandcontributestoafundamentalunderstandingofconvergentconsensusprocesses.Thisresultextendsexistingonesintheliteratureandhasmanypotentialapplications.Asanillustration,weconsideraspecialcaseofourmodelanddiscusstherobo
4、trendezvousproblemviaacenter-of-gravityalgorithm.IndexTermsConsensus,asynchronousiterations,nonlinearparacontractions.I.INTRODUCTIONInrecentyears,therehasbeengrowinginterestinthecoordinatedcontrolofmulti-agentsystems.Coordinationnormallyimpliessynchronizingagentactionsand
5、exchanginginformationamongtheagents.Consensusseekingamongagentsthereforebecomesoneofthefundamentalproblemsincontroltheory,namelytoreachanagreementregardingacertainquantityofinterestthatdependsonthestateofallagents[1][5].Thisneedstemsfromthefactthatinorderforagentstocoordi
6、natetheirbehaviors,theyneedtousesomesharedknowledgeaboutvariablessuchasdirection,speed,time-to-targetetc.Correspondingauthor.L.FangiswithafinancialservicefirminEvanston,IL.P.J.AntsaklisiswithDept.ofElectr.Eng.,UniversityofNotreDame,NotreDame,IN46556.E-mail:justinlfang@gmail
7、.com,antsaklis.1@nd.eduNovember11,2007DRAFT2Recentresearchrevealstwotrendsbeyondthefundamentalconvergenceanalysesofconsensusalgorithms.Onetrendconcernstheperformanceissuesofsuchalgorithms.XiaoandBoydshowedthattheconvergencespeedofaconsensusprocesscanbeincreasedbychangingt
8、heweightsoncommunicationlinks[6].Forlargeorrandomnetworks,rewiringonlyasmallportionsofexistingli
