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1、IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.58,NO.3,MARCH2013667DistributedMatrixScalingandApplicationtoAverageConsensusinDirectedGraphsAlejandroD.Domínguez-García,Member,IEEE,andChristoforosN.Hadjicostis,SeniorMember,IEEEAbstract—Weproposeaclassofdistributediterativealgo-Thedistributedconse
2、nsus(oragreement)problemisaspe-rithmsthatenabletheasymptoticscalingofaprimitivecolumncialcaseofdistributedfunctioncalculationwhereeachnodestochasticmatrix,withagivensparsitystructure,toadoublyinthenetworkpossessesaninitialvalueandthenodesneedtostochasticform.Wealsodemonstratetheapplicat
3、ionoftheseal-agreeonthesamevalue,typicallybycalculating(viasomeit-gorithmstotheaverageconsensusprobleminnetworkedmulti-erativealgorithm)thesamefunctionoftheirinitialvalues[1],componentsystems.Morespecifically,weconsiderasettingwhereeachnodeisinchargeofassigningweightsonitsoutgoingedges[8
4、],[9].Aprototypicalapplicationofconsensusisanetworkbasedontheweightsonitsincomingedges.Weestablishthat,asofsensorswithnoisymeasurementsofthesamequantity(e.g.,longasthe(generallydirected)graphthatdescribesthecommu-thetemperatureinaroom)thattrytoaverage(or,moregener-nicationlinksbetweenco
5、mponentsisstronglyconnected,eachofally,obtainaweightedlinearcombinationof)theirinitialmea-theproposedmatrixscalingalgorithmsallowsthesystemcompo-surementssoastohaveamoreaccurateestimateofthemea-nentstoasymptoticallyassign,inadistributedfashion,weightssuredquantity.Theconsensusproblemhas
6、receivedextensivethatcompriseaprimitivedoublystochasticmatrix.Wealsoshowthatthenodescanasymptoticallyreachaverageconsensusbyex-attentionfromthecontrolcommunityduetoitsapplicabilityecutingalineariterationthatusesthetime-varyingweights(astotopicssuchascooperativecontrolandmulti-agentsyste
7、mstheyresultattheendofeachiterationofthechosenmatrix(see,e.g.,[9]–[13],andreferencestherein).Theseworksandscalingalgorithm).othershavedemonstratedthatconsensuscanbereachedunderIndexTerms—Averageconsensus,directedgraph,distributedal-exceedinglyweakconditionsoninteraction(e.g.,no
