0复杂网络建模与一致性及在多移动智能体中的应用

华中科技大学博士学位论文复杂网络建模与一致性及在多移动智能体中的应用姓名：吴正平申请学位级别：博士专业：控制理论与控制工程指导教师：关治洪20070607I1998WattsStrogatz1999BarabàsiAlbertM54MBAIINWNewmanWattsWSWattsStaogtzNWWSIIIAbstractSinceWattsandStrigatz’sworkinsmall-worldnetworkin1998andBarabsiandAlbert’sworkinscale-freein1999,anexplosionofworkaboutcomplexnetworksemerges,fromtheanalysisofthetopologiesofrealnetworks,theevolutionmodelsanddynamicsofcomplexnetworkstotheapplicationsofthecomplexnetworktheory.AndinthefieldofRoboticsandArtificialIntelligence,thecoordinatecontrolofmultiplemotionagentsystem(MMAS)isnowadaysahottopic.Motivatedbytherecentadvancesintheoryofcomplexdynamicalnetwork,weregardMMASasacomplexdynamicalnetwork,wherethenoderepresentsanagent,theedgebetweentwonodesrepresentsthecoordinaterelation(suchassensorrelationorcommunicationrelation)betweentwoagentsandthedynamicsofnoderepresentsthemotiondynamicsofagent.Basedoncomplexdynamicalnetworktheory,themodeconstructionandconsensusproblemofmultiplemotionagentcomplexdynamicalnetworkarestudiedinthisdissertation,andthemainworkandresearchresultslieinthefollowing.MotivatedbythecommunicationnetworkofMMAS,aclassofevolvingnetworkmodelswithphysicalpositionneighbourhoodconnectivityareproposed.Basedonthesemodels,theclusteringcoefficients,averagedistances,degreedistributions,thetolerancetothenetworkdelayandthetimetoreachconsensusfordifferentevolvingparametersindifferentmodelsarestudieddetailedly.ThisstudyshowswiththeincreasingofdepthofneighbourhoodM,theclusteringcoefficientsdecreasenotably,thetimetoreachconsensusbecomesshortedinthesefivemodels.ItalsoshowsthatModel4ismostvulnerabletotime-delayinthesefivemodelsanditsdegreedistributionrepresentsatransitionbetweenthatofanexponentialnetworkandthatofapower-lawscalingnetworkwithMincrease,andtheBarábasi-Albertscale-freemodelisonlyoneofitsspecial(limiting)cases.Westudytherobustnesstonodeandedgefailure,thetolerancetonetworktime-delayandthetimetoreachaconsensusfordifferentcomplexnetworktopologies.Andthetopologiesincludesmall-worldnetwork,scale-freenetwork,nearestneighbourcouplednetwork,starnetworkandglobalcouplednetwork.Bythisstudy,wefindthefollowingresults:First,asatopologywithfeweredges,starnetworkhasarapidconvergencespeedintheconsensusproblem,anditsspeedisfasterthanthatofsmall-worldnetworkandscale-freenetwork,whichhavethesamenumberofnodeandaveragenodedegree.However,starnetworkisvulnerabletotime-delay.Second,thesmall-worldnetworkandscale-freenetworkhavethesimilarconvergencespeedsinconsensusproblem,andtheirconvergencespeedsaremanytimeslargerthanthatofthenearestneighbourcouplednetworkwiththesamenumberofnodeandaveragenodedegree.Third,forglobalnetwork,itsspeedisthefastestamongallnetworks,butitisvulnerabletotime-delay.IVFourth,thereisanearlinearrelationshipbetweentherobustnesstotime-delayandthemaximumnodedegreeofthenetwork,sothemaximumnodedegreeofthenetworkisagoodpredictorfortime-delayrobustnessinallnetworks.Finally,forscale-freenetwork,therobustnesstotime-delaycanbeimprovedsignificantlybyadecouplingprocesstoasmallpartofedgesofthenetwork.Twomethodsofdevisingaspeed-optimizedsmall-worldnetworkinconsensusproblemarepresented.OnebasesonNWmodel(proposedbyNewmanandWatts)andgenetic-algorithm(GA),anotherbasesonWSmodel(proposedbyWattsandStaogtz)andlong-rangenodespreferencereconnection.Itisfoundthat,asweconstructasmall-worldnetworkwithasmallernetworksizeandfixedlong-rangelinksusingNWmodel,wecanoptimizethelong-rangelinkconfigurationusingGAmethodologytoobtainasmall-worldnetworkwithfasterconsensusspeed.Itisalsofindthatintheeverystepofedgesrewiringofsmall-worldconstructionusingWSmodel,asthedistancebetweentworewiringnodesarethelongest,theresultingnetworkisfastersignificantlyinreachingconsensus.Motivatedbyrecentadvancesinconsensustheoryofcomplexdynamicalnetwork,wepresentanovelmotionmodelabouttheformationcontrolandgroupmotioncontrolofMMASforfixedandchanginginteractions.Basedonthismodelandtheconsensustheoryofcomplexnetwork,twotheoremsaboutmotionstabilityofMMASwithfixedandswitchedtopologyarepresentedandproved.Motivatedbyrecentadvancesinsynchronizationtheoryofcomplexdynamicalnetwork,wedevelopanothermethodofcontrollerdesignforformationreachingandgroupmotioncontrollingoftheMMAS.Anovelmotionmodelofthesystemispresented.Basedonthismodel,thedesignmethodofdecentralizedcontrollerforeachagentisinvestigated.Thestabilitypropertyofthesystemisalsoanalyzedandprovedindetail.Thiscontrolmethodisusefulespicallyasthemotiondynamicsofagentiscomplicated.Flockingcontrolisanewpatternofdecentralizedapproachimitatinganimalcooperativebehavior.Aleader-followerflockingcontrolmechanismforchangingtopologyisintroducedbasedonexistedtheoryonflockingofmobileagents,whichmakesflockingmotionbesequencablebehaviour.Thecontroloutputofthisschemeissmoothevenastheagentnetworkisswitching.Finally,asummaryhasbeendoneforallthediscussioninthedisseration.Andtheresearchworkinfurtherstudyispresented.Keywords:Complexdynamicalnetwork,Multiplemobileagentssystem,Consensus,Synchronization,Genetic-algorithm,Formationcontrolandgroupmotioncontrol,Flockingcontrol_____11200021211