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1、ExpertSystemswithApplications37(2010)5347–5352ContentslistsavailableatScienceDirectExpertSystemswithApplicationsjournalhomepage:www.elsevier.com/locate/eswaChaoticsynchronizationusingPIDcontrolcombinedwithpopulationbasedincrementallearningalgorithmLeandrodosSantosCoelho*,RafaelBartnik
2、GrebogiIndustrialandSystemsEngineeringGraduateProgram,LAS/PPGEPS,PontificalCatholicUniversityofParaná,PUCPR,ImaculadaConceição,1155,80215-901Curitiba,Paraná,BrazilarticleinfoabstractKeywords:Evolutionaryalgorithms(EAs)refertoabroadclassofoptimizationalgorithms,whichtakesomeinspi-Evolut
3、ionaryalgorithmsrationfromevolutionarysystemsinthenaturalworld.Inrecentyears,anewclassofEAscalledestima-Optimizationtionofdistributionalgorithms(EDAs)hasemergedbasedonprobabilisticmodelingofthesearchspace.ChaoticsynchronizationInstancesofEDAsincludepopulationbasedincrementallearning(P
4、BIL)algorithm.ThePBILalgorithmisEstimationofdistributionalgorithmsaneasytounderstandheuristicoptimizationtechniquethatisinspiredbythegeneticalgorithmandtheControlsystemcompetitivelearningparadigm.PBILincludesmanyofthefeaturesfromthegeneticalgorithmsuchasbinarystringrepresentation,then
5、otionofindividuals,fitnessmeasuresandmutations.ContrarytothegeneticalgorithmitdoesnotmaintainapopulationofindividualsbutinsteadPBILcontainsaprobabilityvector.Ateachgenerationanewpopulationofindividualsissampledaccordingtotheprobabilitiesspec-ifiedintheprobabilityvector.Thepopulationisev
6、aluatedandtheprobabilityvectorisupdatedbydrag-gingittowardsthebestindividualinthepopulation.Inrecentyears,theinvestigationofsynchronizationofchaoticsystemshasattractedmuchattentionofresearchers.Chaossynchronizationhasbeenappliedinmanyfieldssuchassecurecommunication,chemical,engineering
7、,andbiologicalsystems,amongoth-ers.Thispaperpresentsthesynchronizationoftwoidenticaldiscretechaoticsystemssubjectthediffer-entinitialconditionsbydesigningaproportional–integral–derivative(PID)controller.Inaddition,thetuningofthePIDcontrollerbasedonamodifiedPBILalgorithmusingsimilaritya
8、nalys
