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1、SCIENCECHINAInformationSciences.RESEARCHPAPER.January2017,Vol.60012204:1–012204:13doi:10.1007/s11432-015-1031-6Iterativelearningcontrolforone-dimensionalfourthorderdistributedparametersystemsQinFU*,PanpanGU&JianrongWUSchoolofMathematicsandPhysics,SuzhouUniversityofScienceandTechnolog
2、y,Suzhou215009,ChinaReceivedMay7,2016;acceptedJune3,2016;publishedonlineNovember22,2016AbstractThispaperaddressestheproblemofiterativelearningcontrolalgorithmforhighorderdistributedparametersystemsinthepresenceofinitialerrors.Andtheconsidereddistributedparametersystemsarecomposedofth
3、eone-dimensionalfourthorderparabolicequationsortheone-dimensionalfourthorderwaveequations.Accordingtothecharacteristicsofthesystems,iterativelearningcontrollawsareproposedforsuchfourthorderdistributedparametersystemsbasedontheP-typelearningscheme.Whenthelearningschemeisappliedtothesy
4、stems,theoutputtrackingerrorsonL2spacearebounded,andfurthermore,thetrackingerrorsonL2spacecantendtozeroalongtheiterationaxisintheabsenceofinitialerrors.Simulationexamplesillustratetheeffectivenessoftheproposedmethod.KeywordsP-typelearningscheme,iterativelearningcontrol,distributedpara
5、metersystems,fourthorderparabolicequation,fourthorderwaveequationCitationFuQ,GuPP,WuJR.Iterativelearningcontrolforone-dimensionalfourthorderdistributedparametersystems.SciChinaInfSci,2017,60(1):012204,doi:10.1007/s11432-015-1031-61IntroductionSincethecompletealgorithmofiterativelearn
6、ingcontrol(ILC)wasfirstproposedbyArimotoetal.[1],ithasbecomethehotissuesofcyberneticsandhasattractedbroadattentioninrecentyears[2–5].ThebasicideaofILCistoimprovethecontrolsignalforthepresentoperationcyclebyfeedingbackthecontrolerrorinthepreviouscycle.AndtheclassicalformulationofILCdes
7、ignproblemisasfollows:findanupdatemechanismfortheoutputtrajectoryofanewcyclebasedontheinformationfrompreviouscyclessothattheoutputtrajectoryconvergesasymptoticallytothedesiredreferencetrajectory.Owingtoitssimplicityandeffectiveness,ILChasbeenfoundtobeagoodalternativeinmanyareasandappli
8、cations,see[
