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1、Proceedingsofthe34thConferenceonDecision13ControlNewOrleans,LA-December1995WM08150NewResultsforHammersteinSystemIdentification*SundeepRangant,GregWolodkintandKameshwarPoollatAbstractoriginallyproposedin[9],usesarelaxationapproach.TheLTIsystemandthenonlinearityareindividu-Anovelapproachispres
2、entedfortheanalysisandallylinearlyparametrizedsothatthepredictioner-designofidentificationalgorithmsforHammersteinrorisseparatelylinearintheparametersforeachmodels,whichconsistofastaticnonlinearityfollowedcomponent.TheparameterscanthenbeidentifiedbyanLTIsystem.Weexaminetwoidentificationbymin
3、imizingthepredictionerrorthroughanit-problems.Inthefirstproblem,thesystemisexcitederativesequenceofstandardleast-squareproblems.withwhitenoiseandtheLTIsystemisFIR,andweThedifficultywiththemethodisthatitrequireslin-findasimpleexplicitsolutionfortheoptimalparam-earparametrizationsandtheconverg
4、enceoftheal-eterestimateandshowthatforsufficientlylargedatagorithmisnotfullyunderstood[11].lengthsastandarditerativetechniquegloballycon-vergestothisoptimalvalue.Inthesecondprob-Inthesecondprocedure[2,6,7,10,141,thesystemlem,theLTIsystemisgiveninstate-spaceformandisexcitedbywhitenoiseandthei
5、mpulseresponseweshowthatstandardstate-spacealgorithmscanbecoefficientsoftheLTIsystemcanthenbeobtainedeasilymodifiedtoidentifyHammersteinmodels.frominput-outputcorrelations.WiththeLTIsys-temidentified,thenonlinearitycanbeidentifiedwithleast-squaresmethods.Themaindifficultyhereisthe1Introducti
6、onwhitenoiseinputassumption.Asidefromrestrictingtheinput,theassumptionintroducesstatisticalinef-TheHammersteinmodel,whichconsistsofastaticficiencyduetothenon-whitenessofanyparticularnonlinearityfollowedbyalineartime-invariant(LTI)realizationoftheinputprocessoverafinitetimepe-system,hasproven
7、successfulinprovidingasim-riod.plenonlinearmodelappropriateforawidenumberofapplicationsincludingactuatormodeling,audi-OurapproachfortheFIRidentificationproblemwithtoryandvisualidentification,non-Gaussiansignalwhitenoiseinputbeginssimilartothecorrel
