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1、IMAJournalofMathematicalControlandInformation(2008)25,367−392doi:10.1093/imamci/dnn002AdvanceAccesspublicationonMay25,2008IdentificationofMIMOHammersteinsystemswithnon-linearfeedbackDAPENGLUO†CenterofExcellence,EatonCorporation,13100EastMichiganAvenue,Galesburg,MI49053,USAANDALEXANDERLEONESSA‡M
2、echanicalEngineering,VirginiaPolytechnicInstituteandStateUniversity,Blacksburg,VA24061-0238,USA[Receivedon25October2007;acceptedon20January2008]DownloadedfromSubspaceidentificationalgorithmsareproposedinthispaperforaclassofmulti-inputmulti-output(MIMO)discrete-timeclosed-loopHammersteinsystems.
3、Inparticular,instrumentalvariable(IV)tech-niquesareappliedtosolvethecorrelationsbetweentheinputsignalsandthesignalsthatarefedbackimamci.oxfordjournals.orgintothesystem.AnaugmentedIVidentificationapproachisintroducedtoaddressaproblemrelatedtotheapplicationofthenumericalefficientRQdecompositionalg
4、orithmtoarank-decreasedcorrelationmatrix.Thecontributionofthispaperistoprovideaunifiedapproachtoidentifyaclassofnon-linearclosed-loopsystemsandsolvetherelatednumericalissuesduringtheimplementation.Analysisandnumericalexamplesarepresentedtodemonstratethevalidityofthealgorithmsproposedinthispaper
5、.atPekingUniversityonMay13,2011Keywords:subspaceidentification;non-linearidentification;instrumentalvariable.1.IntroductionTheidentificationofnon-linearmulti-inputmulti-output(MIMO)Hammersteinsystems,whicharecommonlyencounteredinmodelanalysisandcontrol,isstillconsideredtobeachallengingproblem.Sta
6、te-spacemodelsrepresentanexcellentchoiceforobtainingaminimalrealizationofMIMOsystemsaswellasprovidingaplatformformoderncontroltechniques.Consequently,subspaceidentificationmethodsarewidelyappliedintheidentificationofsuchsystems.Althoughopen-loopsubspaceidentifi-cationalgorithmsarewellstudiedandap
7、pliedtolinearsystemswithgreatsuccess(Overschee&Moor,1994,1996a,b),fewapplicationscanbefoundtosystemswithgeneralnon-linearitiesandlargeoperat-ingranges.Furthermore,itisoftennecessarytoperformidentificationexperimentsonsystemsoperatingincl
