Identification of nonlinear systems using a piecewise-linear Hammerstein model

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1、Systems&ControlLetters54(2005)145–158www.elsevier.com/locate/sysconleIdentificationofnonlinearsystemsusingapiecewise-linearHammersteinmodelGregorDolanc∗,StankoStrmˇcnikDepartmentofSystemsandControl,JozefStefanInstitute,Jamova39,1000Ljubljana,SlovenijaReceived1July2003;receivedinrevisedform1Apri

2、l2004;accepted20July2004Availableonline11September2004AbstractInthepaperamethodfornonlinearsystemidentificationisproposed.Itisbasedonapiecewise-linearHammersteinmodel,whichislinearintheparameters.Themodelandtheidentificationalgorithmareadaptedtoallowtheparameteridentificationinthepresenceofaspeci

3、alformoftheexcitationsignal.Theidentificationmethodisderivedfromarecursiveleast-squaresalgorithm,whichisproperlyadaptedtotakeintoaccounttheproposedmodelstructureandthepropertiesoftheidentificationsignal.Theapplicabilityoftheapproachisillustratedbyanexampleinwhichadiscontinuousnonlinearstaticfunc

4、tionisconnectedtoadynamicblock.©2004ElsevierB.V.Allrightsreserved.Keywords:Nonlinearsystems;Hammersteinsystems;Piecewise-linearfunctions;Systemidentification;Parameterestimation1.Introductionacombinationofnonlinearstaticandlineardynamicblock,e.g.WienerandHammersteinmodels.Efficientcontrolofnonli

5、nearsystemsisstillrecog-Inthispaper,identificationusingtheHammer-nizedasamajorchallengeforcontrolscientistsandsteinmodelisconsidered.Theproblemhasbeenengineers.Inthiscontextappropriateidentificational-approachedbydifferentauthors,whohaveproposedgorithms,whichprovidemodelsforanalysisoftheavariety

6、ofmethodsforestimationoftheparam-processandsynthesisofthecontrol,areextremelyetersofthenonlinearandlinearpartofthemodelimportant.Thealgorithmsmainlydependontheun-(e.g.iterativemethods[11,12],noniterativeover-derlyingstructureofthenonlinearmodel.Aratherparameterizationmethods[2,6,9]aswellasnonp

7、ara-classicalwayofdealingwiththisproblemistousemetricmethods[1,4]).Besidethesemainapproaches,somespecialmethodshavealsobeenapplied(likein-strumentalvariables[13],orthemaximum-likelihood∗principle[3,5]).AlsotheestimationofparametersofCor