on-line identification of nonlinear time-variant systems - thomas f. junge

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1、ProceedingsoftheAmericanControlConferenceAlbuquerque,NewMexicoJune19970-7a03-3a32-41971$10.00oI997AACCOn-lineIdentificationofNonlinearTime-VariantSystemsUsingStructurallyAdaptiveRadialBasisFunctionNetworksThomasF.JungeandHeinzUnbehauenControlEhgineeringLaboratory(ESR)Facult

2、yofElectricalEngineering,Ruhr-UniversityBochumD-44780Bochum,GermanyPhone:++492347004072Telefax:++492347094101E-mail:jungeOesr.ruhr-uni-bochum.deAbstractstoragecapacitymakesthisapproachimpossibleforreal-timeapplicati-ons.ThispaperpresentsanewalgorithmtotrainDirectLinearFeedt

3、hroughRadialBasisFunction(DLF-RBF)networks,especiallydesignedfiron-Theaiminthispaperistodevelopatrainingalgorithmthatincorporateslineidentificationoftime-variantnonlineardynamicalsystems.Thetheideaofon-linestructuraladaptation,andadaptingtheRBFcenteralgorithmbasicallyexplor

4、esthenetwork’sinputspaceandthemodelpositionsandthewidthsusinganerrorsensitiveclusteringalgorithmerrortodetermineautomaticallythenumberofRBFneurons,andtowhichconsiderstheshapeofthelocalapproximation(adaptiveerroradapttheircenterpositions(adaptiveerrordependentclusterind.Thed

5、ependentclustering).TheoutputlayerweightsareadaptedusingaRLSwidthsandtheoutputlayerweightsareadaptedusingtwoinseriesalgorithminitspredictorform[SI.Thealgorithmisalsodevelopedforconnectedrecursiveleastsquaresalgorithms.Thisleadstoparsimo-theDLF-RBFnetworkstructure,takinginto

6、considerationthatanetworkniousmodelsofSISOorMIMO&amicalvstems,aprimordiaIaimwithbothlinearandnonlinearcharacteristicsseemstobemoreappro-whensolvingnonlinearsystemident8cationproblems.Theefectivenesspriatefortheidentificationofsystemswhichpossessunknowncharacte-andthepeforma

7、nceofthenewmethodisdemonstratedbytheident$-ristics[9].Thispaperisorganizedasfollows.Inthenextsection,thecatiohoftwohighlynonlinearsystems,(atime-invariantandatim-identificationofnonlineardynamicalMIMOsystemsusingDLF-RBFvariantone).networksisposedasamultidimensionalfunctiona

8、lapproximationproblem.InSection3,anewon-linetrainingalgorithmforDLF-RBFKeywords:on