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1、422IEEETRANSACTIONSONNEURALNETWORKS,VOL.6,NO.2,MARCH1995High-OrderNeuralNetworkStructuresforIdentificationofDynamicalSystemsEliasB.Kosmatopoulos,MariosM.Polycarpou,Member,IEEE,ManolisA.Christodoulou,SeniorMember,IEEE,andPetrosA.Ioannou,Fellow,lEEEAbstract-Severalcontinuous-timean
2、ddiscrete-timerecurrenttimerecurrentleamingalgorithm[7],andthedynamicback-neuralnetworkmodelshavebeendevelopedandappliedtopropagation[SI.Thelastapproachisbasedonthecompu-variousengineeringproblems.Oneofthedifficultiesencoun-tationofsensitivitymodelsforgeneralizedneuralnetworks.te
3、redintheapplicationofrecurrentnetworksisthederivationofefficientlearningalgorithmsthatalsoguaranteestabilityofThesegeneralizedneuralnetworks,whichwereoriginallytheoverallsystem.Thispaperstudiestheapproximationandproposedin[9],combinefeedforwardneuralnetworksandlearningpropertieso
4、foneclassofrecurrentnetworks,knowndynamicalcomponentsintheformofstablerationaltransferashigh-orderneuralnetworks,andappliesthesearchitecturesfunctions.totheidentificationofdynamicalsystems.Inrecurrenthigh-Althoughthetrainingmethodsmentionedabovehavebeenorderneuralnetworksthedynam
5、iccomponentsaredistributedthroughoutthenetworkintheformofdynamicneurons.Itissuccessfullyusedinmanyempiricalstudies,theyshareshownthatifenoughhigh-orderconnectionsareallowedthensomefundamentaldrawbacks.Onedrawbackisthefactthisnetworkiscapableofapproximatingarbitrarydynamicalthat,i
6、ngeneral,theyrelyonsometypeofapproximationsystems.Identificationschemesbasedonhigh-ordernetworkforcomputingthepartialderivative.Furthermore,thesearchitecturesaredesignedandanalyzed.trainingmethodsrequireagreatdealofcomputationaltime.Athirddisadvantageistheinabilitytoobtainanalyti
7、calI.INTRODUCTIONresultsconcemingtheconvergenceandstabilityoftheseHEuseofmultilayerneuralnetworksforpattemrecog-schemes.Tnitionandformodelingof“static”systemsiscurrentlyRecently,therehasbeenaconcentratedefforttowardsthewellknown(see,forexample,[11)-givenpairsofinput-outputdesigna
8、ndanalysisofleamingalgorithmsthatarebase
