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1、Approximationofnon-autonomousDynamicSystemsbyContinuousTimeRecurrentNeuralNetworksC.KAMBHAMPATI,F.GARCES*,K.WARWICKDepartmentofCybernetics,UniversityofReadingWhiteknights,POBox225,ReadingRG66AYEngland,UKAbstractThisworkprovidesaframeworkfortheapproxima
2、tionofadynamicsystemoftheformX=f(x)+g(x)ubyDynamicRecurrentNeuralNetwork(DRNNs).Thisextendspreviousworkinwhichapproximaterealisationofautonomousdynamicsystemswasproven.Givencertainconditions,thefirstpoutputneuralunitsofadynamicn-dimensionalneuralmodela
3、pproximateatadesiredproximityap-dimensionaldynamicsystemwithn>p.Theneuralarchitecturestudiedisthensuccessfullyimplementedinanonlinearmultivariablesystemidentificationstudycase.1.IntroductionIdentificationofdynamicsystemsisoftenanimportantprerequisitefo
4、rasuccessfulanalysisandcontrollerdesign.Duetothenonlinearnatureofmostoftheprocessesencounteredinengineeringapplications,therehasbeenextensiveresearchcoveringthefieldofnonlinearsystemidentification[Billings,19801.Developingaprecisemodelforlinearisationi
5、spossiblehowever,thiscanbetimeconsumingandsuchamodelmightevenbeunsuitableforcontrolpurposes.Itisherethatneuralnetworkscomeupasafeasiblesolution.Theuniversalapproximationpropertiesofstaticneuralnetworks[Funahashi,19891makethemausefultoolforthemodellingo
6、fnonlinearsystems.Thisproblemofnonlinearmodellingusingneuralnetworkshasbeenextensivelyproposed[NarendraandParthasarathy,19901.[ChenandBillings,19921,[Choietal.,19961and[TanandVandewalle,19951areexamplesoflaterapproachesusingmultilayerperceptronsandradi
7、albasisfunctions.Addingintemaldynamicstoneuralnetworksfornonlinearsystemmodellingseemedtobeanecessaryenhancementandseveraltechniquesareproposed:[AdwankarandBanavar,19971,[NarendraandParthasarathy,19901and[ZhangandFadali,19961.Theyshowinsimulationstheno
8、nlinearidentificationpropertiesofdynamicneuralnetworksbutis[FunahashiandNakamura,19931and[KimuraandNakano,19981whoprovethatdynamicneuralnetworkscanrealisefinitetrajectoriesofn-dimensionalautonomousdynamicsystemsoftheform.i=f(x).Itwaslat
