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1、414IEEETRANSACTIONSONNEURALNETWORKS,VOL.16,NO.2,MARCH2005DirectAdaptiveControllerforNonaf?neNonlinearSystemsUsingSelf-StructuringNeuralNetworksJang-HyunPark,Sung-HoeHuh,Seong-HwanKim,Sam-JunSeo,andGwi-TaeParkAbstract—Adirectadaptivestate-feedbackcontrolleris
2、pro-controlmethodsareroughlydividedintotwocategories,oneisposedforhighlynonlinearsystems.Weconsideruncertainoradirectadaptivecontrolandtheotherisanindirectadaptiveill-de?nednonaf?nenonlinearsystemsandemployaneuralnet-control.work(NN)with?exiblestructure,i.e.
3、,anonlinevariationoftheInthedirectadaptivecontrolmethod[12]–[14],theoutputnumberofneurons.TheNNapproximatesandadaptivelycancelsanunknownplantnonlinearity.AcontrollawandadaptivelawsofaNNbecomesacontrolinput,andanoptimalcontrollerisfortheweightsinthehiddenlaye
4、randoutputlayeroftheNNareobtainedbyadaptation.Intheindirectone[7]–[11],[18],NNsestablishedsothatthewholeclosed-loopsystemisstableinthearecombinedwiththeinput-outputlinearizationscheme,andsenseofLyapunov.Moreover,thetrackingerrorisguaranteedtoestimatetheunkno
5、wnnonlinearitiesofthecontrolledsystem.beuniformlyasymptoticallystable(UAS)ratherthanuniformlyThen,anadaptiveinput-outputlinearizingcontrolinputisgen-ultimatelybounded(UUB)withtheaidofanadditionalrobusti-fyingcontrolterm.Theproposedcontrolalgorithmisrelativel
6、yeratedusingtheestimates.Inallofthem,thecontrolinputandsimpleandrequiresnorestrictiveconditionsonthedesigncon-adaptivelawsfortheweightsoftheNNshavebeendesignedstantsforthestability.Theef?ciencyoftheproposedschemeisforthewholeclosed-loopsystemtobestableinthes
7、enseofshownthroughthesimulationofasimplenonaf?nenonlinearLyapunov.system.Inevitably,reconstructionerrorsmustoccurifthestructureofIndexTerms—Neuralnetwork(NN),nonaf?nenonlineartheNN(thenumberofhiddenlayersandneurons)isnotin?n-system,robustadaptivecontrol.itel
8、yrich,andtheseerrorsareintroducedintotheclosed-loopsystemanddeterioratethestability.Tocompensateforthere-I.INTRODUCTIONconstructionerrors,themethodofaddingaslidingmodeinputtermiswidelyused[9],[1
