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1、IEEETRANSACTIONSONNEURALNETWORKS,VOL.21,NO.8,AUGUST20101339BriefPapersAdaptiveNeuralControlforOutputFeedbackNonlinearSystemsUsingaBarrierLyapunovFunctionItiswellknownthatNNapproximation-basedcontrolreliesonuniversalapproximationpropertyinacompactsetinorderBeibeiRen,Member,IEEE,Shuz
2、hiSamGe,Fellow,IEEE,toapproximateunknownnonlinearitiesintheplantdynamics.KengPengTee,Member,IEEE,andForanyinitialcompactset0,aslongastheargumentsTongHengLee,Member,IEEE0oftheunknownfunctionstartfromandremainwithinacompactsuperset,asshowninFig.1[8],NNapproximationisvalid.Therefor
3、e,howtodetermineapriorithecompactsupersetAbstractInthisbrief,adaptiveneuralcontrolispresentedandhowtoensuretheargumentsoftheunknownfunc-foraclassofoutputfeedbacknonlinearsystemsinthepresenceofunknownfunctions.Theunknownfunctionsarehandledtionremainwithinthecompactsuperset,aretwoo
4、penviaon-lineneuralnetwork(NN)controlusingonlyoutputandchallengingproblemsintheneuro-controlarea[2].Onemeasurements.AbarrierLyapunovfunction(BLF)isintroducedmethodofensuringthattheNNapproximationconditionholdstoaddresstwoopenandchallengingproblemsintheneuro-isbycarefulselectionofth
5、econtrolparameters,viarigorouscontrolarea:1)foranyinitialcompactset,howtodeterminetransientperformanceanalysis,sothatthesystemstatesdoapriorithecompactsuperset,onwhichNNapproximationisvalid;and2)howtoensurethattheargumentsofthenottransgressthecompactsupersetofapproximation[6],unkn
6、ownfunctionsremainwithinthespecifiedcompactsuperset.[8],butthecompactsupersetisonlygivenqualitatively,notByensuringboundednessoftheBLF,weactivelyconstrainthequantitively.Anothermethodistorelyonslidingmodecontrolargumentoftheunknownfunctionstoremainwithinacompactoperatinginparallelt
7、otheapproximation-basedcontrol,suchsupersetsuchthattheNNapproximationconditionshold.Thethatthecompactsupersetisrenderedpositivelyinvariantsemiglobalboundednessofallclosed-loopsignalsisensured,andthetrackingerrorconvergestoaneighborhoodofzero.[5],[27].Thecompactsupersetcanbespecifi
8、edapriori,Simulationresult
