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1、80IEEETRANSACTIONSONFUZZYSYSTEMS,VOL.18,NO.1,FEBRUARY2010AdaptiveFuzzyControlofNonlinearSystemsinPureFeedbackFormBasedonInput-to-StateStabilityTian-PingZhang,HuiWen,andQingZhuAbstract—Usingmeanvaluetheoremandbacksteppingtech-handlesystemswithunknowndeadzones,adapt
2、ivedead-zonenique,arobustadaptivefuzzycontrolschemeisproposedforainverseswereproposedin[13]and[14].Inthepaper[19],adap-classofpure-feedbacknonlinearsystemswithunknowndeadzonetiveoutputfeedbackcontrolusingbacksteppingandsmoothanddisturbancesviainput-to-statestabili
3、ty.Takagi–Sugeno(T–S)inversefunctionofthedeadzonewasproposedforaclassoftypefuzzylogicsystemsareusedtoapproximatetheuncertainnonlinearfunctionsandfewerlearningparametersneedtobead-single-inputsingle-output(SISO)nonlinearsystemswithun-justedonline.Basedonsmallgainth
4、eorem,theclosed-loopcontrolknowndeadzone.Adaptiveneuralcontrolwasdevelopedforasystemisproventobesemigloballyuniformlyultimatelybounded,classofuncertainmulti-inputmulti-output(MIMO)nonlinearandthetrackingerrorconvergestoaneighborhoodofzerobystatetime-varyingdelaysy
5、stemsintriangularcontrolstructurechoosingappropriateparameters.Simulationresultsdemonstratewithunknownnonlineardeadzonesandgainsignsin[20].theeffectivenessofthecontrolscheme.AdaptivedynamicsurfacecontrolisdevelopedforaclassofIndexTerms—Adaptivecontrol,backstepping
6、,deadzone,fuzzypure-feedbacknonlinearsystemswithunknowndeadzoneandcontrol,input-to-statestability(ISS),pure-feedbacksystems,smallperturbeduncertaintiesusingNNsin[21].gaintheorem.BesidesLyapunovmethod,theinput-to-statestability(ISS)approachisalsoausefultooltodesign
7、andanalyzecontrolI.INTRODUCTIONsystems.TheISStheorywasfirstlyproposedbySontag[22],NRECENTyears,adaptivecontrolforuncertainnonlin-andthesmallgaintheoremisgivenin[23].Combiningback-Iearsystemshasreceivedmuchattentionbasedonuniver-steppingtechniquewithgeneralizedsmall
8、gainapproach,thesalfunctionapproximators,suchasneuralnetworks(NNs)orsynthesisofstablerobustadaptivefuzzytrackingcontrollerwasfuzzylogicsystems[1][5].Ada
