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1、IEEETRANSACTIONSONFUZZYSYSTEMS,VOL.21,NO.2,APRIL2013275AdaptiveFuzzyControlviaObserverDesignforUncertainNonlinearSystemsWithUnmodeledDynamicsYan-JunLiu,ShaochengTong,andC.L.PhilipChen,Fellow,IEEEAbstract—Inthispaper,theproblemsofstabilityandtrackingpropertyoftheneuralnetwor
2、ks(NNs)[15],theadaptivecontrolcontrolforaclassoflarge-scalenonlinearsystemswithunmod-techniquehasalsoobtainedmanysigni?cantresults.eleddynamicsareaddressedbydesigningthedecentralizedadap-Severaladaptivefuzzyorneuralcontrolapproachesweretivefuzzyoutputfeedbackapproach.Becaus
3、ethedynamicsur-designedfornonlinearsingle-inputsingle-output(SISO)facecontroltechniqueisintroduced,thedesignedcontrollerscanavoidtheissueof“explosionofcomplexity,”whichcomesfromthe[16][20],[55],[56]andmultiple-inputandmultiple-outputtraditionalbacksteppingdesignproceduretha
4、tdealswithlarge-(MIMO)[21],[22]systemswiththematchingcondition.Thescalenonlinearsystemswithunmodeleddynamics.Inaddition,amotivationbehindthisstudyistodevelopadaptivecontrolforreduced-orderobserverisdesignedtoestimatethoseimmeasur-nonlinearsystemswhichdonotsatisfythematching
5、conditionablestates.BasedontheLyapunovstabilitymethod,itisprovenbasedonthebacksteppingdesign[23],[24],[28].Moreover,bythatallthesignalsintheclosed-loopsystemarebounded,andthesystemoutputstrackthereferencesignalstoasmallneighborhoodusingbacksteppingdesignandtheapproximationp
6、ropertyofoftheoriginbychoosingthedesignparametersappropriately.ThetheFLSsortheNNs,severaladaptivecontrolalgorithmsweresimulationexamplesaregiventoverifytheeffectivenessofthedevelopedin[25][27]toachievethetrackingperformanceforproposedtechniques.nonlinearinterconnectedsystem
7、sinthenestedformwithcom-IndexTerms—Adaptivecontrol,nonlinearsystems,outputfeed-pletelyunknownfunctions.However,amajorconstraintinthesebackcontrol,unmodeleddynamics.resultsisthatthesystemstatevariablesareassumedtobemea-surable.Theadaptiveoutputfeedbackcontrolofnonlinearsyste
8、msI.INTRODUCTIONwasstudiedin[30][36]and[57]toguaranteethetrackingURINGthepasttwode
