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1、478IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.50,NO.3,JUNE2003IdentificationandControlofContinuous-TimeNonlinearSystemsviaDynamicNeuralNetworksX.M.Ren,A.B.Rad,P.T.Chan,andWaiLunLoAbstract—Inthispaper,wepresentanalgorithmfortheonlineMoreover,forunknownnonlinearsystems,thereisno
2、identificationandadaptivecontrolofaclassofcontinuous-timeeffectivemethodtodesignadaptivecontrollerstoensurenonlinearsystemsviadynamicneuralnetworks.Theplantcon-goodtrackingperformance.Recently,neuralnetworkshavesideredisanunknownmulti-input/multi-outputcontinuous-timebeenemploy
3、edintheidentificationandcontrolofunknownhigherordernonlinearsystem.Thecontrolschemeincludestwoparts:adynamicneuralnetworkisemployedtoperformsystemnonlinearsystemsowingtotheirmassiveparallelism,fastidentificationandacontrollerbasedontheproposeddynamicadaptationandlearningcapabil
4、ity[6]–[13].Untilnow,themostneuralnetworkisdevelopedtotrackareferencetrajectory.widelyusedneuralnetworkshavebeenfeedforwardneuralStabilityanalysisfortheidentificationandthetrackingerrorsnetworksanddynamicneuralnetworks.ManyresearchersuseisperformedbymeansofLyapunovstabilitycrit
5、erion.Finally,thefeedforwardneuralnetworksastherepresentationofaweillustratetheeffectivenessofthesemethodsbycomputersimulationsoftheDuffingchaoticsystemandone-linkrigidnonlinearoperatorintheright-handsideofthedynamicmodelrobotmanipulator.Thesimulationresultsdemonstratethattheeq
6、uation[6]–[8].Forexample,forthecontrolofunknownmodel-baseddynamicneuralnetworkcontrolschemeisappro-feedbacklinearizablecontinuous-timesystemswithrelativepriateforcontrolofunknowncontinuous-timenonlinearsystemsdegree,LiuandChen[7]employedthestaticfeedforwardwithoutputdisturbance
7、noise.neuralnetworkstomodelnonlinearfunctionsinthesystem.IndexTerms—Adaptivecontrol,continuous-timenonlinearsys-Thecontrollerwasdesignedbasedontheneuralnetworktems,dynamicneuralnetworks,systemidentification.modelstocontrolthesystemtotrackareferencetrajectory,andalocalconvergenc
8、eofthetrackingerrorwasalsodiscussed.I.INTRODUCTIONDesp