基于变系统参数的ADALINE神经网络与外部扰动的倒立摆系统监控网络自适应控制研究

I.J.IntelligentSystemsandApplications,2012,8,53-61PublishedOnlineJuly2012inMECS()DOI:10.5815/ijisa.2012.08.07Copyright©2012MECSI.J.IntelligentSystemsandApplications,2012,8,53-61SupervisedOnlineAdaptiveControlofInvertedPendulumSystemUsingADALINEArtificialNeuralNetworkwithVaryingSystemParametersandExternalDisturbanceSudeepSharma,VijayKumar,RajKumarElectronics&ComputerEngineeringDepartment,IITRoorkee,Roorkee,[e-mail],[e-mail],[e-mail]—GeneralizedAdaptiveLinearElement(GADALINE)ArtificialNeuralNetwork(ANN)asanArtificialIntelligence(AI)techniqueisusedinthispapertoonlineadaptivecontrolofaNon-linearInvertedPendulum(IP)system.TheANNcontrollerisdesignedwithspecificationsas:networktypeisthree(Input,HiddenandOutput)layeredFeed-ForwardNetwork(FFN),trainingisdonebyWidrow-HoffsdeltaruleorLeastMeanSquarealgorithm(LMS),thatupdatesweightandbiasstatestominimizetheerrorfunction.Theresearchisfocusedonhowtoadaptthecontrolactionstosolvetheproblemof“parametervariations”.ThemethodisappliedtotheNonlinearIPmodelwiththeapplicationofsomeuncertainties,andtheexperimentalresultsshowthatthesystemrespondsverywelltohandlethoseuncertainties.IndexTerms—GeneralizedAdaptiveLinearElement(GADALINE)ArtificialIntelligence(AI)Invertedpendulum(IP);ArtificialNeuralNetwork(ANN);Feed-ForwordNetwork(FFN);LeastMeanSquarealgorithm(LMS).I.IntroductionTheinvertedpendulumproblemisaclassicalexampleofanunstablenonlineardynamicsystem.Therefore,muchattentionhasbeengiventoexploreabettersolutionforitandfurther,tosolveothersimilarcontrolproblems.Nonlinearsystemcontrolnowoccupiesanincreasinglyimportantpositionintheareaofprocesscontrolengineeringasreflectedbythetremendousincreaseinthenumberofresearchpaperspublishedinthisarea.Artificialneuralnetworkprovedtobeausefultoolindealingwithapplicationssuchaspatternrecognition,signalprocessing,imageprocessingandvariouscomplexcontrolsandmappingproblemsetc.Neuralnetworkshavebeenappliedsuccessfullytoidentifyandcontrolofdynamicsystemsbecauseoftheirlearningcapacityandabilitytotolerateincorrectornoisydata[1].Theuniversalapproximationcapabilitiesofthemultilayerperceptronmakeitapopularchoiceformodelingnonlinearsystemsandforimplementinggeneral-purposenonlinearcontrollers.Aconventionalcontrollerwhichisdiscussedin[2]isusedtocollectthetrainingdatatodevelopNeuralNetworkcontrollerforainvertedpendulumsystem.Multilayerneuralnetworkconsistsofsinglelayereachforinputsandoutputsandoneormorehiddenlayers,eachlayercanhaveoneormoreno’sofneurons.Thelinkingweightsareupdatedbytheback-propagationalgorithm.Itcancontroldifferentsystemsthroughquicklearningprocessandhasperfectperformances.Ni(1996)proposedamethodforidentificationandcontrolofnonlineardynamicsystemarecurrentmodelwasappliedasidentifier[3].Gupata(1999)presentedanimprovementtoback-propagationalgorithmbasedontheuseofanindependent,adaptivelearningrateparameterforeachweightwithadaptivenonlinearfunction[4].LMalgorithmisaneffectiveoptimizationtechniquethatcanguidetheweightoptimization[5].Neuralnetworkhasbeenwidelyappliedforstatefeedbackcontrollerdesign,nonlinearsystemcontrol,nonlineardynamicalsystemidentification,optimalcontrolsynthesisandthree-dimensionalmedicalimage[6-10].TheADALINEneuralnetworkisrevisitedandgeneralizedin[11]byintroducingamomentumtermintheLMSlearningalgorithm.Themomentumtermhelpstospeedupthelearningprocessandreducethezigzageffectduringconvergenceperiodoflearning.ThispaperusestheregularizedLMalgorithmtoofflinetraintheconnectingweightsofneuralnetworkandforonlinetrainingofADALINEANNLSMalgorithmisused.Theobjectiveofthispaperistodevelopbothonlineandofflineneuralnetwork-basednonlinearcontrollerforIPsystemandprovidearapid,reliablesolutionforthecontrolalgorithm.II.ADALINEArtificialNeuralNetworkADALINEisoneofthebasicmodelsusedfordataprediction.ThismethodhasnotfoundmuchapplicationtopredictnonlinearsystemdynamicsbecauseitisslowinconvergencethereforemultipleADALINEunitsarecombinedtogetherandnamedasMADALINEin[11]tocapturethedynamicbehaviorofthefeedbackcontrollawandtocontroltheIPsystem.Ageneralized(ADALINE)neuralnetwork,calledGADALINE,foronlineidentificationoflineartimevaryingsystems54SupervisedOnlineAdaptiveControlofInvertedPendulumSystemUsingADALINEArtificialNeuralNetworkwithVaryingSystemParametersandExternalDisturbanceCopyright©2012MECSI.J.IntelligentSystemsandApplications,2012,8,53-61whichcanbedescribedbyadiscretetimemodel.GADALINEisalinearrecurrenttypeofneuralnetwork.Insuchnetworks,thecurrentsystemoutputisdependentonpastoutputsandonboththecurrentandpastinputs.SotheGADALINEneedstohaveoutputfeedbackandtorememberpastinput/outputdata.TheauthorfurthergeneralizestheadaptivelearningbyaddingamomentumtermtotheGADALINEweightadjustment.ThismomentumtermisturnedononlyduringconvergenceperiodandtheGADALINE'slearningcurveisthereforesmoothedbyturningoffthemomentumoncethelearningerroriswithinagivensmallnumber.Thelowcomputationalcomplexitymakesthismethodsuitableforonlinesystemidentificationandrealtimeadaptivecontrolapplicati