自适应神经网络观测器在混沌系统中的应用(IJISA-V6-N2-5)

I.J.IntelligentSystemsandApplications,2014,02,37-43PublishedOnlineJanuary2014inMECS()DOI:10.5815/ijisa.2014.02.05Copyright©2014MECSI.J.IntelligentSystemsandApplications,2014,02,37-43ApplicationofAdaptiveNeuralNetworkObserverinChaoticSystemsMiladMalekzadehFacultyofElectricalandComputerEngineering,BabolUniversityofTechnology,Babol,IranE-mail:[e-mail]ofElectricalandComputerEngineering,BabolUniversityofTechnology,Babol,IranE-mail:[e-mail]ultyofElectricalandComputerEngineering,BabolUniversityofTechnology,Babol,IranE-mail:[e-mail]ntrolEng,ShahidBeheshtiUniv.,Tehran,IranE-mail:[e-mail]—Chaoscontrolisanimportantsubjectincontroltheory.Chaoscontrolusuallyconfrontswithsomeproblemsduetounavailabilityofstatesorlosingthesystemcharacteristicsduringthemodelingprocess.Inthissituation,usinganappropriateobserverincontrolstrategymayovercometheproblem.Inthispaper,statesareestimatedusinganobserverwithouthavingcompletepriorinformationfromnonlineartermbasedonneuralnetwork.Simulationresultsverifyperformanceoftheproposedstructureinestimatingnonlineartermspecificallyforanonlinepracticaluse.IndexTerms—NonlinearObserver,AdaptiveNeuralNetwork,ChaosControl,PendulumSystem,ModifiedDuffingSystemI.IntroductionChaosphenomenonisaddressedinvariousfieldsofengineeringandseveralmulti-disciplinarysubjects.Chaosmaybeofabeneficialphenomenonlikecircuitsecuretelecommunication[1],althoughthechaoshasadestructiveeffectsinphysicalandpracticalapplications.Duetocomplicateddynamicofsuchthesesystems,identificationand/ortheestimationmayfailtocomplywiththeneeds.Furthermorewhenthereislackofenoughpriorinformationwheretwoapproachesarepossible:1)Usingacontrollertocopewithuncertaintiesofsystem[2].2)Orgaininganobserverinthecloselooppathofthesystem.Accordinglyanadaptiveneuralnetworkispresentedinthisstudytoestimatechaoticstatesevenanonlineuse.Thisabilityhelpsdesignertocontrolchaoticsystemwithsatisfactoryperformance.Differentobserversarepresentedtoconstructaproperstructuretoestimatestatesofsystems.ThisincludesnonlinearobserverssuchasEKFandUKF[4-7].Afirstnonlinearadaptiveobserverwaspresentedin[8]whereasseveralotherobserverswereproposedin[9-11].Inthecurrentstudyanadaptiveneuralnetworkobserverwillbeusedwhentheweightsaretunedonline[12].Akeyissueinusingneuralnetworksisthemethodoftrainingnetworks.Trainingprocesscanbeperformedeitheronlineoroffline.Theproposedobserverwillbeonlinetrainedwhilstthereisnoneedofpriorknowledgeaboutnonlineartermsduringtheestimationprocedure.Thispaperisorganizedasfollows:Neuralnetworkwillbebrieflyexplainedinsectiontwo.InsectionIIIcharacteristicoftheadaptiveobserverwillbedescribed.Theobserverwillbeusedtoestimatestateofachaoticpendulumsysteminsectionfour.TheworkwillbecontinuedtoobservestatesamodifiedDuffingsystem.FinallyaconclusionendsthediscussionatsectionV.II.BriefreviewofNeuralNetworksNeuralnetworkisinspiredfrombiologicalsystem.PreliminaryaschematicformofneuralnetworkisshowninFig.1.38ApplicationofAdaptiveNeuralNetworkObserverinChaoticSystemsCopyright©2014MECSI.J.IntelligentSystemsandApplications,2014,02,37-43Fig.1:Amodelofneuralnetworkwithonelayerwheretheinputandtherelevantweightsvectorsofneuralnetworkare:12[.........]nxxxxand12[.........]nvvvvrespectively.Theoutputisdenotedbyywhilst0visabiasterm.Theactivationfunctionisalsoshownbywhichmaybeofastepfunction,purelinorasigmoidtransferfunction.Outputofneuralnetworkwithonelayerisstatedbythefollowingequation:01()()njjjytvxv(1)InputHiddenlayerOutputFig.2:Atwo-layerneuralnetworkmodel[12]Inordertomodelthebehaviorofcomplexsystem,neuralnetworkstructurewillbeenhanced.Afirstkindofpromotionwillbetakenplaceswhenthenumberoflayersandneuronsofneuralnetworkareincreased.Accordingtothispurpose,theconceptofisdemonstrated.Astructureofmulti-layerneuralnetworkusingtwolayersispresentedinFig.2.Althoughatwo-layerneuralnetworkisbeneficial,usingthreelayerswithsufficientneuroninhiddenlayersisfoundeffectivetosimulatemostofnonlinearsystems.III.AdaptiveNeuralNetworkObserverInthissectionastructureofadaptiveneuralnetwork[12]willbedescribed.Considerthefollowingsingleinput-singleoutputnonlinearplantswhenpairof(,)ACisobservable:[()()()]TxAxbfxgxudtyCx(2)WherenxR,yR,uRandnbRarestates,output,controlsignalanditscoefficientswhereas()dt(isanunknowndisturbancewithknownupperbounded.Terms,:nfgRRdenoteunknownsmoothnonlinearfunctions.Apartfrom,thelineartermisalsodefinedinacanonicalformwhichasinthefollowing:TxAxyCx(3)Where:010...01001...00..00...100000000AC(4)Anonlinearstateobserverproposedasfollows:ˆˆˆˆˆˆˆ[()()()][]ˆTTxAxbfxgxuvtkyCxyCx(5)whereˆxdenotesanestimationofstatexwhereas12[.........]TnKkkkistheobservergain.Itischosensuchthattheterm()TAKCmustbestrictlyHurwitz.Term()vtprovidesarobusttermofobservertoreduceeffectsofdisturbanceonsystem.Therestofvariablesarethesameasin(3).Inthefollowingtheobserverdesignispresented.ApplicationofAdap