modelling, identification and stable adaptive control of continuous-time nonlinear dynamical systems using neural networks

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1、1992ACC/WA2Modelling,IdentificationandStableAdaptiveControlofContinuous-TimeNonlinearDynamicalSystemsUsingNeuralNetworksMariosMPolycarpouandPetrosA.IoannouDepartmentofElectricalEngineering-SystemsUniversityofSouthernCaliforniaLosAngeles.CA90089-2563,U.S.AAbstractTheapproximationcapabilitiesofst

2、aticsigmoidaltypenetworksandofradialbasisfunctionnetworkshavebeenstudiedbyseveralSeveralempiricalstudieshavedemonstratedthefeasibilityofem-researchgroups(seefore.g.[6J-7]).InSection2weusetheseresultsployingneuralnetworksasmodelsofnonlineardynamicalsystems.toshowthataproposedgeneralnetworkconfig

3、urationcomposedofThispaperdevelopstheappropriatemathematicaltoolsforsynthe-staticneuralnetworksanddynamicalcomponents(suchasstablefil-sizingandanalyzingstableneuralnetworkbaedidentificationandters)formsatypeofrecurrentnetworkcapableofapproximatingacontrolschemes.Feedforwardnetwokarchitecturesar

4、ecombinedlargeclamofdynamicalsystems.Moreprecisely,itisshownthatwithdynamicalelements,intheformofstablefilters,toconstructathereexistasetofweightssuchthatforagiveninput,theout-generalrecurrentnetworkconfigurationwhichisshowntobecapableputsoftherealsystemandtheproposedrecurrentneuralnetworkofapp

5、roximatingalargeclamsofdynamicalsystems.Adaptiveiden-modelremainarbitrarilycloseoverafiniteintervaloftime.InSec-tificationandcontrolschemes,basedonneuralnetworkmodels,aretion3wedevelopandanalyzeaneuralnetrkbasedidentificationdevelopedusingtheLyapunovsynthesisapproachwiththeprojectionscheme.TheL

6、yapunovsynthesisapproachisusedtoderiveadapmodificationmethod.Theseschemesareshowntoguaranteestabilitytivelawsforadjustingtheweightsofthenetwork.Theseadaptiveoftheoverallsystem,eveninthepresenceofmodellingerrors.Acru-lawsaremodifiedaccordingtotheprojectionalgorithminordertocialcharacteristicofth

7、emethodsandformulationsdevelopedinthisdealwithmodellingerrorsthatmayariseduetotheinadequacyofpaperisthegeneralityoftheresultswhichallowstheirapplicationthenetworktoapproximatetheunknownnonlinearityevenif"op-tovariousneuralnetworkm