资源描述：
《approximation of dynamical time-variant systems by continuous-time recurrent neural networks》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、656IEEETRANSACTIONSONCIRCUITSANDSYSTEMSII:EXPRESSBRIEFS,VOL.52,NO.10,OCTOBER2005ApproximationofDynamicalTime-VariantSystemsbyContinuous-TimeRecurrentNeuralNetworksXiao-DongLi,JohnK.L.Ho,andTommyW.S.ChowAbstract—Thispaperstudiestheapproximationabilityofcon-torytotheequilibrium,therea
2、reaconsiderableamountofre-tinuous-timerecurrentneuralnetworkstodynamicaltime-variantsultsontheapproximationcapabilityoftheNNreported.Forsystems.Itprovesthatanyfinitetimetrajectoryofagivendynam-instance,ithasbeenmathematicallyprovedthatagivencon-icaltime-variantsystemcanbeapproximated
3、bytheinternalstatetinuousmappingonacompactsetcouldbeapproximatelyre-ofacontinuous-timerecurrentneuralnetwork.Givenseveralspe-cialformsofdynamicaltime-variantsystemsortrajectories,thisalizedbyusingathree-layerFNNtoanyprecision[3][5].Lipapershowsthattheycanallbeapproximatelyrealizedby
4、thein-[6]showedthatadiscrete-timetrajectoryonaclosedfinitein-ternalstateofasimplerecurrentneuralnetwork.tervalcouldberepresentedexactlyusingadiscrete-timeRNN.IndexTerms—Approximation,dynamicaltime-variantsystems,JinandNikiforuk[7]alsostudiedtheapproximationproblemrecurrentneuralnetwo
5、rks.ofapproximatingnonlineardiscrete-timestate-spacetrajecto-rieswithinputusingdiscrete-timeRNN.Inthecaseofcontin-uous-timeRNN,FunahashiandNakamura[8]studiedtheap-I.INTRODUCTIONproximationofcontinuous-timedynamicsystemsusingaHop-Nrecentyears,therehavebeenalotofresearchworksfocusingfi
6、eld-typeRNN.Theyprovedthatacontinuous-timedynamicalIonthetheoreticalaspectsofneuralnetworks(NNs)-basedsystemwithoutinput,i.e.,,canbeapproximatedbyautomaticcontrolsystem.ThisislargelyduetotheincreasingaclassofRNNtoanarbitrarydegreeofaccuracy[8].Thedy-demandforapplicationsinsystemiden
7、tification,intelligentcon-namicalsystem,,studiedbyFunahashiandNaka-trolsystem,andsignalprocessing.TheperformanceofNN-basedmurais,infact,aspecialtypeofdynamicalsystemsnotusuallyapplicationsreliesheavilyuponthefunctionalapproximationca-associatedwithacontrolenvironment.Recently,Chowand
8、LipabilityoftheNN.M
