具有分布滞后的系统：自适应辨识与预测(IJISA-V8-N3-1)

I.J.IntelligentSystemsandApplications,2016,3,1-13PublishedOnlineMarch2016inMECS()DOI:10.5815/ijisa.2016.03.01Copyright©2016MECSI.J.IntelligentSystemsandApplications,2016,3,1-13SystemwithDistributedLag:AdaptiveIdentificationandPredictionNikolayKarabutovMoscowstateuniversityofinformationtechnology,radioengineering,electronics/DepartmentofProblemsControl;Moscow,RussiaE-mail:[e-mail],[e-mail]—Adaptivealgorithmsofparametricidentifica-tionofdiscretesystemswithlagvariablesareproposed.Adaptivealgorithms(AA)inthepresenceoflaginputvariablesaredeveloped.TheconvergenceoftheAAandtheboundednessofthetrajectoriestheadaptivesystemisproved.ConvergencedomainААdependsonoperatingdisturbance.Modelswithmultiplicativeparameters(MPM)forthedecreaseofanumberestimatedparame-tersareoffered.TheprocessforselectionofthevectorofbaseparametersMPMwasdeveloped.Theperformanceofadaptivesystemidentificationforthiscaseisproved.Itisshownthatparametersofsystemestimationattheap-plicationofmultiplicativeidentificationmustbechosenfromaconditionofminimizationofthecriterionofthepredictionerror.Transformationofinterdependencebe-tweenthelaggedvariablesisoffered,allowingeliminat-ingtheireffectonsystemwork.Inthesecondpartofwork,themethodofsynthesisААidentificationofthesystemscontaininglaggedoutputvariablesisoffered.Weconsideracaseoflinearcorrelationbetweenanoutputofthesystemandoperatingdisturbance.Forasolutionofaproblem,wesuggestfulfillinganestimationofoperatingdisturbance.Correspondingproceduresaredescribedandprovedtheirefficiency.Simulationresultsarepresentedthatconfirmtheefficiencyoftheadaptivemethods.IndexTerms—Adaptivealgorithm,identification,dis-tributedlag,convergence,model,decisionmaking.I.INTRODUCTIONLagmodelsareusedtoadescriptionofworkengineer-ing[1-3]andeconomicsystems[4-7],andalsoinmedi-cine[8-10].Accountinglagvariablesleadstoseveralproblemsthatthesolutionoftheproblemparametricidentificationcomplicated.Themainoftheseproblemsistherelationship(correlation,multicollinearity)betweenvariables[4-6].Ineconomicsystems,thisinteractionarisesbetweenthedependentandindependentvariablesandtheoperatingdisturbances.Variousmodelsofap-proximationofparametersatdistributedlags(parametricschemes)areappliedtoattenuationofsuchinterferencesontheidentificationprocess.Thisreducesthenumberofestimatedparametersoftheobject.InidentificationsystemswidelyapplytheparametrictheКоускscheme[5,11].Itisbasedonachangeofcoef-ficientsofamodelonadecreasinggeometricprogression.Fishermodel[4,12]isbasedonthechangeofmodelcoefficientsforagivendecreasingarithmeticprogression.Arithmeticalandgeometricalmodelsareapplied,whenplantparametersdecreasefromthefirstmembersofaprogression[13].Consideringit,S.Almon[14]modifiedFishermodel.Hehasappliedthepolynomiallawofachangeoffactors.In[12]parametricschemebasedontheuseoflogarithmicnormaldistribution.Thissameconceptbasedontheapplicationofexponentialdistributionlaw,isconsideredin[15].In[16]appliedthePascaldistribu-tion,whichleadstoasimpleformforthecoefficients.Aprioridefineofrelationshipintheparametricschemeintheformofarationalpolynomialisconsideredin[17].Otherapproachestodefineoffactorsatdistributedlagsareconsideredin[7].Applicationofparametricschemesinsystemswithadistributedlagisadominatingdirectioninaneconomet-rics.Usually,variousmodificationsspecifiedaboveschemesforthepurposeofdecreaseofanumberofesti-matedparameters[18]areapplied.Themainpurposeofsuchschemesistheidentificationofparameterswiththehelpamethodofleastsquaresoramaximumlikelihood[4,18].Inconditionsofaprioriuncertainty,thisap-proachtoidentificationisnotalwayseffectiveandre-quiresadditionaltime-consumingresearch.Forasolutionoftheproblemsinherentparametricschemes,modelsofadaptiveorrationalexpectations[19]apply.Parametricschemestheproblemofconsistentestimationonfinitesamplesgenerates.Consideringthesedifficulties,applica-tionofadaptivemethodsistheperspectiveapproachtoanestimationofparameters.Theadaptiveapproachisappliedforthesynthesisofmodelsdescribingthechangeofeconomicindicators.Soin[20]theexpandedKalmanfilterisapplied.Theadap-tivealgorithmoftuningparametersofthefilterisrecur-siveprocedureofleastsquares.Notethattheauthorsoftheconceptofadaptivecanattachdifferentmeanings.Adaptation[21]canbeachoiceofstructuremodelonthebasisoftheapplicationsearchofthesetcandidates.In[22]proposedaheuristicprocedure,whichisinterpretedasadaptive.In[23]applytheleastsquaresmethodfortuningparametersofalinearadaptivemodelwithadis-tributedlagontheinput.TheparametricschemeofachangeoffactorsofthemodelissetApriori.Itallowstominimizethenumberofadjustedparameters.Thestruc-tureofmodelbyresultsofsimulationischosen.In[24]theproblemofanestimationparameterssystemwitha2SystemwithDistributedLag:AdaptiveIdentificationandPredictionCopyright©2016MECSI.J.IntelligentSystemsandApplications,2016,3,1-13lineardistributedlagonanindependentvariableiscon-sidered.Itisassumedthatthemodelcoefficientsdecreasewithincreasinglag.Thesolutionofaproblemanestima-tionparametersonthebasisofquadraticfunctiona