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1、Vol.31,No.3ACTAAUTOMATICASINICAMay,2005ShapingofOutputPDFBasedontheRationalSquare-rootB-splineModel1)ZHOUJing-Lin1YUEHong1,2WANGHong1,21(InstituteofAutomation,ChineseAcademyofSciences,Beijing100080)2(ControlSystemCentre,theUniversityofManchester,Manchester,M60QD,U.K.)(E
2、-mail:jinglin.zhou@mail.ia.ac.cn)AbstractThispaperpresentsanewmethodforthemodelingandcontroloftheoutputprobabilitydensityfunctions(PDFs)oflinearstochasticsystems.Atfirst,anewPDFapproximationmethod,namelytherationalsquare-rootB-splinemodelisproposedandtheinnovativeconcept
3、ofpseudo-weightsisintroduced.ThenewmodelisthencomparedwiththeexistingB-splinemodelsintermsoffeasibledomains.Next,acontrollerisdevelopedtorealizetheoutputPDFtrackingperformance.AnalternativeminimalentropycontrolstrategyisalsoprovidedforthecasethatnotargetPDFisavailable.F
4、inally,illustrativeexamplesindicatetheeffectivenessoftheproposedalgorithms.KeywordsDynamicstochasticsystems,probabilitydensityfunction(PDF),B-splineneuralnetwork,robustcontrol,minimumentropycontrol1IntroductionAsrequiredbyanumberofpracticalsystemssuchastheparticlesizedis
5、tributioncontrolandmolecularweightdistributioncontrolinpolymerizationprocesses,3Dsolidsdensitydistributioncontrolinpaperindustries,particlesizedistributioncontrolinpowderindustries,etc.,theshapecontrolofthe[1∼7]outputPDFofgeneralstochasticsystemshasbeenasubjectofresearc
6、hinrecentyears,whichisnamedasstochasticdistributioncontrol(SDC).TheadvantagesoftheshapecontrolofoutputPDFhavebeenrecognizedinthattheshapeofPDFincludescompleteinformationaboutboththesystemdynamicsandthePDFofthesystemdistributions.Traditionalstatisticssuchasmeanandvarianc
7、eareeasilycalculatedfromthePDF,whiletheshapeofPDFcomprisesawealthofadditionalinformation.[8]Intheshapecontrol,threemajorapproacheshavebeendeveloped:1)closed-loopPDFcontrol,2)[9]processPDFcontroland3)outputPDFcontrol(SDC).Inthispaper,ourattentionsfocusonSDC.Themainpurpos
8、eofSDCsystemsistoselectacrispcontrolinputthatcanmaketheoutputPDFtofollowatargetPDF.Thisisdifferentfromthetradit
