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1、StochasticOptimalControlTheDiscreteTimeCaseThisisVolume139inMATHEMATICSINSCIENCEANDENGINEERINGASeriesofMonographsandTextbooksEditedbyRICHARDBELLMAN,UniversityofSouthernCaliforniaThecompletelistingofbooksinthisseriesisavailablefromthePublisheruponrequest.StochasticOptimalContr
2、olTheDiscreteTimeCaseDIMITRIP.BERTSEKASDEPARTMENTOFELECTRICALENGINEERINGANDCOORDINATEDSCIENCELABORATORYUNIVERSITYOFILLINOISURBANA,ILLINOISSTEVENE.SHREVEDEPARTMENTOFMATHEMATICALSCIENCESUNIVERSITYOFDELAWARENEWARK,DELAWAREACADEMICPRESSNewYorkSanFranciscoLondon1978ASubsidiaryofHa
3、rcourtBraceJovanovich,PublishersCOPYRIGHT©1978,BYACADEMICPRESS,INC.ALLRIGHTSRESERVED.NOPARTOFTHISPUBLICATIONMAYBEREPRODUCEDORTRANSMITTEDINANYFORMORBYANYMEANS,ELECTRONICORMECHANICAL,INCLUDINGPHOTOCOPY,RECORDING,ORANYINFORMATIONSTORAGEANDRETRIEVALSYSTEM,WITHOUTPERMISSIONINWRITI
4、NGFROMTHEPUBLISHER.ACADEMICPRESS,INC.IIIFifthAvenue,NewYork.NewYork10003UnitedKingdomEditionpublishedbyACADEMICPRESS,INC.(LONDON)LTD.24/28OvalRoad,LondonNWI7DXLibraryofCongressCataloginginPublicationDataBertsekas,DimitriPStochasticoptimalcontrol.(Mathematicsinscienceandengine
5、ering;v.Includesbibliographicalreferencesandindex.1.Dynamicprogramming.2.Stochasticprocesses.3.Measuretheory.I.Shreve,StevenE.,jointauthor.II.Title.III.Series.T57.83.B49519.7'0377-25727ISBN0-12-093260-1AMS(MOS)1970SubjectClassifications:28A05,49C15,60B05,62C99,90A05PRINTEDINT
6、HEUNITEDSTATESOFAMERICAToJoannaandSteve'sMomandDadThispageintentionallyleftblankContentsPrefacexiAcknowledgmentsxiiiChapterIIntroduction1.1StructureofSequentialDecisionModels1.2Discrete-TimeStochasticOptimalControlProblems-MeasurabilityQuestions51.3ThePresentWorkRelatedtotheL
7、iterature13PartIANALYSISOFDYNAMICPROGRAMMINGMODELSChapter2MonotoneMappingsUnderlyingDynamicProgrammingModels2.1NotationandAssumptions252.2ProblemFormulation282.3ApplicationtoSpecificModels292.3.1DeterministicOptimalControl302.3.2StochasticOptimalControl-CountableDisturbanceSp
8、ace312.3.3StochasticOptimalControl-OuterIntegralFormulation352.3.4St
