singular optimal control problems (david j. bell, david h. jacobson)

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1、SingularOptimalControlProblemsThisisVolume1I7inMATHEMATICS1NSCIENCEANDENGINEERINGASeriesofMonographsandTextbooksEditedbyRICHARDBELLMAN,UniversityofSouthernCaliforniaThecompletelistingofbooksinthisseriesisavailablefromthePublisheruponrequest.SingularOptimalControlProblemsDAVIDJ.BELLDepartmentof

2、MathematicsandControlSystemsCentreUniversityofManchesterInstituteofScienceandTechnologyManchester,EnglandandDAVIDH.JACOBSONNationalResearchInstituteforMathematicalSciencesCouncilforScientificandIndustrialResearch,SouthAfrica(HonoraryProfessorintheUniversiiyoftheWitwatersrand)1975AcademicPressL

3、ondon:NewYork:SanFranciscoASubsidiaryofHarcourtBraceJovanovich,PublishersACADEMICPRESSINC.(LONDON)LTD.24-28OvalRoad1,ondonNWIU.S.Editionpublishedhi.ACADEMICPRESSINC.IIIFifthAvenueNewYork.NewYork10003Copyright01975byACADEMiCPRESSINC.(LONDON)LTD.AllRighisRe.wr

4、nanyformbyphotostat,microfilm.oranyothermeans.withoutwrittenpermissionfromthepublishersLibraryofCongressCatalogCardNumber.75-21610ISBN:0-12-085060-5I’rinlcdin(;rc;itHritainhkGalliard(Pi-inter)L.td.GreatYarrnouthPREFACEThemoderntheoryofoptimalcontrolhasitsbeginningsinthepioneeringworkofmensuch

5、asHohmanninEuropeandGoddardintheUnitedStates.Thesemen,andotherslikethem,dreamtofthedaywhenspacetravelwouldbecomeareality.Itistheworkofthesepioneerswhichhashelpedtobringtheirdreamstopartialfulfillmentinsuchabriefperiodoftime.Theoptimizationproblemsofspaceflightdynamicssuchasminimumfuelandminimu

6、mtimewerequicklyrealizedtobeproblemsinthecalculusofvariations.ItwasthusthatthisveryoldandestablishedbranchofMathematicsreceivedyetanothernewleaseoflife,apatternwhichhasbeenrepeatedsinceitsbirthintheseventeenthcentury.ProblemsofhighperformanceaircraftbecameimportantneartheendoftheSecondWorldWar

7、.Maximumrangeofaircraftforagivenquantityoffuelandminimumtimetoclimbweretypicaloptimizationproblemswhicharose.Thesetoowereclearlyproblemsbelongingtothesameclassasthosefromspacedynamicsalthoughcomplicatedbythepresenceofaerodynamicliftandd