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1、JOURNALOFGUIDANCE,CONTROL,ANDDYNAMICSVol.31,No.2,March–April2008OptimalFeedbackControl:Foundations,Examples,andExperimentalResultsforaNewApproachI.MichaelRoss∗andPooyaSekhavat†NavalPostgraduateSchool,Monterey,California93943AndrewFleming‡U.S.Navy,Washington,D.C.2003andQiGong§NavalPostgraduateSchool
2、,Monterey,California93943DOI:10.2514/1.29532Typicaloptimalfeedbackcontrolsarenonsmoothfunctions.Nonsmoothcontrolsraisefundamentaltheoreticalproblemsontheexistenceanduniquenessofstatetrajectories.ManyoftheseproblemsarefrequentlyaddressedincontrolapplicationsthroughtheconceptofaFilippovsolution.Inrec
3、entyears,thesimplerconceptofasolutionhasemergedasapracticalandpowerfulmeanstoaddressthesetheoreticalissues.Inthispaper,weadvancethenotionofCarathéodory–solutionsthatstemfromtheequivalencebetweenclosed-loopandfeedbacktrajectories.Inrecognizingthatfeedbackcontrolsarenotnecessarilyclosed-formexpress
4、ions,wedevelopasamplingtheoremthatindicatesthattheLipschitzconstantofthedynamicsisafundamentalsamplingfrequency.Theseideasleadtoanewsetoffoundationsforachievingfeedbackwhereinoptimalityprinciplesareinterwoventoachievestabilityandsystemperformance,whereasthecomputationofoptimalcontrolsisatthelevelof
5、firstprinciples.WedemonstratetheseprinciplesbywayofpseudospectralmethodsbecausethesetechniquescangenerateCarathéodory–solutionsatasufficientlyfastsamplingrateevenwhenimplementedinaMATLAB®environmentrunningonlegacycomputerhardware.Tofacilitateanexpositionoftheproposedideastoawideaudience,weintroducet
6、hecoreprinciplesonlyandrelegatetheintricatedetailstonumerousrecentreferences.TheseprinciplesarethenappliedtogeneratepseudospectralfeedbackcontrolsfortheslewmaneuveringofNPSAT1,aspacecraftconceived,designed,andbuiltattheNavalPostgraduateSchoolandscheduledtobelaunchedinfall2007.I.Introductionkt;xt
7、ut2Ut;xt(2)CONSIDERtheproblemofgeneratingfeedbackcontrolsforthegeneralnonlinearsystemItiswellrecognized[1,2]thatthisisoneofthemostdifficultproblemsincontroltheory.Inthispaper,weaddtwoadditionalx_fx
