Optimal-Feedback-Control-Foundations-Examples-and-Experimental-Results.pdf

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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,thesimplerconceptofa
solutionhasemergedasapracticalandpowerfulmeanstoaddressthesetheoreticalissues.Inthispaper,weadvancethenotionofCarathéodory–
solutionsthatstemfromtheequivalencebetweenclosed-loopandfeedbacktrajectories.Inrecognizingthatfeedbackcontrolsarenotnecessarilyclosed-formexpress

4、ions,wedevelopasamplingtheoremthatindicatesthattheLipschitzconstantofthedynamicsisafundamentalsamplingfrequency.Theseideasleadtoanewsetoffoundationsforachievingfeedbackwhereinoptimalityprinciplesareinterwoventoachievestabilityandsystemperformance,whereasthecomputationofoptimalcontrolsisatthelevelof

5、?rstprinciples.WedemonstratetheseprinciplesbywayofpseudospectralmethodsbecausethesetechniquescangenerateCarathéodory–
solutionsatasuf?cientlyfastsamplingrateevenwhenimplementedinaMATLAB?environmentrunningonlegacycomputerhardware.Tofacilitateanexpositionoftheproposedideastoawideaudience,weintroducet

6、hecoreprinciplesonlyandrelegatetheintricatedetailstonumerousrecentreferences.TheseprinciplesarethenappliedtogeneratepseudospectralfeedbackcontrolsfortheslewmaneuveringofNPSAT1,aspacecraftconceived,designed,andbuiltattheNavalPostgraduateSchoolandscheduledtobelaunchedinfall2007.I.Introductionkt;xt

7、
ut2Ut;xt(2)CONSIDERtheproblemofgeneratingfeedbackcontrolsforthegeneralnonlinearsystemItiswellrecognized[1,2]thatthisisoneofthemostdif?cultproblemsincontroltheory.Inthispaper,weaddtwoadditionalx_
fx