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1、Thankyouforyourinterestinthisbook!Pleasenotethatthecurrentversion–whichisbasedonasetoflecturenotesusedbyUIUCstudents–issignificantlydifferentfromtheversionthatwillbepublishedbyPrincetonUniversityPress.Specifically,thiscopydoesnotreflectnumerous(althoughmostlyminor)correct
2、ionsandeditingdoneduringthepublicationprocess,andthefinalbookformattingwillresultindifferentpagenumbersandoveralllayout.Youarewelcometobrowseanddownloadthispreliminarycopy,butforserioususeIrecommendgettingtheactualbook.DanielLiberzonliberzon@uiuc.eduAugust9,2011iiDANIELLI
3、BERZONSincethebuildingoftheuniverseisperfectandiscreatedbythewisdomcreator,nothingarisesintheuniverseinwhichonecannotseethesenseofsomemaximumorminimum.LeonhardEulerThewordscontroltheory"are,ofcourse,ofrecentorigin,butthesubjectitselfismucholder,sinceitcontainstheclassica
4、lcalculusofvariationsasaspecialcase,andthe rstcalculusofvaria-tionsproblemsgobacktoclassicalGreece.HectorJ.SussmannCoverillustrationbyPolinaBen-Sirac2009ContentsPrefacevii1Introduction11.1Optimalcontrolproblem...................................11.2Somebackgroundon nite-di
5、mensionaloptimization...................31.2.1Unconstrainedoptimization.............................31.2.2Constrainedoptimization..............................91.3Previewofin nite-dimensionaloptimization........................141.3.1Functionspaces,norms,andlocalminima...
6、..................141.3.2Firstvariationand rst-ordernecessarycondition.................161.3.3Secondvariationandsecond-orderconditions...................171.3.4Globalminimaandconvexproblems........................191.4NotesandreferencesforChapter1.........................
7、....202CalculusofVariations212.1Examplesofvariationalproblems..............................212.1.1Dido'sisoperimetricproblem............................212.1.2Lightre
ectionandrefraction............................222.1.3Catenary.......................................232.
8、1.4Brachistochrone...................................242.2Basiccalculusofvariationsproblem......
