CALCULUS OF VARIATIONS AND OPTIMAL CONTROL THEORY.pdf

《CALCULUS OF VARIATIONS AND OPTIMAL CONTROL THEORY.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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......