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1、ControlTheoryIIBao-ZhuGuoO±ce:SH1158;Homepage:http://lsc.amss.ac.cn=»bzguo/)Monday10:00-12:00;Friday10:00-12:00;Lectureroom:SH1126SchoolofComputationalandAppliedMathematicsUniversityofWitwatersrand,SouthAfrica1IntroductionControltheoryarisesinmostmodernapplications.Itbecomescertainlyoneo
2、fthemostinterdisci-plinarysubjectthathasbeenstronglyinvolvedinthedevelopmentofthecontemporarysociety.Ontheotherhand,controltheoryhasbeenadisciplinewheremanymathematicalideasandmethodshavemelttoproduceanewbodyofimportantmathematics.Accordingly,itisnowadaysarichcrossingpointofengineeringan
3、dmathematics.Thiscoursewilladdressmathematicaltheoryinseveralcontroltopics.Inthebeginningofthecourse,weshallhaveabriefreviewofitsorigins,historyandthewayapplicationsandinteractionsofcontroltheorywithothersciencesandtechnologieshaveconductedthedevelopmentofthediscipline.Duetothefactthatth
4、estudentshaveattendseveralspecialtopicsofcontroltheory,wefocuson¯nite-dimensionalsystems,thesystemsdescribedbytheordinarydi®erentialequations.Somenewtopicsareintroduced.Finally,weintroduceseveralexamplesthatcanbeformulatedintoin¯nitedimensionalsystems,thesystemsdescribedbythepartialdi®er
5、entialequations.Referencebooks(1).JerzyZabczyk,MathematicalControlTheory{AnIntroduction,BirkhÄauser,Boston,1992.(2).EduardoD.Sontag,MathematicalControlTheory:DeterministicFiniteDimensionalSystems,SecondEdition,Springer,NewYork,1998.(3).K.M.Zhou,J.C.DoyleandK.Glover,RobustandOptimalContro
6、l,Prentice-Hall,Inc.,1995.(4).T.GladandL.Ljung,ControlTheory,TaylorandFrancis,London,2000.2Originsandbasicideas,conceptsandingredientsThemostmaterialsofthissectioncomefromthefollowingpaper:E.Fern¶andez-CaraandE.Zuazua,Onthehistoryandperspectivesofcontroltheory,MatapliNo.74(2004),47-73.Th
7、ewordcontrolhasadoublemeaning.First,controllingasystemcanbeunderstoodsimplyastestingorcheckingthatitsbehaviorissatisfactory.Inadeepsense,tocontrolisalsotoact,toputthingsinordertoguaranteethatthesystembehavesasdesired.Aearlierhistoryofcontrolengineeringcanbefoundinthebook:
