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1、MathematicalControlTheoryBao-ZhuGuoO±ce:SH1158;Homepage:http://lsc.amss.ac.cn=»bzguo/)Monday:10:15-11:00;11:15-12:00am;Classroom:CB128SchoolofComputationalandAppliedMathematicsUniversityofWitwatersrand,SouthAfrica1IntroductionControltheoryarisesinmostmod
2、ernapplications.Itbecomescertainlyoneofthemostinterdisci-plinarysubjectthathasbeenstronglyinvolvedinthedevelopmentofthecontemporarysociety.Ontheotherhand,controltheoryhasbeenadisciplinewheremanymathematicalideasandmethodshavemelttoproduceanewbodyofimport
3、antmathematics.Accordingly,itisnowadaysarichcrossingpointofengineeringandmathematics.Thiscoursewilladdressmathematicaltheoryinseveralcontroltopics.Inthebeginningofthecourse,weshallhaveabriefreviewofitsorigins,historyandthewayapplicationsandinteractionsof
4、controltheorywithothersciencesandtechnologieshaveconductedthedevelopmentofthediscipline.Duetothefactthatthestudentshaveattendseveralspecialtopicsofcontroltheory,wefocuson¯nite-dimensionalsystems,thesystemsdescribedbytheordinarydi®erentialequations.Somene
5、wtopicsareintroduced.Finally,weintroduceseveralexamplesthatcanbeformulatedintoin¯nitedimensionalsystems,thesystemsdescribedbythepartialdi®erentialequations.Referencebooks(1).JerzyZabczyk,MathematicalControlTheory{AnIntroduction,BirkhÄauser,Boston,1992.(2
6、).EduardoD.Sontag,MathematicalControlTheory:DeterministicFiniteDimensionalSystems,SecondEdition,Springer,NewYork,1998.(3).K.M.Zhou,J.C.DoyleandK.Glover,RobustandOptimalControl,Prentice-Hall,Inc.,1995.(4).T.GladandL.Ljung,ControlTheory,TaylorandFrancis,Lo
7、ndon,2000.2Originsandbasicideas,conceptsandingredientsThemostmaterialsofthissectioncomefromthefollowingpaper:E.Fern¶andez-CaraandE.Zuazua,Onthehistoryandperspectivesofcontroltheory,MatapliNo.74(2004),47-73.Thewordcontrolhasadoublemeaning.First,controllin
8、gasystemcanbeunderstoodsimplyastestingorcheckingthatitsbehaviorissatisfactory.Inadeepsense,tocontrolisalsotoact,toputthingsinordertoguaranteethatthesystembehavesasdesired.Aearlierhistoryofcontrolengineeringcanbefoundintheb
