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1、PrefacetotheSecondEditionThemostsigni?cantdi?erencesbetweenthiseditionandthe?rstareasfollows:?Additionalchaptersandsectionshavebeenwritten,dealingwith:–nonlinearcontrollabilityviaLie-algebraicmethods,–variationalandnumericalapproachestononlinearcontrol,includingabrief
2、introductiontotheCalculusofVariationsandtheMinimumPrinciple,–time-optimalcontroloflinearsystems,–feedbacklinearization(single-inputcase),–nonlinearoptimalfeedback,–controllabilityofrecurrentnets,and–controllabilityoflinearsystemswithboundedcontrols.?Thediscussiononnon
3、linearstabilizationhasbeenexpanded,introducingthebasicideasofcontrol-Lyapunovfunctions,backstepping,anddampingcontrol.?Thechapterondynamicprogrammingandlinear-quadraticproblemshasbeensubstantiallyedited,sothatthematerialonlinearsystemscanbereadinafullyindependentmanne
4、rfromthenonlinearpreliminaries.?Afairlylargenumberoferrorsandtyposhavebeencorrected.?Alistofsymbolshasbeenadded.Iwouldliketostronglyencouragereaderstosendmesuggestionsandcom-mentsbye-mail(sontag@control.rutgers.edu),andalsotovisitthefollowingWebsite:http://www.math.ru
5、tgers.edu/?sontag/viiviiiPrefacetotheSecondEditionwhereIexpecttopostupdates,additionalmaterialandreferences,links,anderrata.Thecurrentcontentsofthetextfarexceedwhatcanbedoneinayear,ifallmaterialiscoveredandcompleteproofsaregiveninlectures.However,thereareseveralwaysto
6、structureayear-longcourse,ortwosuchcourses,basedonpartsofthebook.Forexample,onemaycoveronlythelineartheory,skippingtheoptionalsectionsaswellasthechaptersonnonlinearcontrollabilityandmultiplier(variational)methods.Aseparatecourse,fairlyindependent,couldcoverthemoreadva
7、ncednonlinearmaterial.Ultimately,thetopicsshouldre?ectstudentandfacultybackgroundandinterests,andI’llbehappytodiscusssyllabiwithpotentialinstructors.Iwishtothankallthosecolleagues,students,andreaderswhohavesentmesuggestionsandcomments,includinginparticularBrianIngalls
8、,GerardoLa?erriere,MichaelMaliso?,andKonradReif.AmostspecialacknowledgmentgoestoJoseLuisMancillaAguilarandSarahKoskie,whopoi
