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1、fmFebruary23,2010AdaptiveControlofParabolicPDEsThispageintentionallyleftblankfmFebruary23,2010AdaptiveControlofParabolicPDEsAndreySmyshlyaevandMiroslavKrsticPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDfmFebruary23,2010Copyrightc2010byPrincetonUniversityP
2、ressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireOX201TWpress.princeton.eduAllRightsReservedLibraryofCongressCataloging-in-PublicationDataSmysh
3、lyaev,Andrey.AdaptivecontrolofparabolicPDEs/AndreySmyshlyaevandMiroslavKrstic.p.cm.Includesbibliographicalreferencesandindex.ISBN978-0-691-14286-9(hardcover:alk.paper)1.Differentialequations,Parabolic.2.Distributedparametersystems.3.Adaptivecontrolsyste
4、ms.I.Krstic,Miroslav.II.Title.QA374.S592010515.3534dc222009048242BritishLibraryCataloging-in-PublicationDataisavailableThisbookhasbeencomposedinTimesPrintedonacid-freepaper.∞TypesetbySRNovaPvtLtd,Bangalore,IndiaPrintedintheUnitedStatesofAmerica10987654
5、321fmFebruary23,2010ContentsPrefaceixChapter1.Introduction11.1ParabolicandHyperbolicPDESystems11.2TheRolesofPDEPlantInstability,ActuatorLocation,UncertaintyStructure,RelativeDegree,andFunctionalParameters21.3ClassofParabolicPDESystems31.4Backstepping41.
6、5ExplicitlyParametrizedControllers51.6AdaptiveControl51.7OverviewoftheLiteratureonAdaptiveControlforParabolicPDEs61.8InverseOptimality71.9OrganizationoftheBook71.10Notation9PARTINONADAPTIVECONTROLLERS11Chapter2.StateFeedback132.1ProblemFormulation132.2B
7、acksteppingTransformationandPDEforItsKernel142.3ConvertingthePDEintoanIntegralEquation172.4AnalysisoftheIntegralEquationbySuccessiveApproximationSeries192.5StabilityoftheClosed-LoopSystem222.6DirichletUncontrolledEnd242.7NeumannActuation262.8Simulation2
8、72.9Discussion272.10NotesandReferences33Chapter3.Closed-FormControllers353.1TheReaction-DiffusionEquation353.2AFamilyofPlantswithSpatiallyVaryingReactivity383.3SolidPropellantRocketModel403.4PlantswithSpatiallyVaryingDiffusivity4
