无限维最优化和控制论（影印版）

　　This book studies existence and necessary conditions， such as Pontryagin's maximum principle for optimal control problems described by ordinary and partial differential equations. These necessary conditions are obtained from Kuhn-Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints， state constraints， and target conditions. Evolution partial differential equations are studied using semigroup theory， abstract differential equations in linear spaces， integral equations， and interpolation theory. Existence of optimal controls is established for arbitrary control sets by means of a general theory of relaxed controls. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type; the latter case deals with pointwise constraints on the solution and the gradient. The book also includes results on convergence of suboptimal controls. H. O. Fattorini is Professor of Mathematics at the University of California， Los Angeles.本书为英文版。

暂缺《无限维最优化和控制论（影印版）》作者简介

Foreword
PartIFiniteDimensionalControlProblems
1CalculusofVariationsandControlTheory
1.1CalculusofVariations:SurfaceofRevolutionofMinimumArea
1.2InterpretationoftheResults
1.3MechanicsandCalculusofVariations
1.4OptimalControl:FuelOptimalLandingofaSpaceVehicle
1.5OptimalControlProblemsDescribedbyOrdinaryDifferentialEquations
1.6CalculusofVariationsandOptimalControl.SpikePerturbations
1.7OptimalControl:MinimumDragNoseShapeinHypersonicFlow
1.8ControlofFunctionalDifferentialEquations:OptimalForestGrowth
1.9ControlofPartialDifferentialEquations
1.10FiniteDimensionalandInfiniteDimensionalControlProblems
2OptimalControlProblemsWithoutTargetConditions
2.0ElementsofMeasureandIntegrationTheory
2.1ControlSystemsDescribedbyOrdinaryDifferentialEquations
2.2ExistenceTheoryforOptimalControlProblems
2.3TrajectoriesandSpikePerturbations
2.4CostFunctionalsandSpikePerturbations
2.5OptimalControlProblemswithoutTargetCondition:TheHamiltonianFormalism
2.6InvarianceoftheHamiltonian
2.7TheLinear-QuadraticProblem:ExistenceandUniquenessofOptimalControls
2.8TheUnconstrainedLinear-QuadraticProblem:Feedback,theRiccatiEquation
2.9TheConstrainedLinear-QuadraticProblem
3AbstractMinimizationProblems:TheMinimumPrinciplefortheTimeOptimalProblem
3.1AbstractMinimizationProblems
3.2Ekeland'sVariationalPrinciple
3.3TheAbstractTimeOptimalProblem
3.4TheControlSpaces
3.5ContinuityoftheSolutionMap
3.6ContinuityoftheSolutionOperatoroftheVariationalEquation
3.7TheMinimumPrinciplefortheTimeOptimalProblem
3.8TimeOptimalCaptureofaWanderingParticle
3.9TimeOptimalStoppingofanOscillator
3.10HigherDimensionalProblems
4TheMinimumPrincipleforGeneralOptimalControlProblems
4.1TheAbstractMinimizationProblem
4.2TheMinimumPrincipleforProblemswithFixedTerminalTime
4.3OptimalCaptureofaWanderingParticleinFixedTime,I
4.4SingularIntervalsandSingularArcs
4.5OptimalCaptureofaWanderingParticleinFixedTime,II
4.6TheMinimumPrincipleforProblemswithVariableTerminalTime
4.7FuelOptimalSoftLandingofaSpaceVehicle
4.8FuelOptimalSoftLandingofaSpaceVehicle
4.9TheLinear-QuadraticProblemandtheMinimumDragNoseShapeProblem
4.10NonlinearProgrammingProblems:TheKuhn-TuckerTheorem
PartIIInfiniteDimensionalControlProblems
5DifferentialEquationsinBanachSpacesandSemigroupTheory
5.0BanachSpacesandTheirDuals.LinearOperators.IntegrationofVectorValuedFunctions
5.1PartialDifferentialEquationsasOrdinaryDifferentalEquationsinBanachSpaces
5.2AbstractCauchyProblemsint>0
5.3AbstractCauchyProblemsin-5.4EvolutionEquations
5.5SemilinearEquationsinBanachSpaces.PerturbationTheory
5.6WaveEquations
5.7SemilinearWaveEquations:LocalExistence
5.8SemilinearEquationsinBanachSpaces:GlobalExistence
5.9SemilinearWaveEquations:GlobalExistence
6AbstractMinimizationProblemsinHilbertSpaces
6.1ControlSystems:ContinuityoftheSolutionMap
6.2PatchPerturbationsandDirectionalDerivatives
6.3ContinuityoftheSolutionOperatoroftheVariationalEquation
6.4AbstractMinimizationProblemsAgain
6.5TheMinimumPrinciplefortheTimeOptimalProblem
6.6TheMinimumPrincipleforGeneralControlProblems
6.7OptimalProblemsforSomeLinearandSemilinearEquations
6.8SemilinearWaveEquationsAgain
6.9TheTimeOptimalProblemforaSemilinearWaveEquation,I
6.10SomeRemarksonAdjointEquations
6.11SomeRemarksonControllability
6.12TheTimeOptimalProblemforaSemilinearWaveEquation,II
7AbstractMinimizationProblemsinBanachSpaces
7.1SomeGeometryofBanachSpaces
7.2AbstractMinimizationProblemsfortheLastTime
7.3TheMinimumPrincipleinBanachSpaces
7.4FractionalPowersofInfinitesimalGenerators.AnalyticSemigroups.Duality
7.5EllipticOperatorsinL2Spaces
7.6EllipticOperatorsinLpandCSpaces.Duality
7.7SemilinearAbstractParabolicEquations
7.8SemilinearAbstractParabolicEquations:GlobalExistence
7.9LinearAbstractParabolicEquations.Duality
7.10PatchPerturbationsandDirectionalDerivatives
8InterpolationandDomainsofFractionalPowers
8.1TraceSpacesandSemigroups
8.2InterpolationandFractionalPowers
8.3InterpolationandSobolevSpaces
8.4ParabolicEquations
8.5FractionalPowersandtheComplexInterpolationMethod
8.6TheNavier-StokesEquations
9LinearControlSystems
9.1LinearSystems:TheMinimumPrinciple
9.2TheMinimumPrinciplewithFullControl
9.3Bang-BangTheoremsandApproximateControllability
9.4ExactandApproximateControllability
9.5ControllabilitywithFiniteDimensionalControls
9.6ControllabilityandtheMinimumPrinciple
10OptimalControlProblemswithStateConstraints
10.1OptimalControlProblemswithStateConstraints
10.2IntegrationwithRespecttoVector-ValuedMeasures
10.3TheMinimumPrinciplewithStateConstraints
10.4SaturationoftheStateConstraint
10.5SurfaceofRevolutionofMinimumAreaasaControlProblem
10.6OtherApplications
11OptimalControlProblemswithStateConstraints
11.1AbstractParabolicEquations:TheMeasure-DrivenAdjointVariationalEquation
11.2AbstractParabolicEquations:TheMinimumPrinciplewithStateConstraints
11.3ApplicationstoParabolicDistributedParameterSystems
11.4ParabolicDistributedParameterSystems,I
11.5ParabolicDistributedParameterSystems,II
11.6LinearSystems:TheMinimumPrinciplewithStateConstraints
11.7ControlProblemsfortheNavier-StokesEquations
11.8ControlProblemsfortheNavier-StokesEquations:ThePointTargetCase
11.9ConvergenceofSuboptimalControls,I
11.10ConvergenceofSuboptimalControls,II
11.11ParabolicEquations
11.12TheNavier-StokesEquations
PartIIIRelaxedControls
12SpacesofRelaxedControls.TopologyandMeasureTheory
12.0WeakTopologiesinLinearSpaces
12.1ExistenceTheoryofOptimalControlProblems:Measure-ValuedControls
12.2SpacesofVectorValuedFunctionsandTheirDuals,I
12.3FinitelyAdditiveMeasures:Integration
12.4MeasuresandLinearFunctionalsinFunctionSpaces
12.5SpacesofRelaxedControls
12.6ApproximationinSpacesofMeasuresandSpacesofRelaxedControls
12.7TopologyandMeasureTheory
12.8TheFilippovImplicitFunctionTheorem
12.9SpacesofVectorValuedFunctionsandTheirDuals,II
13RelaxedControlsinFiniteDimensionalSystems
13.1InstallationofRelaxedControlsinFiniteDimensionalSystems
13.2ApproximationofRelaxedTrajectoriesbyOrdinaryTrajectories
13.3TheFilippovImplicitFunctionTheoremintheCompactCase
13.4DifferentialInclusions
13.5ExistenceTheoremsforRelaxedOptimalControlProblems
13.6ExistenceTheoremsforOrdinaryOptimalControlProblems
13.7TheMinimumPrincipleforRelaxedOptimalControlProblems
13.8NoncompactControlSets
14RelaxedControlsinInfiniteDimensionalSystems
14.1ControlSystems:LimitsofTrajectories
14.2SemilinearSystemsLinearintheControl.ApproximationbyExtremalTrajectories
14.3InstallationofRelaxedControlsinInfiniteDimensionalSystems
14.4DifferentialInclusions
14.5ExistenceTheoremsforOptimalControlProblems,I
14.6ExistenceTheoremsforOptimalControlProblems,II
14.7AbstractParabolicEquations,I
14.8AbstractParabolicEquations,II
14.9ExistenceUnderCompactnessoftheNonlinearTerm
14.10ExistenceWithoutCompactness
References
Index