无限维最优化和控制论 英文版PDF|Epub|txt|kindle电子书版本网盘下载

无限维最优化和控制论 英文版PDF格式电子书版下载

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Part Ⅰ Finite Dimensional Control Problems1

1 Calculus of Variations and Control Theory3

1.1 Calculus of Variations：Surface of Revolution of Minimum Area3

1.2 Interpretation of the Results8

1.3 Mechanics and Calculus of Variations9

1.4 Optimal Control：Fuel Optimal Landing of a Space Vehicle11

1.5 Optimal Control Problems Described by Ordinary Differential Equations12

1.6 Calculus of Variations and Optimal Control.Spike Perturbations13

1.7 Optimal Control：Minimum Drag Nose Shape in Hypersonic Flow17

1.8 Control of Functional Differential Equations：Optimal Forest Growth18

1.9 Control of Partial Differential Equations20

1.10 Finite Dimensional and Infinite Dimensional Control Problems25

2 Optimal Control Problems Without Target Conditions26

2.0 Elements of Measure and Integration Theory26

2.1 Control Systems Described by Ordinary Differential Equations42

2.2 Existence Theory for Optimal Control Problems51

2.3 Trajectories and Spike Perturbations60

2.4 Cost Functionals and Spike Perturbations66

2.5 Optimal Control Problems without Target Condition：The Hamiltonian Formalism67

2.6 Invariance of the Hamiltonian71

2.7 The Linear-Quadratic Problem：Existence and Uniqueness of Optimal Controls76

2.8 The Unconstrained Linear-Quadratic Problem：Feedback,the Riccati Equation78

2.9 The Constrained Linear-Quadratic Problem82

3 Abstract Minimization Problems：The Minimum Principle for the Time Optimal Problem84

3.1 Abstract Minimization Problems84

3.2 Ekeland's Variational Principle87

3.3 The Abstract Time Optimal Problem92

3.4 The Control Spaces100

3.5 Continuity of the Solution Map101

3.6 Continuity of the Solution Operator of the Variational Equation102

3.7 The Minimum Principle for the Time Optimal Problem104

3.8 Time Optimal Capture of a Wandering Particle107

3.9 Time Optimal Stopping of an Oscillator111

3.10 Higher Dimensional Problems118

4 The Minimum Principle for General Optimal Control Problems122

4.1 The Abstract Minimization Problem122

4.2 The Minimum Principle for Problems with Fixed Terminal Time125

4.3 Optimal Capture of a Wandering Particle in Fixed Time，Ⅰ129

4.4 Singular Intervals and Singular Arcs137

4.5 Optimal Capture of a Wandering Particle in Fixed Time，Ⅱ138

4.6 The Minimum Principle for Problems with Variable Terminal Time143

4.7 Fuel Optimal Soft Landing of a Space Vehicle146

4.8 Fuel Optimal Soft Landing of a Space Vehicle149

4.9 The Linear-Quadratic Problem and the Minimum Drag Nose Shape Problem151

4.10 Nonlinear Programming Problems：The Kuhn-Tucker Theorem159

Part Ⅱ Infinite Dimensional Control Problems167

5 Differential Equations in Banach Spaces and Semigroup Theory169

5.0 Banach Spaces and Their Duals.Linear Operators.Integration of Vector Valued Functions169

5.1 Partial Differential Equations as Ordinary Differential Equations in Banach Spaces189

5.2 Abstract Cauchy Problems in t≥0192

5.3 Abstract Cauchy Problems in-∞＜t＜∞203

5.4 Evolution Equations207

5.5 Semilinear Equations in Banach Spaces.Perturbation Theory210

5.6 Wave Equations226

5.7 Semilinear Wave Equations：Local Existence234

5.8 Semilinear Equations in Banach Spaces：Global Existence239

5.9 Semilinear Wave Equations：Global Existence246

6 Abstract Minimization Problems in Hilbert Spaces251

6.1 Control Systems：Continuity of the Solution Map251

6.2 Patch Perturbations and Directional Derivatives253

6.3 Continuity of the Solution Operator of the Variational Equation262

6.4 Abstract Minimization Problems Again263

6.5 The Minimum Principle for the Time Optimal Problem273

6.6 The Minimum Principle for General Control Problems279

6.7 Optimal Problems for Some Linear and Semilinear Equations283

6.8 Semilinear Wave Equations Again288

6.9 The Time Optimal Problem for a Semilinear Wave Equation，Ⅰ291

6.10 Some Remarks on Adjoint Equations293

6.11 Some Remarks on Controllability298

6.12 The Time Optimal Problem for a Semilinear Wave Equation，Ⅱ303

7 Abstract Minimization Problems in Banach Spaces310

7.1 Some Geometry of Banach Spaces310

7.2 Abstract Minimization Problems for the Last Time316

7.3 The Minimum Principle in Banach Spaces325

7.4 Fractional Powers of Infinitesimal Generators.Analytic Semigroups.Duality329

7.5 Elliptic Operators in L2 Spaces340

7.6 Elliptic Operators in Lp and C Spaces.Duality343

7.7 Semilinear Abstract Parabolic Equations347

7.8 Semilinear Abstract Parabolic Equations：Global Existence359

7.9 Linear Abstract Parabolic Equations.Duality364

7.10 Patch Perurbations and Directional Derivatives377

8 Interpolation and Domains of Fractional Powers385

8.1 Trace Spaces and Semigroups385

8.2 Interpolation and Fractional Powers393

8.3 Interpolation and Sobolev Spaces399

8.4 Parabolic Equations402

8.5 Fractional Powers and the Complex Interpolation Method412

8.6 The Navier-Stokes Equations418

9 Linear Control Systems426

9.1 Linear Systems：The Minimum Principle426

9.2 The Minimum Principle with Full Control437

9.3 Bang-Bang Theorems and Approximate Controllability444

9.4 Exact and Approximate Controllability452

9.5 Controllability with Finite Dimensional Controls458

9.6 Controllability and the Minimum Principle467

10 Optimal Control Problems with State Constraints474

10.1 Optimal Control Problems with State Constraints474

10.2 Integration with Respect to Vector-Valued Measures475

10.3 The Minimum Principle with State Constraints490

10.4 Saturation of the State Constraint498

10.5 Surface of Revolution of Minimum Area as a Control Problem501

10.6 Other Applications506

11 Optimal Control Problems with State Constraints509

11.1 Abstract Parabolic Equations：The Measure-Driven Adjoint Variational Equation509

11.2 Abstract Parabolic Equations：The Minimum Principle with State Constraints517

11.3 Applications to Parabolic Distributed Parameter Systems523

11.4 Parabolic Distributed Parameter Systems，Ⅰ528

11.5 Parabolic Distributed Parameter Systems，Ⅱ537

11.6 Linear Systems：The Minimum Principle with State Constraints548

11.7 Control Problems for the Navier-Stokes Equations558

11.8 Control Problems for the Navier-Stokes Equations：The Point Target Case562

11.9 Convergence of Suboptimal Controls，Ⅰ564

11.10 Convergence of Suboptimal Controls，Ⅱ570

11.11 Parabolic Equations575

11.12 The Navier-Stokes Equations583

Part Ⅲ Relaxed Controls601

12 Spaces of Relaxed Controls.Topology and Measure Theory603

12.0 Weak Topologies in Linear Spaces603

12.1 Existence Theory of Optimal Control Problems：Measure-Valued Controls614

12.2 Spaces of Vector Valued Functions and Their Duals，Ⅰ618

12.3 Finitely Additive Measures：Integration628

12.4 Measures and Linear Functionals in Function Spaces635

12.5 Spaces of Relaxed Controls642

12.6 Approximation in Spaces of Measures and Spaces of Relaxed Controls648

12.7 Topology and Measure Theory654

12.8 The Filippov Implicit Function Theorem659

12.9 Spaces of Vector Valued Functions and Their Duals，Ⅱ666

13 Relaxed Controls in Finite Dimensional Systems674

13.1 Installation of Relaxed Controls in Finite Dimensional Systems674

13.2 Approximation of Relaxed Trajectories by Ordinary Trajectories677

13.3 The Filippov Implicit Function Theorem in the Compact Case679

13.4 Differential Inclusions683

13.5 Existence Theorems for Relaxed Optimal Control Problems685

13.6 Existence Theorems for Ordinary Optimal Control Problems690

13.7 The Minimum Principle for Relaxed Optimal Control Problems692

13.8 Noncompact Control Sets699

14 Relaxed Controls in Infinite Dimensional Systems709

14.1 Control Systems：Limits of Trajectories709

14.2 Semilinear Systems Linear in the Control.Approximation by Extremal Trajectories711

14.3 Installation of Relaxed Controls in Infinite Dimensional Systems720

14.4 Differential Inclusions725

14.5 Existence Theorems for Optimal Control Problems，Ⅰ730

14.6 Existence Theorems for Optimal Control Problems，Ⅱ738

14.7 Abstract Parabolic Equations，Ⅰ742

14.8 Abstract Parabolic Equations，Ⅱ748

14.9 Existence Under Compactness of the Nonlinear Term754

14.10 Existence Without Compactness759

References773

Index795