Infinite Dimensional Optimization and Control Theory

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Cover; Series Page; Title; Copyright; Dedication; FOREWORD; Acknowledgments; Part I Finite Dimensional Control Problems; 1 Calculus of Variations and Control Theory; 1.1. Calculus of Variations: Surface of Revolution of Minimum Area; 1.2. Interpretation of the Results; 1.3. Mechanics and Calculus of Variations; 1.4. Optimal Control: Fuel Optimal Landing of a Space Vehicle; 1.5. Optimal Control Problems Described by Ordinary Differential Equations; 1.6. Calculus of Variations and Optimal Control. Spike Perturbations; 1.7. Optimal Control: Minimum Drag Nose Shape in Hypersonic Flow. 1.8. Control of Functional Differential Equations: Optimal Forest Growth1.9. Control of Partial Differential Equations: Optimal Cooling of a Plate and Optimal Stabilization of a Vibrating Membrane; 1.10. Finite Dimensional and Infinite Dimensional Control Problems; 2 Optimal Control Problems Without Target Conditions; 2.0. Elements of Measure and Integration Theory. The Lebesgue Integral. Metric, Banach, and Hilbert Spaces; 2.1. Control Systems Described by Ordinary Differential Equations; 2.2. Existence Theory for Optimal Control Problems; 2.3. Trajectories and Spike Perturbations. 2.4. Cost Functionals and Spike Perturbations2.5. Optimal Control Problems without Target Condition: The Hamiltonian Formalism; 2.6. Invariance of the Hamiltonian; 2.7. The Linear-Quadratic Problem: Existence and Uniqueness of Optimal Controls; 2.8. The Unconstrained Linear-Quadratic Problem: Feedback, the Riccati Equation; 2.9. The Constrained Linear-Quadratic Problem; 3 Abstract Minimization Problems: The Minimum Principle for the Time Optimal Problem; 3.1. Abstract Minimization Problems; 3.2. Ekeland's Variational Principle; 3.3. The Abstract Time Optimal Problem; 3.4. The Control Spaces. 3.5. Continuity of the Solution Map3.6. Continuity of the Solution Operator of the Variational Equation; 3.7. The Minimum Principle for the Time Optimal Problem; 3.8. Time Optimal Capture of a Wandering Particle; 3.9. Time Optimal Stopping of an Oscillator; 3.10. Higher Dimensional Problems; 4 Abstract Minimization Problems: The Minimum Principle for General Optimal Control Problems; 4.1. The Abstract Minimization Problem; 4.2. The Minimum Principle for Problems with Fixed Terminal Time; 4.3. Optimal Capture of a Wandering Particle in Fixed Time, I; 4.4. Singular Intervals and Singular Arcs. 4.5. Optimal Capture of a Wandering Particle in Fixed Time, II4.6. The Minimum Principle for Problems with Variable Terminal Time; 4.7. Fuel Optimal Soft Landing of a Space Vehicle: Existence and Identification of the Optimal Control; 4.8. Fuel Optimal Soft Landing of a Space Vehicle: Identification of the Optimal Trajectory; 4.9. Unbounded Control Sets: The Linear-Quadratic Problem and the Minimum Drag Nose Shape Problem; 4.10. Nonlinear Programming Problems: The Kuhn-Thcker Theorem; Miscellaneous Comments for Part I; Part II Infinite Dimensional Control Problems