Analysis and control of nonlinear infinite dimensional systems

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Front Cover; Analysis and Control of Nonlinear Infinite Dimensional Systems; Copyright Page ; Contents; Preface; Notation and Symbols; Chapter 1. Preliminaries; 1.1 The Duality Mapping; 1.2 Compact Mappings in Banach Spaces; 1.3 Absolutely Continuous Functions with Values in Banach Spaces; 1.4 Linear Differential Equations in Banach Spaces; Chapter 2. Nonlinear Operators of Monotone Type; 2.1 Maximal Monotone Operators; 2.2 Generalized Gradients (Subpotential Operators); 2.3 Accretive Operators in Banach Spaces; Bibliographical Notes and Remarks. Chapter 3. Controlled Elliptic Variational Inequalities3.1 Elliptic Variational Inequalities. Existence Theory; 3.2 Optimal Control of Elliptic Variational Inequalities; Bibliographical Notes and Remarks; Chapter 4. Nonlinear Accretive Differential Equations; 4.1 The Basic Existence Results; 4.2 Approximation and Convergence of Nonlinear Evolutions and Semigroups; 4.3 Applications to Partial Differential Equations; Bibliographical Notes and Remarks; Chapter 5. Optimal Control of Parabolic Variational Inequalities; 5.1 Distributed Optimal Control Problems. 5.2 Boundary Control of Parabolic Variational Inequalities5.3 The Time-Optimal Control Problem; 5.4 Approximating Optimal Control Problems via the Fractional Steps Method; Bibliographical Notes and Remarks; Chapter 6. Optimal Control in Real Time; 6.1 Optimal Feedback Controllers; 6.2 A Semigroup Approach to the Dynamic Programming Equation; Bibliographical Notes and Remarks; References; Subject Index