Computational Methods for Optimizing Distributed Systems
Published on 21. August 1984
316 pages
978-0-08-095678-7 (ISBN)
Description
Optimal control theory of distributed parameter systems has been a very active field in recent years; however, very few books have been devoted to the studiy of computational algorithms for solving optimal control problems. For this rason the authors decided to write this book. Because the area is so broad, they confined themselves to optimal control problems involving first and second boundary-value problems of a linear second-order parabolic partial differential equation. However the techniques used are by no means restricted to these problems. They can be and in some cases already have been applied to problems involving other types of distributed parameter system. The authors aim is to devise computational algorithms for solving optimal control problems with particular emphasis on the mathematical theory underlying the algorithms. These algorithms are obtained by using a first-order strong variational method or gradient-type methods.
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K. L. Teo
Teo Optimal Parameter Syst
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01/1984
Academic Press
€106.19
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Content
- Front Cover
- Computational Methods for Optimizing Distributed Systems
- Copyright Page
- Contents
- Preface
- Chapter I. Mathematical Background
- 1. Introduction
- 2. Some Basic Concepts in Functional Analysis
- 3. Some Basic Concepts in Measure Theory
- 4. Some Function Spaces
- 5. Relaxed Controls
- 6. Multivalued Functions
- 7. Bibliographical Remarks
- Chapter II. Boundary Value Problems of Parabolic Type
- 1. Introduction
- 2. Boundary-Value Problems-Basic Definitions and Assumptions
- 3. Three Elementary Lemmas
- 4. A Priori Estimates
- 5. Existence and Uniqueness of Solutions
- 6. A Continuity Property
- 7. Certain Properties of Solutions of Equation (2.1)
- 8. Boundary-Value Problems in General Form
- 9. A Maximum Principle
- Chapter III. Optimal Control of First Boundary Problems: Strong Variation Techniques
- 1. Introduction
- 2. System Description
- 3. The Optimal Control Problems
- 4. The Hamiltonian Functions
- 5. The Successive Controls
- 6. The Algorithm
- 7. Necessary and Sufficient Conditions for Optimality
- 8. Numerical Consideration
- 9. Examples
- 10. Discussion
- Chapter IV. Optimal Policy of First Boundary Problems: Gradient Techniques
- 1. Introduction
- 2. System Description
- 3. The Optimization Problem
- 4. An Increment Formula
- 5. The Gradient of the Cost Functional
- 6. A Conditional Gradient Algorithm
- 7. Numerical Consideration and an Examples
- 8. Optimal Control Problems with Terminal Inequality Constraints
- 9. The Finite Element Method
- 10. Discussion
- Chapter V. Relaxed Controls and the Convergence of Optimal Control Algorithms
- 1. Introduction
- 2. The Strong Variational Algorithm
- 3. The Conditional Gradient Algorithm
- 4. The Feasible Directions Algorithm
- 5. Discussion
- Chapter VI. Optimal Control Problems Involving Second Boundary-Value Problems
- 1. Introduction
- 2. The General Problem Statement
- 3. Preparatory Results
- 4. A Basic Inequality
- 5. An Optimal Control Problem with a Linear Cost Functional
- 6. An Optimal Control Problem with a Linear System
- 7. The Finite Element Method
- 8. Discussion
- Appendix I: Stochastic Optimal Control Problems
- Appendix II: Certain Results on Partial Differential Equations Needed in Chapters III, IV, and V
- Appendix III: An Algorithm of Quadratic Programming
- Appendix IV: A Quasi-Newton Method for Nonlinear Function Minimization with Linear Constraints
- Appendix V: An Algorithm for Optimal Control Problems of Linear Lumped Parameter Systems
- Appendix VI: Meyer-Polak Proximity Algorithm
- References
- List of Notation
- Index
