Computational Methods for Optimizing Distributed Systems

Charles Teo

• Publisher: Academic Press
• Year: 1984
• Print ISBN: 9780126854800
• eBook ISBN: 9780080956787
• Topic: Computer Science
• Subtopic: Computer Science General
• Index: Computer Science

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.

Table of contents

• Front Cover
• Computational Methods for Optimizing Distributed Systems
• Copyright Page
• Contents
• Preface
• Chapter I. Mathematical Background
• Chapter II. Boundary Value Problems of Parabolic Type
• Chapter III. Optimal Control of First Boundary Problems: Strong Variation Techniques
• Chapter IV. Optimal Policy of First Boundary Problems: Gradient Techniques
• Chapter V. Relaxed Controls and the Convergence of Optimal Control Algorithms
• Chapter VI. Optimal Control Problems Involving Second Boundary-Value Problems
• 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