Computational methods for optimizing distributed systems, Volume 173 (Mathematics in Science and Engineering)

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. Content: Edited by Page iii Copyright page Page iv Dedication Page v Preface Pages xi-xiii K.L. Teo, Z.S. Wu Chapter I Mathematical Background Pages 1-31 Chapter II Boundary Value Problem of Parabolic Type Pages 32-83 Chapter III Optimal Control of First Boundary Problems: Strong Variation Techniques Pages 84-132 Chapter IV Optimal Control of First Boundary Problems: Gradient Techniques Pages 133-190 Chapter V Relaxed Controls and the Convergence of Optimal Control Algorithms Pages 191-234 Chapter VI Optimal Control Problems Involving Second Boundary-Value Problems Pages 235-274 Appendix I Stochastic Optimal Control Problems Pages 275-279 Appendix II Certain Results on Partial Differential Equations Needed in Chapters III, IV, and V Pages 280-282 Appendix III An Algorithm of Quadratic Programming Pages 283-285 Appendix IV A Quasi-Newton Method for Nonlinear Function Minimization with Linear Constraints Pages 286-288 Appendix V An Algorithm for Optimal Control Problems of Linear Lumped Parameter Systems Pages 289-297 Appendix VI Meyer-Polak Proximity Algorithm Pages 298-299 References Review Article Pages 301-312 List of Notation Page 313 Index Pages 315-317 Computational methods for optimizing distributed systems