Optimal Control TheoryThis book is an introduction to the mathematical theory of optimal control of processes governed by ordinary differential eq- tions. It is intended for students and professionals in mathematics and in areas of application who want a broad, yet relatively deep, concise and coherent introduction to the subject and to its relati- ship with applications. In order to accommodate a range of mathema- cal interests and backgrounds among readers, the material is arranged so that the more advanced mathematical sections can be omitted wi- out loss of continuity. For readers primarily interested in appli- tions a recommended minimum course consists of Chapter I, the sections of Chapters II, III, and IV so recommended in the introductory sec tions of those chapters, and all of Chapter V. The introductory sec tion of each chapter should further guide the individual reader toward material that is of interest to him. A reader who has had a good course in advanced calculus should be able to understand the defini tions and statements of the theorems and should be able to follow a substantial portion of the mathematical development. The entire book can be read by someone familiar with the basic aspects of Lebesque integration and functional analysis. For the reader who wishes to find out more about applications we recommend references [2], [13], [33], [35], and [50], of the Bibliography at the end of the book. |
Contents
Examples of Control Problems | 1 |
Formulation of the Control Problem | 14 |
Existence Theorems with Convexity Assumptions | 39 |
Copyright | |
8 other sections not shown
Other editions - View all
Common terms and phrases
absolutely continuous admissible pair admissible trajectories applications arbitrary argument assume Assumption bounded called Cesari property Chapter closed compact compact set components consider constant contained continuous function convex Corollary corresponding defined definition denote depends derivatives differential equations dx dt element equal equations equivalent example EXERCISE existence theorem exists extremal finite fixed follows formulation function function defined function f give given Hence holds hypotheses of Theorem inequality initial point integrable interior interval Lemma linear mapping matrix maximized maximum principle measurable minimizing Moreover Note obtain optimal control optimal pair original positive preceding present problem production prove reader relation relaxed REMARK replaced result satisfy sequence solution space statement Step subsequence subset suppose terminal Theorem 5.1 tion tort trajectory unique variations vector written zero