Introduction to Optimal Control Theory.

MACKI, Jack. & STRAUSS, Aaron.:

ISBN 10: 038790624X / ISBN 13: 9780387906249

Published by New York & Berlin: Springer Verlag, 1982

About this Item

1st. Edn. (Undergraduate Texts in Mathematics). pp. xiii, 165. plus 2pp. publisher's list. A fine hardback copy in the original printed yellow glaxed boards. Seller Inventory # 3765

Bibliographic Details

Title: Introduction to Optimal Control Theory.

Publisher: New York & Berlin: Springer Verlag

Publication Date: 1982

Binding: Hardcover

Edition: 1st Edition

About this title

Synopsis:

This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations. It is not intended as a state-of-the-art handbook for researchers. We have tried to keep two types of reader in mind: (1) mathematicians, graduate students, and advanced undergraduates in mathematics who want a concise introduction to a field which contains nontrivial interesting applications of mathematics (for example, weak convergence, convexity, and the theory of ordinary differential equations); (2) economists, applied scientists, and engineers who want to understand some of the mathematical foundations. of optimal control theory. In general, we have emphasized motivation and explanation, avoiding the "definition-axiom-theorem-proof" approach. We make use of a large number of examples, especially one simple canonical example which we carry through the entire book. In proving theorems, we often just prove the simplest case, then state the more general results which can be proved. Many of the more difficult topics are discussed in the "Notes" sections at the end of chapters and several major proofs are in the Appendices. We feel that a solid understanding of basic facts is best attained by at first avoiding excessive generality. We have not tried to give an exhaustive list of references, preferring to refer the reader to existing books or papers with extensive bibliographies. References are given by author's name and the year of publication, e.g., Waltman [1974].

Synopsis:

This is an introduction to optimal control theory for systems governed by vector ordinary differential equations, up to and including a proof of the Pontryagin Maximum Principle. Though the subject is accessible to any student with a sound undergraduate mathematics background. Theory and applications are integrated with examples, particularly one special example (the rocket car) which relates all the abstract ideas to an understandable setting. The authors avoid excessive generalization, focusing rather on motivation and clear, fluid explanation.