Interdisciplinary Applied Mathematics

Geometric Optimal Control

Theory, Methods and Examples

Authors: Schättler, Heinz, Ledzewicz, Urszula

  • Comprehensive presentation of an up-to-date geometric approach to optimal control, both necessary and sufficient conditions, which has not been done in a book form before
  • Rigorous presentation, written in a easy tutorial style accessible to non-experts and advanced undergraduate and graduate students
  • Palette of fully and in detail worked out, well illustrated, nontrivial examples which are only available in the research literature
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eBook $69.99
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  • ISBN 978-1-4614-3834-2
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  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-1-4614-3833-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-1-4899-8680-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this Textbook

This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.

About the authors

Urszula Ledzewicz is a Distinguished Research Professor in the Department of Mathematics and Statistics at Southern Illinois University. Heinz Schaettler is an Associate Professor at Washington University.

Reviews

From the reviews:

“The monograph under review concerns finite-dimensional deterministic optimal control problems. … The main body of the book is divided into seven chapters. … The variety of fully solved examples that illustrate the theory makes this text a strong educational asset. The book is recommended as a comprehensive textbook for both advanced undergraduate and all levels of graduate courses on optimal control in mathematics and engineering.” (Ovidiu Cârjă, zbMATH, Vol. 1276, 2014)

“The book presents a comprehensive treatment of both necessary and sufficient conditions for optimal control using geometric approach … . The book is of interest to senior and graduate students in engineering and mathematics, and scientists and engineers working in academic and industrial organizations. … The book is a valuable addition to some of the recent books on this ever-green field of Optimal Control … .” (D. Subbaram Naidu, Amazon.com, September, 2013)

“Grown out of well-tested lecture notes, large parts of this volume are suitable as a comprehensive textbook at an advanced undergraduate or at the graduate level, either in mathematics or in engineering … . this most readable text provides a rich and versatile resource which is suitable as a textbook in various settings, is a valuable reference for theory, and which provides a very large collection of model examples that are analyzed completely using state-of-the-art methods.” (Matthias Kawski, Mathematical Reviews, February, 2013)

“Schättler (electrical and systems engineering, Washington Univ.) and Ledzewicz (mathematics and statistics, Southern Illinois Univ.) use a geometric approach to present the theory of optimal control. … authors have developed a general approach that can be applied to a wide variety of control problems. … This book may be of interest to graduate students and researchers working in this area. Summing Up: Recommended. Graduate students and researchers/faculty.” (B. Borchers, Choice, Vol. 50 (5), January, 2013)


Table of contents (7 chapters)

  • The Calculus of Variations: A Historical Perspective

    Schättler, Heinz (et al.)

    Pages 1-81

  • The Pontryagin Maximum Principle: From Necessary Conditions to the Construction of an Optimal Solution

    Schättler, Heinz (et al.)

    Pages 83-194

  • Reachable Sets of Linear Time-Invariant Systems: From Convex Sets to the Bang-Bang Theorem

    Schättler, Heinz (et al.)

    Pages 195-230

  • The High-Order Maximum Principle: From Approximations of Reachable Sets to High-Order Necessary Conditions for Optimality

    Schättler, Heinz (et al.)

    Pages 231-321

  • The Method of Characteristics: A Geometric Approach to Sufficient Conditions for a Local Minimum

    Schättler, Heinz (et al.)

    Pages 323-423

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-3834-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-1-4614-3833-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-1-4899-8680-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Optimal Control
Book Subtitle
Theory, Methods and Examples
Authors
Series Title
Interdisciplinary Applied Mathematics
Series Volume
38
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-3834-2
DOI
10.1007/978-1-4614-3834-2
Hardcover ISBN
978-1-4614-3833-5
Softcover ISBN
978-1-4899-8680-1
Series ISSN
0939-6047
Edition Number
1
Number of Pages
XX, 640
Topics