# The Calculus of Variations and Optimal Control

## An Introduction

Book

Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 24)

1. Front Matter
Pages i-xvi
2. ### Calculus of Variations

1. Front Matter
Pages 1-1
2. George Leitmann
Pages 3-5
3. George Leitmann
Pages 7-24
4. George Leitmann
Pages 25-37
5. George Leitmann
Pages 39-45
6. George Leitmann
Pages 47-53
7. George Leitmann
Pages 55-65
8. George Leitmann
Pages 67-70
9. George Leitmann
Pages 71-73
3. ### Optimal Control

1. Front Matter
Pages 75-75
2. George Leitmann
Pages 77-78
3. George Leitmann
Pages 79-98
4. George Leitmann
Pages 99-123
5. George Leitmann
Pages 125-138
6. George Leitmann
Pages 139-209
7. George Leitmann
Pages 211-239
8. George Leitmann
Pages 241-263
9. George Leitmann
Pages 265-284
10. George Leitmann
Pages 285-299

### Introduction

When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

### Keywords

Calculus of Variations Optimal control calculus control differential equation extrema optimization

#### Authors and affiliations

1. 1.University of CaliforniaBerkeleyUSA

### Bibliographic information

• Book Title The Calculus of Variations and Optimal Control
• Book Subtitle An Introduction
• Authors George Leitmann
• Series Title Mathematical Concepts and Methods in Science and Engineering
• DOI https://doi.org/10.1007/978-1-4899-0333-4
• Copyright Information Springer-Verlag US 1981
• Publisher Name Springer, Boston, MA
• eBook Packages
• Hardcover ISBN 978-0-306-40707-9
• Softcover ISBN 978-1-4899-0335-8
• eBook ISBN 978-1-4899-0333-4
• Edition Number 1
• Number of Pages XVI, 312
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site