文档介绍：cvoc-formatted August 24, 2011 7x10
Calculus of Variations and
Optimal Control Theory
cvoc-formatted August 24, 2011 7x10
cvoc-formatted August 24, 2011 7x10
Calculus of Variations and
Optimal Control Theory
A Concise Introduction
Daniel Liberzon
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
Copyright © 2012 by Princeton University Press
Published by Princeton University Press, 41 William Street, Princeton, New Jersey
08540
In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock,
Oxfordshire OX20 1TW
All Rights Reserved
ISBN: 978-0-691-15187-8
Library of Congress Control Number: 2011935625
British Library Cataloging-in-Publication Data is available
This book has posed in LA TEX
The publisher would like to acknowledge the author of this volume for providing the
digital files from which this book was printed
Printed on acid-free paper ∞
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
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Since the building of the universe is perfect and is created by the
wisdom creator, nothing arises in the universe in which one cannot
see the sense of some maximum or minimum.
—Leonhard Euler
The words “control theory” are, of course, of recent origin, but the
subject itself is much older, since it contains the classical calculus
of variations as a special case, and the first calculus of variations
problems go back to classical Greece.
—Hector J. Sussmann
cvoc-formatted August 24, 2011 7x10
Contents
Preface xiii
1 Introduction 1
Optimal control problem 1
Some background on finite-dimensional optimization 3
Unconstrained optimization . . . . . . . . . . . . . . . 4
Constrained optimization . . . . . . . . . . . . . . . . 11
Preview of infinite-dimensional optimization 17
Function spaces, norms, and local minima . . . . . . . 18
First variation and first-order necessary condition . . . 19