Control Theory from the Geometric Viewpoint
This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced
- PDF / 26,630,148 Bytes
- 415 Pages / 439.37 x 666.142 pts Page_size
- 65 Downloads / 254 Views
Control Theory and Optimization II Sub series Editor: R. V. Gamkrelidze
Springer-Verlag Berlin Heidelberg GmbH
Andrei A. Agrachev Yuri L. Sachkov
Control Theory from the Geometric Viewpoint
Springer
Andrei A. Agrachev SISSA-ISAS 2-4 Via Beirut Trieste 34014 Italy e-mail: [email protected] Yuri L. Sachkov Program Systems Institute Pereslavl-Zalessky 152140 Russia e-mail: [email protected]
Founding editor of the Encyclopaedia of Mathematical Sciences: R. V. Gamkrelidze
Mathematics Subject Classification (2000): 93-01, 93-02, 93B03, 93Boj, 93B17, 93B18, 93B29, 93ClO, 93C15
ISSN 0938-0396
ISBN 978-3-642-05907-0 ISBN 978-3-662-06404-7 (eBook) DOI 10.1007/978-3-662-06404-7 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. springeronline.com Springer-Verlag Berlin Heidelberg 2004 Originally published by Springer-Verlag Berlin Heidelberg New York in 2004 Softcover reprint of the hardcover 1st edition 2004 @
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset by the authors using a Springer LaTeX macro package Cover Design: E. Kirchner, Heidelberg, Germany Printed on acid-free paper 46/3142 db 5 43 2 1 0
To our parents Alexander and Elena Agrachev Leonid and Anastasia Sachkov
Preface
This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is completely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain parameters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological
