Tautological Control Systems
This brief presents a description of a new modelling framework for nonlinear/geometric control theory. The framework is intended to be—and shown to be—feedback-invariant. As such, Tautological Control Systems provides a platform for understanding fundamen
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Andrew D. Lewis
Tautological Control Systems
SpringerBriefs in Electrical and Computer Engineering Control, Automation and Robotics
Series editors Tamer Basar Antonio Bicchi Miroslav Krstic
More information about this series at http://www.springer.com/series/10198
Andrew D. Lewis
Tautological Control Systems
123
Andrew D. Lewis Department of Mathematics and Statistics Queen’s University Kingston Canada
ISSN 2192-6786 ISBN 978-3-319-08637-8 DOI 10.1007/978-3-319-08638-5
ISSN 2192-6794 (electronic) ISBN 978-3-319-08638-5 (eBook)
Library of Congress Control Number: 2014942664 Springer Cham Heidelberg New York Dordrecht London The Author(s) 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The lack of feedback-invariance of mathematical formulations of nonlinear control theory has been a thorn in the side of understanding the basic structure of control systems. Moreover, it is a thorn whose presence has largely come to be accepted, and this has prohibited a complete understanding of certain fundamental structural problems for nonlinear systems. One way to understand the issue is as follows: just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so
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