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In the context of this book, adaptation is taken to mean a feature of a system aimed at achieving the best possible performance, when mathematical models of the environment and the system itself are not fully available. This has applications ranging from theories of visual perception and the processing of information, to the more technical problems of friction compensation and adaptive classification of signals in fixed-weight recurrent neural networks. Largely devoted to the problems of adaptive regulation, tracking and identification, this book presents a unifying system-theoretic view on the problem of adaptation in dynamical systems. Special attention is given to systems with nonlinearly parameterized models of uncertainty. Concepts, methods and algorithms given in the text can be successfully employed in wider areas of science and technology. The detailed examples and background information make this book suitable for a wide range of researchers and graduates in cybernetics, mathematical modelling and neuroscience.
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This page intentionally left blank A DAPTATION IN DYNAMI CAL S YS TEMS In the context of this book, adaptation is taken to mean a feature of a system aimed at achieving the best possible performance when mathematical models of the environment and the system itself are not fully available. This has applications ranging from theories of visual perception and the processing of information to the more technical problems of friction compensation and adaptive classification of signals in fixed-weight recurrent neural networks. Largely devoted to the problems of adaptive regulation, tracking and identification, this book presents a unifying system-theoretic view on the problem of adaptation in dynamical systems. Special attention is given to systems with nonlinearly parametrized models of uncertainty. Concepts, methods, and algorithms given in the text can be successfully employed in wider areas of science and technology. The detailed examples and background information make this book suitable for a wide range of researchers and graduates in cybernetics, mathematical modeling, and neuroscience. I VA N TY U K I N is an RCUK Academic Fellow in the Department of Mathematics, University of Leicester. His research and scientific interests cover many areas, including the analysis, modeling, and synthesis of systems with fragile, nonlinear, chaotic, and meta-stable dynamics. A DAP TAT ION IN DYNAM I CAL SYST E MS IVAN TYUKIN University of Leicester and Saint-Petersburg State Electrotechnical University CAMBRI DGE UNI VER SITY PR ESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521198196 © I. Tyukin 2011 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2011 Printed in the United Kingdom at the University Press, Cambridge A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Tyukin, Ivan. Adaptation in Dynamical Systems / Ivan Tyukin. p. cm Includes bibliographical references and index. ISBN 978-0-521-19819-6 (hardback) 1. Dynamics. 2. Control theory–Mathematical models. 3. Neurosciences–Mathematics. I. Title. QA845.T94 2011 515 .39–dc22 2010051427 ISBN 978 0 521 19819 6 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred t