Stochastic Averaging and Stochastic Extremum Seeking
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization tec
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Series Editors A. Isidori r J.H. van Schuppen r E.D. Sontag r M. Thoma r M. Krstic
For further volumes: www.springer.com/series/61
Shu-Jun Liu r Miroslav Krstic
Stochastic Averaging and Stochastic Extremum Seeking
Shu-Jun Liu Department of Mathematics Southeast University Nanjing, People’s Republic of China
Miroslav Krstic Department Mechanical & Aerospace Engineering University of California, San Diego La Jolla, California, USA
ISSN 0178-5354 Communications and Control Engineering ISBN 978-1-4471-4086-3 ISBN 978-1-4471-4087-0 (eBook) DOI 10.1007/978-1-4471-4087-0 Springer London Heidelberg New York Dordrecht Library of Congress Control Number: 2012941138 © Springer-Verlag London 2012 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
Inspiration for the Book This book was inspired by a seemingly non-mathematical question of understanding the biological phenomenon of bacterial chemotaxis, where it is conjectured that a simple extremum seeking-like algorithm, employing stochastic perturbations instead of the conventional sinusoidal probing, enables bacteria to move in space toward areas with higher food concentration by estimating the gradient of the unknown concentration distribution. While constructing stochastic algorithms that both mimic bacterial
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