Model-Free Stabilization by Extremum Seeking
With this brief, the authors present algorithms for model-free stabilization of unstable dynamic systems. An extremum-seeking algorithm assigns the role of a cost function to the dynamic system’s control Lyapunov function (clf) aiming at its minimization.
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Alexander Scheinker Miroslav Krstić
Model-Free Stabilization by Extremum Seeking 123
SpringerBriefs in Electrical and Computer Engineering Control, Automation and Robotics
Series editors Tamer Başar Antonio Bicchi Miroslav Krstić
More information about this series at http://www.springer.com/series/10198
Alexander Scheinker Miroslav Krstić •
Model-Free Stabilization by Extremum Seeking
123
Alexander Scheinker Low-Level RF Control Group Los Alamos National Laboratory Los Alamos, NM USA
Miroslav Krstić Department of Mechanical and Aerospace Engineering University of California, San Diego La Jolla, CA USA
ISSN 2191-8112 ISSN 2191-8120 (electronic) SpringerBriefs in Electrical and Computer Engineering ISSN 2192-6786 ISSN 2192-6794 (electronic) SpringerBriefs in Control, Automation and Robotics ISBN 978-3-319-50789-7 ISBN 978-3-319-50790-3 (eBook) DOI 10.1007/978-3-319-50790-3 Library of Congress Control Number: 2016959805 Mathematics Subject Classification (2010): 93-01, 93-02 © The Author(s) 2017 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Originating in 1922, in its 95-year history, extremum seeking has served as a tool for model-free real-time optimization of stable dynamic systems. We introduce a paradigm in which not only is the system being optimized allowed to be time varying and open-loop unstable, but also the very goal of extremum seeking is to stabilize the system. The cost function and the control Lyapunov function (CLF) play interchangeable roles, with the unknown optimal set point being implicitly defined through the cost/CLF and coinciding with the equilibrium to be stabilized. Our “extremum seeking for stabilization” (ESS) consists of employing the CLF as the cost function in a slightly modified extremum seeking algorithm. The
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