Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations
This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area o
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Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations
Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations
Alexander Y. Khapalov
Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations
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Alexander Y. Khapalov Department of Mathematics and Statistics Washington State University Pullman, WA, USA
ISBN 978-3-319-60413-8 ISBN 978-3-319-60414-5 (eBook) DOI 10.1007/978-3-319-60414-5 Library of Congress Control Number: 2017943185 © Springer International Publishing AG 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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
To Dasha, Elena and Irina
Foreword
Many mathematical models of controlled distributed-parameter processes choose to employ locally distributed actuators and sensors to describe the admissible governing actions and the methods of collection of available data. An intrinsic feature of such “devices” is that they act in an open set of a given spatial domain and, thus, are infinite-dimensional at every moment of time. Currently, there exists a comprehensive mathematical controllability theory dealing exactly with such actuators (or so-called controls) and sensors. The goal of this monograph is to present a concise controllability theory of partial differential equations in the case when they are equipped with actuators and/or sensors that are finite-dimensional at every moment of time. Typical examples here could be the point “devices,” static or mobile, that are designed to act at isolated spatial points. Such finite-dimensional designs of controlling actions seem to be better suited for many r
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