Uncertain Optimal Control
This book introduces the theory and applications of uncertain optimal control, and establishes two types of models including expected value uncertain optimal control and optimistic value uncertain optimal control. These models, which have continuous-time
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Yuanguo Zhu
Uncertain Optimal Control
Springer Uncertainty Research Series editor Baoding Liu, Beijing, China
Springer Uncertainty Research Springer Uncertainty Research is a book series that seeks to publish high quality monographs, texts, and edited volumes on a wide range of topics in both fundamental and applied research of uncertainty. New publications are always solicited. This book series provides rapid publication with a world-wide distribution. Editor-in-Chief Baoding Liu Department of Mathematical Sciences Tsinghua University Beijing 100084, China http://orsc.edu.cn/liu Email: [email protected] Executive Editor-in-Chief Kai Yao School of Economics and Management University of Chinese Academy of Sciences Beijing 100190, China http://orsc.edu.cn/yao Email: [email protected]
More information about this series at http://www.springer.com/series/13425
Yuanguo Zhu
Uncertain Optimal Control
123
Yuanguo Zhu Department of Mathematics Nanjing University of Science and Technology Nanjing, China
ISSN 2199-3807 ISSN 2199-3815 (electronic) Springer Uncertainty Research ISBN 978-981-13-2133-7 ISBN 978-981-13-2134-4 (eBook) https://doi.org/10.1007/978-981-13-2134-4 Library of Congress Control Number: 2018952608 © Springer Nature Singapore Pte Ltd. 2019 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. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
If a dynamical system is disturbed by uncertain factors, it may be described by an uncertain differential equation. A problem of optimizing an index subject to an uncertain differential equation is called an uncertain optimal control problem. It is a novel topic on optimal control based on the uncertainty theory. This book is to introduce the theory and a
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