Sliding Modes in Control and Optimization
The book is devoted to systems with discontinuous control. The study of discontinuous dynamic systems is a multifacet problem which embraces mathematical, control theoretic and application aspects. Times and again, this problem has been approached by math
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dim I. Utkin
Sliding Modes in Control and Optimization
With 24 Figures
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo HongKong Barcelona Budapest
Prof. VADIM I. UTKIN Institute of Control Sciences 65 Profsyuznaya Moscow GSP-312 USSR
Original Russian language edition, entitled: B. III. YTKMH "CKOJ1b3S1~Me pe>KMMbl M MX npMMeHeHMe B 3a,qayax onTMMM3a4MM M ynpaBJ1eHMSI» HAYKA, MocKBa, 1981 r. All rights reserved.
ISBN-13:978-3-642-84381-5 e-ISBN-13:978-3-642-84379-2 DOl: lO.1007/978-3-642-84379-2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September9, 1965, in its current version and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin, Heidelberg 1992 Softcoverreprint of the hardcover 1st edition 1992 The use of registered names, rademarks, 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. Typesetting: Thomson India Ltd., New Delhi, India. 2161/3020543210 - Printed on acid-free paper
Preface
The book is devoted to systems with discontinuous control. The study of discontinuous dynamic systems is a multifacet problem which embraces mathematical, control theoretic and application aspects. Times and again, this problem has been approached by mathematicians, physicists and engineers, each profession treating it from its own positions. Interestingly, the results obtained by specialists in different disciplines have almost always had a significant effect upon the development of the control theory. It suffices to mention works on the theory of oscillations of discontinuous nonlinear systems, mathematical studies in ordinary differential equations with discontinuous righthand parts or variational problems in nonclassic statements. The unremitting interest to discontinuous control systems enhanced by their effective application to solution of problems most diverse in their physical nature and functional purpose is, in the author's opinion, a cogent argument in favour of the importance of this area of studies. It seems a useful effort to consider, from a control theoretic viewpoint, the mathematical and application aspects of the theory of discontinuous dynamic systems and determine their place within the scope of the present-day control theory. The first attempt was made by the author in 1975-1976 in his course on "The Theory of Discontinuous Dynamic Systems" and "The Theory of Variable Structure Systems" read to post-graduates at the University of Illinois, USA, and then presented in 1978-1979 at the seminars held in the Laboratory
