Bilinear Control Systems Matrices in Action
A control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. The study of bilinear control systems began in the 1960s and has since developed into a fascinating field, vital fo
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David L. Elliott
Bilinear Control Systems Matrices in Action
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Prof. David Elliott University of Maryland Inst. Systems Research College Park MD 20742 USA
Editors: S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA [email protected]
J.E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, CA 91125 USA [email protected]
L. Sirovich Laboratory of Applied Mathematics Department of Biomathematical Sciences Mount Sinai School of Medicine New York, NY 10029-6574 [email protected]
ISSN 0066-5452 ISBN 978-1-4020-9612-9 e-ISBN 978-1-4020-9613-6 DOI 10.1007/978-1-4020-9613-6 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009920095 Mathematics Subject Classification (2000): 93B05, 1502, 57R27, 22E99, 37C10 c Springer Science+Business Media B.V. 2009 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The mathematical theory of control became a field of study half a century ago in attempts to clarify and organize some challenging practical problems and the methods used to solve them. It is known for the breadth of the mathematics it uses and its cross-disciplinary vigor. Its literature, which can be found in Section 93 of Mathematical Reviews, was at one time dominated by the theory of linear control systems, which mathematically are described by linear differential equations forced by additive control inputs. That theory led to well-regarded numerical and symbolic computational packages for control analysis and design. Nonlinear control problems are also important; in these either the underlying dynamical system is nonlinear or the controls are applied in a nonadditive way. The last four decades have seen the development of theoretical work on nonlinear control problems based on differential manifold theory, nonlinear analysis, and several other mathematical disciplines. Many of the problems that had been solved in linear control theory, plus others that are new and distinctly nonlinear, have been addressed; some resulting general definitions and theorems are adapted in this book to the bilinear case. A nonlinear control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. Such multiplicative controls (valves, interest rates, switches, catalysts, etc.) are common in engineering design and also are used as models of natural phenomena with variable growth r
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