I 1Ii),' Arturo Locatelli Optimal Control An Introduction Birkhauser Verlag Basel Boston Berlin Author Arturo Locatelli Dipartimento di Elettronica e Informazione Politecnico di Milano Piazza L. da Vinci 32 20133 Milano Italy e-mail:
[email protected] 2000 Mathematical Subject Classification 49-01 A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Deutsche Bibliothek Cataloging-in-Publication Data Locatelli, Arturo: Optimal control : an introduction / Arturo Locatelli. - Basel ; Boston ; Berlin : Birkhauser, 2001 ISBN 3-7643-6408-4 ISBN 3-7643-6408-4 Birkhauser Verlag, Basel - Boston - Berlin 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, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. ® 2001 Birkhauser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland Member of the BertelsmannSpringer Publishing Group Cover design: Micha Lotrovsky, CH-4106 Therwil, Switzerland Printed on acid-free paper produced of chlorine-free pulp. TCF Printed in Germany ISBN 3-7643-6408-4 987654321 www.birkhauser.ch to Franca and my parents Contents Preface . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . I Global methods 2 3 The Hamilton-Jacobi theory 2.1 Introduction . . . . . . . . . 2.2 Global sufficient conditions 2.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The LQ problem 3.1 Introduction . . . . . . . . . . 3.2 Finite control horizon . . . . 3.3 Infinite control horizon . . . . 3.4 The optimal regulator . . . . 3.4.1 Stability properties . . 3.4.2