Domain of Attraction Analysis and Control via SOS Programming
The stability of equilibrium points plays a fundamental role in dynamical systems. For nonlinear dynamical systems, which represent the majority of real plants, an investigation of stability requires the characterization of the domain of attraction (DA) o
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Graziano Chesi
Domain of Attraction Analysis and Control via SOS Programming
ABC
Series Advisory Board P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis
Author Prof. Graziano Chesi University of Hong Kong Dept. Electrical & Electronic Engine Pokfulam Road Hong Kong Chow Yei Ching Bldg China, People’s Republic Telephone: 85222194362 Fax: 85225598738 Email: [email protected]
ISBN 978-0-85729-958-1
e-ISBN 978-0-85729-959-8
DOI 10.1007/978-0-85729-959-8 Lecture Notes in Control and Information Sciences
ISSN 0170-8643
Library of Congress Control Number: 2011935380 c 2011 Springer-Verlag London Limited 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed on acid-free paper 987654321 springer.com
To my parents, Adele and Luigi
And to my family, Shing Chee, Isabella and Sofia That sacrificed many weekends to allow me to write this book
Preface
Stability of equilibrium points plays a fundamental role in dynamical systems. For nonlinear dynamical systems, which represent the majority of real plants, investigating stability requires characterizing the domain of attraction (DA) of an equilibrium point, i.e. the set of initial conditions from which the trajectory of the system converges to such a point. Unfortunately, it is well-known that estimating the DA, or even more attempting to control it, are very difficult problems due to the complex relationship of this set with the model of the system. This book addresses the estimation and control of the DA of equilibrium points via the newborn SOS programming, i.e. optimization techniques that have been recently developed based on polynomials that are sum of squares of polynomials (denoted hereafter as SOS polynomials) and that amount to solving convex optimization problems with linear matrix inequality (LMI) constraints, also known as semidefinite programs (SDPs). It is shown for the first time in the literature how these issues can be addressed under a unified framework in various cases depending on the nature of the considered nonlinear systems, including the cases of polynomial systems, uncertain polynomial systems, and nonlinear non-polynomial systems (poss
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