Optimal Control of Constrained Piecewise Affine Systems
One of the most important and challenging problems in control is the derivation of systematic tools for the computation of controllers for constrained nonlinear systems that can guarantee closed-loop stability, feasibility, and optimality with respect to
- PDF / 2,920,328 Bytes
- 209 Pages / 439.37 x 666.142 pts Page_size
- 31 Downloads / 223 Views
Frank J. Christophersen
Optimal Control of Constrained Piecewise Affine Systems
ABC
Series Advisory Board F. Allgower, ¨ P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis
Author Dr. Frank J. Christophersen ETH Zurich Automatic Control Laboratory Physikstrasse 3 8092 Zurich Switzerland e-mail: [email protected]
Library of Congress Control Number: 2007927162 ISSN print edition: 0170-8643 ISSN electronic edition: 1610-7411 ISBN-10 3-540-72700-0 Springer Berlin Heidelberg New York ISBN-13 978-3-540-72700-2 Springer Berlin Heidelberg New York 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 for prosecution under the German Copyright Law. Typesetting: by the authors and SPS using a Springer LATEX macro package Printed on acid-free paper
SPIN: 12027606
89/SPS
543210
. . . for M. & J.
Noise is the key; life is full of noise. Only death is silent. A LEC E MPIRE
P REFACE
One of the most important and challenging problems in control is the derivation of systematic tools for the computation of controllers for general constrained nonlinear or hybrid systems [vS00] (combining continuous-valued dynamics with logic rules) that can guarantee (among others) closed-loop stability, feasibility, and optimality with respect to some objective function. The focus of this book lies on the class of constrained discrete-time piecewise affine (PWA) systems [Son81]. This particular subclass of hybrid systems is obtained by partitioning the extended state-input space into regions and associating a different affine state update equation with each region. Under mild assumptions this modeling framework is equivalent to many other hybrid system classes reported in the literature [HDB01], and represents itself as a powerful modeling tool to capture general nonlinearities (e.g. by local approximation), constraints, saturations, switches, discrete inputs, and other hybrid modeling phenomena in dynamical systems. Although piecewise affine systems are a subclass of general nonlinear systems, most of the (classical) control theory developed for nonlinear control does not apply, due to commonly made continuity and smoothness requirements.
VIII
P REFACE
The flexibility of this modeling framework and the recent technological advances in the fields of optimization and control theory have lead to a considerable interest in academia and industry in piecewise affine systems; not to mention that many engineering systems naturally express themselves or approximate nicely as piecewise affine systems, or can be ‘straightforwardly’ tra
Data Loading...
