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Model Predictive Control: Theory, Computation, and Design 2nd Edition 9377307809759 ISBN 9780975937730

Model Predictive Control: Theory, Computation, and Design 2nd Edition James B. Rawlings Department of Chemical and Biological Engineering University of Wisconsin Madison, Wisconsin, USA David Q. Mayne Department of Electrical and Electronic Engineering Imperial College London London, England Moritz M. Diehl Department of Microsystems Engineering and Department of Mathematics University of Freiburg Freiburg, Germany b Hill Publishing DN o Madison, Wisconsin

This book was set in Lucida using LATEX, and printed and bound by Worzalla. It was printed on Forest Stewardship CouncilÉ certi®ed acid- free recycled paper. Cover design by Cheryl M. and James B. Rawlings. Copyright c 2017 by Nob Hill Publishing, LLC All rights reserved. Nob Hill Publishing, LLC Cheryl M. Rawlings, publisher Madison, WI 53705 orders@nobhillpublishing.com http://www.nobhillpublishing.com No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Library of Congress Control Number: 2017909542 Printed in the United States of America. First Edition First Printing Electronic Download Electronic Download (2nd) Electronic Download (3rd) Electronic Download (4th) Electronic Download (5th) Second Edition First Printing Electronic Download August 2009 November 2013 April 2014 July 2014 October 2014 February 2015 October 2017 October 2018

To Cheryl, Josephine, and Stephanie, for their love, encouragement, and patience.

Preface to the Second Edition In the eight years since the publication of the ®rst edition, the ®eld of model predictive control (MPC) has seen tremendous progress. First and foremost, the algorithms and high-level software available for solv- ing challenging nonlinear optimal control problems have advanced sig- ni®cantly. For this reason, we have added a new chapter, Chapter 8, ªNumerical Optimal Control,º and coauthor, Professor Moritz M. Diehl. This chapter gives an introduction into methods for the numerical so- lution of the MPC optimization problem. Numerical optimal control builds on two ®elds: simulation of differential equations, and numeri- cal optimization. Simulation is often covered in undergraduate courses and is therefore only brie¯y reviewed. Optimization is treated in much more detail, covering topics such as derivative computations, Hessian approximations, and handling inequalities. Most importantly, the chap- ter presents some of the many ways that the speci®c structure of opti- mal control problems arising in MPC can be exploited algorithmically. We have also added a software release with the second edition of the text. The software enables the solution of all of the examples and exercises in the text requiring numerical calculation. The software is based on the freely available CasADi language, and a high-level set of Octave/MATLAB functions, MPCTools, to serve as an interface to CasADi. These tools have been tested in several MPC short courses to audiences composed of researchers and practitioners. The software can be down- loaded from www.che.wisc.edu/~jbraw/mpc. In Chapter 2, we have added sections covering the following topics: economic MPC MPC with discrete actuators We also present a more recent form of suboptimal MPC that is prov- ably robust as well as computationally tractable for online solution of nonconvex MPC problems. In Chapter 3, we have added a discussion of stochastic MPC, which has received considerable recent research attention. In Chapter 4, we have added a new treatment of state estimation with persistent, bounded process and measurement disturbances. We have also removed the discussion of particle ®ltering. There are two vi

vii reasons for this removal; ®rst, we wanted to maintain a manageable total length of the text; second, all of the available sampling strate- gies in particle ®ltering come up against the ªcurse of dimensionality,º which renders the state estimates inaccurate for dimension higher than about ®ve. The material on particle ®ltering remains available on the text website. In Chapter 6, we have added a new section for distributed MPC of nonlinear systems. In Chapter 7, we have added the software to compute the critical regions in explicit MPC. Throughout the text, we support the stronger KL-de®nition of asymp- totic stability, in place of the classical de®nition used in the ®rst edition. The most signi®cant notational change is to denote a sequence with a; b; c; : : : instead of with fa; b; c; : : :g as in the ®rst edition. JBR DQM MMD Madison, Wis., USA London, England Freiburg, Germany

Preface Our goal in this text is to provide a comprehensive and foundational treatment of the theory and design of model predictive control (MPC). By now several excellent monographs emphasizing various aspects of MPC have appeared (a list appears at the beginning of Chapter 1), and the reader may naturally wonder what is offered here that is new and different. By providing a comprehensive treatment of the MPC foun- dation, we hope that this text enables researchers to learn and teach the fundamentals of MPC without continuously searching the diverse control research literature for omitted arguments and requisite back- ground material. When teaching the subject, it is essential to have a collection of exercises that enables the students to assess their level of comprehension and mastery of the topics. To support the teaching and learning of MPC, we have included more than 200 end-of-chapter exer- cises. A complete solution manual (more than 300 pages) is available for course instructors. Chapter 1 is introductory. It is intended for graduate students in en- gineering who have not yet had a systems course. But it serves a second purpose for those who have already taken the ®rst graduate systems course. It derives all the results of the linear quadratic regulator and optimal Kalman ®lter using only those arguments that extend to the nonlinear and constrained cases to be covered in the later chapters. Instructors may ®nd that this tailored treatment of the introductory systems material serves both as a review and a preview of arguments to come in the later chapters. Chapters 2±4 are foundational and should probably be covered in any graduate level MPC course. Chapter 2 covers regulation to the ori- gin for nonlinear and constrained systems. This material presents in a uni®ed fashion many of the major research advances in MPC that took place during the last 20 years. It also includes more recent topics such as regulation to an unreachable setpoint that are only now appearing in the research literature. Chapter 3 addresses MPC design for robustness, with a focus on MPC using tubes or bundles of trajectories in place of the single nominal trajectory. This chapter again uni®es a large body of research literature concerned with robust MPC. Chapter 4 covers state estimation with an emphasis on moving horizon estimation, but also viii

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