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    Cover
    Nonlinear Model Predictive Control
    ISBN 9780857295002
    Preface
    Contents
    Chapter 1: Introduction
    1.1 What Is Nonlinear Model Predictive Control?
    1.2 Where Did NMPC Come from?
    1.3 How Is This Book Organized?
    1.4 What Is Not Covered in This Book?
    References
    Chapter 2: Discrete Time and Sampled Data Systems
    2.1 Discrete Time Systems
    2.2 Sampled Data Systems
    2.3 Stability of Discrete Time Systems
    2.4 Stability of Sampled Data Systems
    2.5 Notes and Extensions
    2.6 Problems
    References
    Chapter 3: Nonlinear Model Predictive Control
    3.1 The Basic NMPC Algorithm
    3.2 Constraints
    3.3 Variants of the Basic NMPC Algorithms
    3.4 The Dynamic Programming Principle
    3.5 Notes and Extensions
    3.6 Problems
    References
    Chapter 4: Infinite Horizon Optimal Control
    4.1 Definition and Well Posedness of the Problem
    4.2 The Dynamic Programming Principle
    4.3 Relaxed Dynamic Programming
    4.4 Notes and Extensions
    4.5 Problems
    References
    Chapter 5: Stability and Suboptimality Using Stabilizing Constraints
    5.1 The Relaxed Dynamic Programming Approach
    5.2 Equilibrium Endpoint Constraint
    5.3 Lyapunov Function Terminal Cost
    5.4 Suboptimality and Inverse Optimality
    5.5 Notes and Extensions
    5.6 Problems
    References
    Chapter 6: Stability and Suboptimality Without Stabilizing Constraints
    6.1 Setting and Preliminaries
    6.2 Asymptotic Controllability with Respect to l
    6.3 Implications of the Controllability Assumption
    6.4 Computation of alpha
    6.5 Main Stability and Performance Results
    6.6 Design of Good Running Costs l
    6.7 Semiglobal and Practical Asymptotic Stability
    6.8 Proof of Proposition 6.17
    6.9 Notes and Extensions
    6.10 Problems
    References
    Chapter 7: Variants and Extensions
    7.1 Mixed Constrained-Unconstrained Schemes
    7.2 Unconstrained NMPC with Terminal Weights
    7.3 Nonpositive Definite Running Cost
    7.4 Multistep NMPC-Feedback Laws
    7.5 Fast Sampling
    7.6 Compensation of Computation Times
    7.7 Online Measurement of alpha
    7.8 Adaptive Optimization Horizon
    7.9 Nonoptimal NMPC
    7.10 Beyond Stabilization and Tracking
    References
    Chapter 8: Feasibility and Robustness
    8.1 The Feasibility Problem
    8.2 Feasibility of Unconstrained NMPC Using Exit Sets
    8.3 Feasibility of Unconstrained NMPC Using Stability
    8.4 Comparing Terminal Constrained vs. Unconstrained NMPC
    8.5 Robustness: Basic Definition and Concepts
    8.6 Robustness Without State Constraints
    8.7 Examples for Nonrobustness Under State Constraints
    8.8 Robustness with State Constraints via Robust-optimal Feasibility
    8.9 Robustness with State Constraints via Continuity of VN
    8.10 Notes and Extensions
    8.11 Problems
    References
    Chapter 9: Numerical Discretization
    9.1 Basic Solution Methods
    9.2 Convergence Theory
    9.3 Adaptive Step Size Control
    9.4 Using the Methods Within the NMPC Algorithms
    9.5 Numerical Approximation Errors and Stability
    9.6 Notes and Extensions
    9.7 Problems
    References
    Chapter 10: Numerical Optimal Control of Nonlinear Systems
    10.1 Discretization of the NMPC Problem
    Full Discretization
    Recursive Discretization
    Multiple Shooting Discretization
    10.2 Unconstrained Optimization
    10.3 Constrained Optimization
    Active Set SQP Methods
    Interior-Point Methods
    10.4 Implementation Issues in NMPC
    Structure of the Derivatives
    Condensing
    Optimality and Computing Tolerances
    10.5 Warm Start of the NMPC Optimization
    Initial Value Embedding
    Sensitivity Based Warm Start
    Shift Method
    10.6 Nonoptimal NMPC
    10.7 Notes and Extensions
    10.8 Problems
    References
    Appendix NMPC Software Supporting This Book
    A.1 The MATLAB NMPC Routine
    A.2 Additional MATLAB and MAPLE Routines
    A.3 The C++ NMPC Software
    Glossary
    Index
    Communications and Control Engineering For other titles published in this series, go to www.springer.com/series/61
    Series Editors A. Isidori r J.H. van Schuppen r E.D. Sontag r M. Thoma r M. Krstic Published titles include: Stability and Stabilization of Infinite Dimensional Systems with Applications Zheng-Hua Luo, Bao-Zhu Guo and Omer Morgul Nonsmooth Mechanics (Second edition) Bernard Brogliato Nonlinear Control Systems II Alberto Isidori L2-Gain and Passivity Techniques in Nonlinear Control Arjan van der Schaft Control of Linear Systems with Regulation and Input Constraints Ali Saberi, Anton A. Stoorvogel and Peddapullaiah Sannuti Robust and H∞ Control Ben M. Chen Computer Controlled Systems Efim N. Rosenwasser and Bernhard P. Lampe Control of Complex and Uncertain Systems Stanislav V. Emelyanov and Sergey K. Korovin Robust Control Design Using H∞ Methods Ian R. Petersen, Valery A. Ugrinovski and Andrey V. Savkin Model Reduction for Control System Design Goro Obinata and Brian D.O. Anderson Control Theory for Linear Systems Harry L. Trentelman, Anton Stoorvogel and Malo Hautus Functional Adaptive Control Simon G. Fabri and Visakan Kadirkamanathan Positive 1D and 2D Systems Tadeusz Kaczorek Identification and Control Using Volterra Models Francis J. Doyle III, Ronald K. Pearson and Babatunde A. Ogunnaike Non-linear Control for Underactuated Mechanical Systems Isabelle Fantoni and Rogelio Lozano Robust Control (Second edition) Jürgen Ackermann Flow Control by Feedback Ole Morten Aamo and Miroslav Krstic Learning and Generalization (Second edition) Mathukumalli Vidyasagar Constrained Control and Estimation Graham C. Goodwin, Maria M. Seron and José A. De Doná Randomized Algorithms for Analysis and Control of Uncertain Systems Roberto Tempo, Giuseppe Calafiore and Fabrizio Dabbene Switched Linear Systems Zhendong Sun and Shuzhi S. Ge Subspace Methods for System Identification Tohru Katayama Digital Control Systems Ioan D. Landau and Gianluca Zito Multivariable Computer-controlled Systems Efim N. Rosenwasser and Bernhard P. Lampe Dissipative Systems Analysis and Control (Second edition) Bernard Brogliato, Rogelio Lozano, Bernhard Maschke and Olav Egeland Algebraic Methods for Nonlinear Control Systems Giuseppe Conte, Claude H. Moog and Anna M. Perdon Polynomial and Rational Matrices Tadeusz Kaczorek Simulation-based Algorithms for Markov Decision Processes Hyeong Soo Chang, Michael C. Fu, Jiaqiao Hu and Steven I. Marcus Iterative Learning Control Hyo-Sung Ahn, Kevin L. Moore and YangQuan Chen Distributed Consensus in Multi-vehicle Cooperative Control Wei Ren and Randal W. Beard Control of Singular Systems with Random Abrupt Changes El-Kébir Boukas Nonlinear and Adaptive Control with Applications Alessandro Astolfi, Dimitrios Karagiannis and Romeo Ortega Stabilization, Optimal and Robust Control Aziz Belmiloudi Control of Nonlinear Dynamical Systems Felix L. Chernous’ko, Igor M. Ananievski and Sergey A. Reshmin Periodic Systems Sergio Bittanti and Patrizio Colaneri Discontinuous Systems Yury V. Orlov Constructions of Strict Lyapunov Functions Michael Malisoff and Frédéric Mazenc Controlling Chaos Huaguang Zhang, Derong Liu and Zhiliang Wang Stabilization of Navier–Stokes Flows Viorel Barbu Distributed Control of Multi-agent Networks Wei Ren and Yongcan Cao
    Lars Grüne r Jürgen Pannek Nonlinear Model Predictive Control Theory and Algorithms
    Lars Grüne Mathematisches Institut Universität Bayreuth Bayreuth 95440 Germany lars.gruene@uni-bayreuth.de Jürgen Pannek Mathematisches Institut Universität Bayreuth Bayreuth 95440 Germany juergen.pannek@uni-bayreuth.de ISSN 0178-5354 ISBN 978-0-85729-500-2 DOI 10.1007/978-0-85729-501-9 Springer London Dordrecht Heidelberg New York e-ISBN 978-0-85729-501-9 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2011926502 Mathematics Subject Classification (2010): 93-02, 92C10, 93D15, 49M37 © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as per- mitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publish- ers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of 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 laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: VTeX UAB, Lithuania Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
    For Brigitte, Florian and Carla LG For Sabina and Alina JP
    Preface The idea for this book grew out of a course given at a winter school of the In- ternational Doctoral Program “Identification, Optimization and Control with Ap- plications in Modern Technologies” in Schloss Thurnau in March 2009. Initially, the main purpose of this course was to present results on stability and performance analysis of nonlinear model predictive control algorithms, which had at that time recently been obtained by ourselves and coauthors. However, we soon realized that both the course and even more the book would be inevitably incomplete without a comprehensive coverage of classical results in the area of nonlinear model pre- dictive control and without the discussion of important topics beyond stability and performance, like feasibility, robustness, and numerical methods. As a result, this book has become a mixture between a research monograph and an advanced textbook. On the one hand, the book presents original research results obtained by ourselves and coauthors during the last five years in a comprehensive and self contained way. On the other hand, the book also presents a number of results—both classical and more recent—of other authors. Furthermore, we have included a lot of background information from mathematical systems theory, op- timal control, numerical analysis and optimization to make the book accessible to graduate students—on PhD and Master level—from applied mathematics and con- trol engineering alike. Finally, via our web page www.nmpc-book.com we provide MATLAB and C++ software for all examples in this book, which enables the reader to perform his or her own numerical experiments. For reading this book, we assume a basic familiarity with control systems, their state space representation as well as with concepts like feedback and stability as provided, e.g., in undergraduate courses on control engineering or in courses on mathematical systems and control theory in an applied mathematics curriculum. However, no particular knowledge of nonlin- ear systems theory is assumed. Substantial parts of the systems theoretic chapters of the book have been used by us for a lecture on nonlinear model predictive con- trol for master students in applied mathematics and we believe that the book is well suited for this purpose. More advanced concepts like time varying formulations or peculiarities of sampled data systems can be easily skipped if only time invariant problems or discrete time systems shall be treated. vii
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