Grüne / Pannek Nonlinear Model Predictive Control

Theory and Algorithms
2. Auflage 2017
ISBN: 978-3-319-46024-6
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 463 Seiten

Reihe: Communications and Control Engineering

This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine-the core of any nonlinear model predictive controller-works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC.
The second edition has been substantially rewritten, edited and updated to reflect the significant advances that have been made since the publication of its predecessor, including:

•a new chapter on economic NMPC relaxing the assumption that the running cost penalizes the distance to a pre-defined equilibrium;
•a new chapter on distributed NMPC discussing methods which facilitate the control of large-scale systems by splitting up the optimization into smaller subproblems;
•an extended discussion of stability and performance using approximate updates rather than full optimization;
•replacement of the pivotal sufficient condition for stability without stabilizing terminal conditions with a weaker alternative and inclusion of an alternative and much simpler proof in the analysis; and
•further variations and extensions in response to suggestions from readers of the first edition.
Though primarily aimed at academic researchers and practitioners working in control and optimization, the text is self-contained, featuring background material on infinite-horizon optimal control and Lyapunov stability theory that also makes it accessible for graduate students in control engineering and applied mathematics.


Lars Grüne has been Professor for Applied Mathematics at the University of Bayreuth, Germany, since 2002 and head of the Chair of Applied Mathematics since 2009. He received his Diploma and Ph.D. in Mathematics in 1994 and 1996, respectively, from the University of Augsburg and his habilitation from the J.W. Goethe University in Frankfurt/M in 2001. He held visiting positions at the Universities of Rome 'La Sapienza' (Italy), Padova (Italy), Melbourne (Australia), Paris IX - Dauphine (France) and Newcastle (Australia). Professor Grüne is Editor-in-Chief of the journal Mathematics of Control, Signals and Systems (MCSS), Associate Editor for the Journal of Optimization Theory and Applications (JOTA) and the Journal of Applied Mathematica and Mechanics (ZAMM) and member of the Managing Board of the GAMM - International Association of Applied Mathematics and Mechanics. Professor Grüne co-authored four books, more than 100 papers and chapters in peer reviewed journals and books and more than 80 articles in conference proceedings. He is member of the steering committee of the International Symposium on Mathematical Theory of Networks and Systems (MTNS) and member of the Program Comittees of various other conferences, including IFAC-NOLCOS symposia, the European Control Conference and the IEEE Conference on Decision and Control. In 2012, Professor Grüne was awarded the Excellence in Teaching Award ('Preis für gute Lehre') from the State of Bavaria. His research interests lie in the area of mathematical systems and control theory with a focus on numerical and optimization-based methods for stability analysis and stabilization of nonlinear systems. Jürgen Pannek has been Professor in the Department of Production Engineering at the University of Bremen (Germany) since 2014. He received his Diploma in Mathematical Economics and his Ph.D. in Mathematics from the University of Bayreuth in 2005 and 2009. He was visiting lecturer at the University of Birmingham (England) in 2008 and Curtin University of Perth (Australia) from 2010 to 2011. Thereafter, he worked as scientific assistant in the Department of Aerospace Engineering at the University of the Federal Armed Forces Munich (Germany). In his research, he focuses on the area of system and control theory from the application point of view regarding robotics, logistics and cyberphysical systems.

Autoren/Hrsg.

Grüne, Lars

Pannek, Jürgen

Inhaltsverzeichnis

1;Preface to the Second Edition;7
2;Preface to the First Edition;9
3;Contents;11
4;1 Introduction;15
4.1;1.1 What Is Nonlinear Model Predictive Control?;15
4.2;1.2 Where Did NMPC Come From?;17
4.3;1.3 How Is This Book Organized?;19
4.4;1.4 What Is Not Covered in This Book?;23
4.5;References;24
5;2 Discrete Time and Sampled Data Systems;26
5.1;2.1 Discrete Time Systems;26
5.2;2.2 Sampled Data Systems;29
5.3;2.3 Stability of Discrete Time Systems;42
5.4;2.4 Stability of Sampled Data Systems;50
5.5;2.5 Notes and Extensions;53
5.6;References;56
6;3 Nonlinear Model Predictive Control;57
6.1;3.1 The Basic NMPC Algorithm;57
6.2;3.2 Constraints;60
6.3;3.3 Variants of the Basic NMPC Algorithms;64
6.4;3.4 The Dynamic Programming Principle;70
6.5;3.5 Notes and Extensions;76
6.6;References;80
7;4 Infinite Horizon Optimal Control;82
7.1;4.1 Definition and Well Posedness of the Problem;82
7.2;4.2 The Dynamic Programming Principle;85
7.3;4.3 Relaxed Dynamic Programming;91
7.4;4.4 Notes and Extensions;97
7.5;References;100
8;5 Stability and Suboptimality Using Stabilizing Terminal Conditions;102
8.1;5.1 The Relaxed Dynamic Programming Approach;102
8.2;5.2 Equilibrium Endpoint Constraint;103
8.3;5.3 Lyapunov Function Terminal Cost;110
8.4;5.4 Suboptimality and Inverse Optimality;118
8.5;5.5 Notes and Extensions;126
8.6;References;129
9;6 Stability and Suboptimality Without Stabilizing Terminal Conditions;131
9.1;6.1 Setting and Preliminaries;131
9.2;6.2 Bounds on VN and Asymptotic Controllability with Respect to ell;135
9.3;6.3 Implications of the Bound on VN;139
9.4;6.4 Computation of ?;140
9.5;6.5 Main Stability and Performance Results;145
9.6;6.6 Design of Good Stage Costs ell;154
9.7;6.7 Semiglobal and Practical Asymptotic Stability;164
9.8;6.8 Proof of Proposition 6.18;173
9.9;6.9 Notes and Extensions;182
9.10;References;186
10;7 Feasibility and Robustness;187
10.1;7.1 The Feasibility Problem;187
10.2;7.2 Feasibility of Unconstrained NMPC Using Exit Sets;190
10.3;7.3 Feasibility of Unconstrained NMPC Using Stability;194
10.4;7.4 Comparing NMPC with and Without Terminal Conditions;198
10.5;7.5 Robustness: Basic Definition and Concepts;202
10.6;7.6 Robustness Without State Constraints;204
10.7;7.7 Examples for Nonrobustness Under State Constraints;209
10.8;7.8 Robustness with State Constraints via Robust-Optimal Feasibility;214
10.9;7.9 Robustness with State Constraints via Continuity of VN;219
10.10;7.10 Notes and Extensions;225
10.11;References;228
11;8 Economic NMPC;230
11.1;8.1 Setting;230
11.2;8.2 Averaged Performance with Terminal Conditions;232
11.3;8.3 Asymptotic Stability with Terminal Conditions;236
11.4;8.4 Non-averaged and Transient Performance with Terminal Conditions;240
11.5;8.5 Averaged Optimality Without Terminal Conditions;248
11.6;8.6 Practical Asymptotic Stability Without Terminal Conditions;252
11.7;8.7 Non-averaged and Transient Performance Without Terminal Conditions;257
11.8;8.8 Notes and Extensions;264
11.9;References;266
12;9 Distributed NMPC;268
12.1;9.1 Background and Problem Formulation;268
12.2;9.2 Classification of Connectedness;270
12.3;9.3 Problem Classes for Different Levels of Connectedness;281
12.4;9.4 Asymptotic Stability and Convergence;285
12.5;9.5 Communication and Coordination Schemes;290
12.6;9.6 Notes and Extensions;301
12.7;References;303
13;10 Variants and Extensions;305
13.1;10.1 Schemes with Mixed Terminal Conditions;305
13.2;10.2 Unconstrained NMPC with Terminal Weights;309
13.3;10.3 Nonpositive Definite Stage Cost;310
13.4;10.4 Multistep NMPC-Feedback Laws;314
13.5;10.5 Fast Sampling;316
13.6;10.6 Compensation of Computation Times;320
13.7;10.7 Online Measurement of ?;324
13.8;10.8 Adaptive Optimization Horizon;333
13.9;10.9 Nonoptimal NMPC;340
13.10;References;349
14;11 Numerical Discretization;351
14.1;11.1 Basic Solution Methods;351
14.2;11.2 Convergence Theory;356
14.3;11.3 Adaptive Step Size Control;361
14.4;11.4 Using the Methods Within the NMPC Algorithms;365
14.5;11.5 Numerical Approximation Errors and Stability;367
14.6;11.6 Notes and Extensions;371
14.7;References;374
15;12 Numerical Optimal Control of Nonlinear Systems;375
15.1;12.1 Discretization of the NMPC Problem;375
15.2;12.2 Unconstrained Optimization;388
15.3;12.3 Constrained Optimization;393
15.4;12.4 Implementation Issues in NMPC;416
15.5;12.5 Warm Start of the NMPC Optimization;426
15.6;12.6 Nonoptimal NMPC;434
15.7;12.7 Notes and Extensions;438
15.8;References;440
16;Appendix A NMPC Software Supporting This Book;443
17;Appendix B Glossary;449
18;Index;456