Grüne / Pannek Nonlinear Model Predictive Control

Theory and Algorithms
1. Auflage 2011
ISBN: 978-0-85729-501-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 364 Seiten

Reihe: Communications and Control Engineering

Nonlinear Model Predictive Control is a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. 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. NMPC schemes with and without stabilizing terminal constraints are detailed and intuitive examples illustrate the performance of different NMPC variants. An introduction to nonlinear optimal control algorithms gives insight into how the nonlinear optimisation routine - the core of any NMPC controller - works. An appendix covering NMPC software and accompanying software in MATLAB® and C++(downloadable from www.springer.com/ISBN) enables readers to perform computer experiments exploring the possibilities and limitations of NMPC.

Autoren/Hrsg.

Grüne, Lars

Pannek, Jürgen

Inhaltsverzeichnis

1;Nonlinear Model Predictive Control;4
1.1;Preface;7
1.2;Contents;9
2;Chapter 1: Introduction;12
2.1;1.1 What Is Nonlinear Model Predictive Control?;12
2.2;1.2 Where Did NMPC Come from?;14
2.3;1.3 How Is This Book Organized?;16
2.4;1.4 What Is Not Covered in This Book?;20
2.5; References;21
3;Chapter 2: Discrete Time and Sampled Data Systems;23
3.1;2.1 Discrete Time Systems;23
3.2;2.2 Sampled Data Systems;26
3.3;2.3 Stability of Discrete Time Systems;38
3.4;2.4 Stability of Sampled Data Systems;45
3.5;2.5 Notes and Extensions;49
3.6;2.6 Problems;49
3.7; References;51
4;Chapter 3: Nonlinear Model Predictive Control;52
4.1;3.1 The Basic NMPC Algorithm;52
4.2;3.2 Constraints;54
4.3;3.3 Variants of the Basic NMPC Algorithms;59
4.4;3.4 The Dynamic Programming Principle;65
4.5;3.5 Notes and Extensions;71
4.6;3.6 Problems;73
4.7; References;74
5;Chapter 4: Infinite Horizon Optimal Control;76
5.1;4.1 Definition and Well Posedness of the Problem;76
5.2;4.2 The Dynamic Programming Principle;79
5.3;4.3 Relaxed Dynamic Programming;84
5.4;4.4 Notes and Extensions;90
5.5;4.5 Problems;92
5.6; References;93
6;Chapter 5: Stability and Suboptimality Using Stabilizing Constraints;95
6.1;5.1 The Relaxed Dynamic Programming Approach;95
6.2;5.2 Equilibrium Endpoint Constraint;96
6.3;5.3 Lyapunov Function Terminal Cost;103
6.4;5.4 Suboptimality and Inverse Optimality;109
6.5;5.5 Notes and Extensions;117
6.6;5.6 Problems;118
6.7; References;120
7;Chapter 6: Stability and Suboptimality Without Stabilizing Constraints;121
7.1;6.1 Setting and Preliminaries;121
7.2;6.2 Asymptotic Controllability with Respect to l;124
7.3;6.3 Implications of the Controllability Assumption;127
7.4;6.4 Computation of alpha;129
7.5;6.5 Main Stability and Performance Results;133
7.6;6.6 Design of Good Running Costs l;141
7.7;6.7 Semiglobal and Practical Asymptotic Stability;150
7.8;6.8 Proof of Proposition 6.17;158
7.9;6.9 Notes and Extensions;167
7.10;6.10 Problems;169
7.11; References;170
8;Chapter 7: Variants and Extensions;172
8.1;7.1 Mixed Constrained-Unconstrained Schemes;172
8.2;7.2 Unconstrained NMPC with Terminal Weights;175
8.3;7.3 Nonpositive Definite Running Cost;177
8.4;7.4 Multistep NMPC-Feedback Laws;181
8.5;7.5 Fast Sampling;183
8.6;7.6 Compensation of Computation Times;187
8.7;7.7 Online Measurement of alpha;190
8.8;7.8 Adaptive Optimization Horizon;198
8.9;7.9 Nonoptimal NMPC;205
8.10;7.10 Beyond Stabilization and Tracking;214
8.11; References;216
9;Chapter 8: Feasibility and Robustness;218
9.1;8.1 The Feasibility Problem;218
9.2;8.2 Feasibility of Unconstrained NMPC Using Exit Sets;221
9.3;8.3 Feasibility of Unconstrained NMPC Using Stability;224
9.4;8.4 Comparing Terminal Constrained vs. Unconstrained NMPC;229
9.5;8.5 Robustness: Basic Definition and Concepts;232
9.6;8.6 Robustness Without State Constraints;234
9.7;8.7 Examples for Nonrobustness Under State Constraints;239
9.8;8.8 Robustness with State Constraints via Robust-optimal Feasibility;244
9.9;8.9 Robustness with State Constraints via Continuity of VN;248
9.10;8.10 Notes and Extensions;253
9.11;8.11 Problems;256
9.12; References;256
10;Chapter 9: Numerical Discretization;258
10.1;9.1 Basic Solution Methods;258
10.2;9.2 Convergence Theory;263
10.3;9.3 Adaptive Step Size Control;267
10.4;9.4 Using the Methods Within the NMPC Algorithms;271
10.5;9.5 Numerical Approximation Errors and Stability;273
10.6;9.6 Notes and Extensions;276
10.7;9.7 Problems;278
10.8; References;279
11;Chapter 10: Numerical Optimal Control of Nonlinear Systems;281
11.1;10.1 Discretization of the NMPC Problem;281
11.1.1; Full Discretization;285
11.1.2; Recursive Discretization;287
11.1.3; Multiple Shooting Discretization;289
11.2;10.2 Unconstrained Optimization;294
11.3;10.3 Constrained Optimization;298
11.3.1; Active Set SQP Methods;303
11.3.2; Interior-Point Methods;315
11.4;10.4 Implementation Issues in NMPC;321
11.4.1; Structure of the Derivatives;322
11.4.2; Condensing;326
11.4.3; Optimality and Computing Tolerances;327
11.5;10.5 Warm Start of the NMPC Optimization;330
11.5.1; Initial Value Embedding;331
11.5.2; Sensitivity Based Warm Start;334
11.5.3; Shift Method;336
11.6;10.6 Nonoptimal NMPC;337
11.7;10.7 Notes and Extensions;341
11.8;10.8 Problems;343
11.9; References;343
12;Appendix NMPC Software Supporting This Book;346
12.1; A.1 The MATLAB NMPC Routine;346
12.2; A.2 Additional MATLAB and MAPLE Routines;348
12.3; A.3 The C++ NMPC Software;350
13;Glossary;352
14;Index;358