Nonlinear Model Predictive Control (eBook)

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.

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