Nonlinear Model Predictive Control (eBook)

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