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