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