Preface	7
	Contents	9
	Part I Theory	22
	The Essentials of Model Predictive Control	23
	1 Introduction	23
	2 Background	24
	2.1 Intuition	24
	2.2 History	25
	3 Basics of Model Predictive Control (MPC)	32
	4 Stability of MPC	35
	5 Exogenous Inputs	37
	6 Robustness	39
	7 Example	40
	7.1 Background	41
	7.2 Dynamics	41
	7.3 Delay	43
	7.4 Performance Measure	43
	7.5 Noise and Other Disturbances	44
	7.6 Problem	44
	7.7 Solution	44
	7.8 Results	45
	7.9 Discussion	46
	8 Conclusions	46
	References	46
	Dynamic Programming, Optimal Control and Model PredictiveControl	48
	1 Introduction	48
	2 Setting, Definitions and Notation	49
	3 Dynamic Programming	52
	4 Stabilizing MPC	54
	4.1 Terminal Conditions	55
	4.2 No Terminal Conditions	56
	5 Economic MPC	59
	5.1 Terminal Conditions	60
	5.2 No Terminal Conditions	62
	6 Conclusions	70
	References	70
	Set-Valued and Lyapunov Methods for MPC	72
	1 Introduction	72
	2 Problem Statement and Assumptions	73
	2.1 Open Loop Optimal Control Problem	73
	2.2 Closed Loop Dynamics	75
	2.3 Standing Assumptions	75
	3 Properties of the Open Loop Optimal Control Problem	76
	3.1 Set-Valued Analysis Background	76
	3.2 Parametric Optimization Background	77
	3.3 Existence and Structure of Optimal Solutions	79
	4 Asymptotic Stability and Related Issues	81
	4.1 Strong Positive Invariance (a.k.a. RecursiveFeasibility)	82
	4.2 Strong Lyapunov Decrease (a.k.a. Cost Reduction)	83
	4.3 Strong Positive Invariance and Strong Asymptotic Stability	84
	4.4 Set-Valued Approach to Robustness of Asymptotic Stability	85
	4.5 Consistent Improvement	86
	5 Set-Valued Control Systems	87
	5.1 Weak Formulation of MPC	88
	5.2 Strong Formulation of MPC	90
	References	91
	Stochastic Model Predictive Control	93
	1 Introduction	93
	2 Stochastic Optimal Control and MPC with Chance Constraints	94
	3 Scenario Tree-Based MPC	96
	3.1 Scenario-Tree Construction	97
	3.2 Scenario-Tree Stochastic Optimization Problem	99
	3.3 Extensions and Applications	100
	4 Polynomial Chaos-Based MPC	102
	4.1 System Model, Constraints, and Control Input Parameterization	102
	4.2 Generalized Polynomial Chaos for Uncertainty Propagation	103
	4.3 Moment-Based Surrogate for Joint Chance Constraint	106
	4.4 Sample-Free, Moment-Based SMPC Formulation	107
	4.5 Extensions	108
	5 Stochastic Tube MPC	108
	5.1 System Model, Disturbance Model and Constraints	108
	5.2 Tube MPC Design	109
	5.3 Theoretical Guarantees	111
	5.4 Mass-Spring-Damper Example	112
	5.5 Extensions	112
	References	113
	Moving Horizon Estimation	116
	1 Introduction	116
	2 Systems of Interest	120
	3 MHE Setup	123
	4 Main Results	127
	5 Numerical Example	130
	6 Conclusions	133
	References	139
	Probing and Duality in Stochastic Model Predictive Control	142
	1 Introduction	142
	2 Stochastic Optimal Control and Duality	143
	2.1 The State, the Information State, and the BayesianFilter	143
	2.2 Stochastic Optimal Control and the Information State	144
	2.3 Duality and the Source of Intractability	145
	3 Stochastic MPC and Deterministic MPC	145
	4 Stochastic Reconstructibility and Its Dependence on Control	146
	4.1 Linear Regression and the Cramér-Rao Lower Bound	147
	4.2 Conditional Entropy Measure of Reconstructibility	148
	5 Three Examples of Dualized Stochastic Control	150
	5.1 Internet Congestion Control in TCP/IP	150
	5.2 Equalization in Cellular Wireless	151
	5.3 Experiment Design in Linear Regression for MPC	154
	6 Tractable Compromise Dualized Stochastic MPC Algorithms	156
	6.1 Non-dual Approaches	157
	6.1.1 Particle-Based Methods	157
	6.1.2 Certainty Equivalence Methods	158
	6.2 Dual Optimal POMDPs	158
	7 Conclusion	159
	References	160
	Economic Model Predictive Control: Some Design Tools and Analysis Techniques	162
	1 Model-Based Control and Optimization	162
	2 Formulation of Economic Model Predictive Control	165
	3 Properties of Economic MPC	168
	3.1 Recursive Feasibility	168
	3.1.1 Terminal Equality Constraints	168
	3.1.2 Terminal Set (or Terminal Inequality Constraint)	169
	3.2 Asymptotic Average Cost	170
	3.2.1 Terminal Feasible Trajectory	170
	3.2.2 Terminal Penalty Function	171
	3.2.3 Adaptive Terminal Weight	172
	3.3 Stability of Economic MPC	173
	3.4 EMPC Without Terminal Ingredients	177
	4 EMPC with Constraints on Average	178
	5 Robust Economic Model Predictive Control	179
	6 Conclusions	181
	References	182
	Nonlinear Predictive Control for Trajectory Tracking and Path Following: An Introduction and Perspective	185
	1 Introduction and Motivation	186
	2 Setpoint Stabilization, Trajectory Tracking, Path Following, and Economic Objectives	189
	2.1 Setpoint Stabilization	189
	2.2 Trajectory Tracking	190
	2.3 Path Following	191
	2.4 Economic Objectives	193
	3 A Brief Review of MPC for Setpoint Stabilization	193
	3.1 Comments on Convergence and Stability	195
	3.2 Setpoint Stabilization of a Lightweight Robot	196
	4 Model Predictive Control for Trajectory Tracking	197
	4.1 Convergence and Stability of Tracking NMPC	198
	4.2 Trajectory-Tracking Control of a Lightweight Robot	199
	5 Model Predictive Control for Path Following	199
	5.1 Convergence and Stability of Output Path-Following NMPC	201
	5.2 Path-Following Control of a Lightweight Robot	202
	5.2.1 Nominal Case	203
	5.2.2 Disturbance Case	205
	5.3 Extensions of Path Following	207
	6 Economic MPC	208
	6.1 Convergence and Stability of Economic MPC	209
	7 Conclusions and Perspectives	210
	References	211
	Hybrid Model Predictive Control	215
	1 Summary	215
	2 Hybrid Model Predictive Control	216
	2.1 Discrete-Time MPC for Discrete-Time Systems with Discontinuous Right-Hand Sides	217
	2.2 Discrete-Time MPC for Discrete-Time Systems with Mixed States	219
	2.3 Discrete-Time MPC for Discrete-Time Systems Using Memory and Logic Variables	220
	2.4 Periodic Continuous-Discrete MPC for Continuous-Time Systems	224
	2.4.1 With Piecewise Continuous Inputs	224
	2.4.2 With Piecewise Constant Inputs	226
	2.5 Periodic Continuous-Time MPC for Continuous-Time Systems Combined with Local Static State-Feedback Controllers	227
	2.6 Periodic Discrete-Time MPC for Continuous-Time Linear Systems with Impulses	228
	3 Towards MPC for Hybrid Dynamical Systems	231
	4 Further Reading	234
	References	234
	Model Predictive Control of Polynomial Systems	237
	1 Introduction	237
	2 Model Predictive Control of Discrete-Time Polynomial Systems	238
	3 Polynomial Optimization Methods	240
	3.1 Sum-of-Squares Decomposition	241
	3.2 Dual Approach via SOS Decomposition	241
	4 Fast Solution Methods for Polynomial MPC	243
	4.1 Convex MPC for a Subclass of Polynomial Systems	243
	4.2 Explicit MPC Using Algebraic Geometry Methods	244
	5 Taylor Series Approximations for Non-polynomial Systems	246
	5.1 Taylor's Theorem	246
	5.2 Example	247
	6 Outlook for Future Research	249
	References	251
	Distributed MPC for Large-Scale Systems	254
	1 Introduction and Motivations	254
	2 Model and Control Problem Decomposition	256
	2.1 Model Decomposition	256
	2.1.1 Non-overlapping Decompositions	258
	2.1.2 Overlapping Decompositions	259
	2.2 Partition Properties and Control	259
	2.3 MPC Problem Separability	260
	3 Decentralized MPC	262
	4 Distributed MPC	263
	4.1 Cooperating DMPC	263
	4.2 Non-cooperating Robustness-Based DMPC	265
	4.3 Distributed Control of Independent Systems	267
	4.4 Distributed Optimization	268
	5 Extensions and Applications	270
	6 Conclusions and Future Perspectives	271
	References	271
	Scalable MPC Design	274
	1 Introduction and Motivations	274
	2 Scalable and Plug-and-Play Design	275
	3 Concepts Enabling Scalable Design for Constrained Systems	278
	3.1 Tube-Based Small-Gain Conditions for Networks	278
	3.1.1 Tube-Based Small-Gain Condition for Networks Using RPI Sets	280
	3.1.2 Tube-Based Small-Gain Condition for Networks Using RCI Sets	281
	3.2 Distributed Invariance	281
	4 Scalable Design of MPC	283
	4.1 PnP-MPC Based on Robustness Against Coupling	283
	4.1.1 PnP-MPC Exploiting the Small-Gain Conditions for Networks Using RPI Sets	285
	4.1.2 PnP-MPC Exploiting the Small-Gain Conditions for Networks Using RCI Sets	286
	4.2 PnP-MPC Based on Distributed Invariance	286
	4.2.1 Implementation of Distributed MPC	286
	4.2.2 Distributed Synthesis	287
	4.2.3 Plug-and-Play and Hot-Transitions	288
	5 Generalizations and Related Approaches	289
	6 Applications	291
	6.1 Frequency Control in Power Networks	291
	6.2 Electric Vehicle Charging in Smart Grids	293
	7 Conclusions and Perspectives	295
	References	296
	Part II Computations	299
	Efficient Convex Optimization for Linear MPC	300
	1 Introduction	300
	2 Formulating and Solving LQR	301
	3 Convex Quadratic Programming	302
	4 Linear MPC Formulations and Interior-Point Implementation	305
	4.1 Linear MPC Formulations	305
	4.2 KKT Conditions and Efficient Interior-Point Implementation	307
	5 Parametrized Convex Quadratic Programming	310
	5.1 Enumeration	311
	5.2 Active-Set Strategy	312
	6 Software	315
	References	315
	Implicit Non-convex Model Predictive Control	317
	1 Introduction	317
	2 Parametric Nonlinear Programming	319
	3 Solution Approaches to Nonlinear Programming	320
	3.1 SQP	321
	3.2 Interior-Point Methods	322
	4 Discretization	323
	4.1 Single Shooting Methods	324
	4.2 Multiple Shooting Methods	325
	4.3 Direct Collocation Methods	326
	5 Predictors & Path-Following	327
	5.1 Parametric Embedding	329
	5.2 Path Following Methods	331
	5.3 Real-Time Dilemma: Should We Convergethe Solutions?	333
	5.4 Shifting	335
	5.5 Convergence of Path-Following Methods	336
	6 Sensitivities & Hessian Approximation	337
	7 Structures	339
	8 Summary	341
	References	342
	Convexification and Real-Time Optimization for MPC with Aerospace Applications	346
	1 Introduction	346
	2 Convexification	348
	2.1 Lossless Convexification of Control Constraints	349
	2.1.1 Theory	350
	2.1.2 Application	354
	2.2 Successive Convexification	356
	2.2.1 Theory	357
	2.2.2 Application	361
	3 Real-Time Computation	363
	4 Concluding Remarks	366
	References	367
	Explicit (Offline) Optimization for MPC	370
	1 Introduction	370
	1.1 From State-Space Models to Multi-Parametric Programming	370
	1.2 When Discrete Elements Occur	374
	2 Multi-Parametric Linear and Quadratic Programming: An Overview	374
	2.1 Theoretical Properties	375
	2.1.1 Literature Review	378
	2.2 Degeneracy	378
	2.2.1 Literature Review	379
	2.3 Solution Algorithms for mp-LP and mp-QP Problems	380
	3 Multi-Parametric Mixed-Integer Linear and Quadratic Programming: An Overview	384
	3.1 Theoretical Properties	384
	3.1.1 On the Notion of Exactness	385
	3.2 Solution Algorithms	386
	3.2.1 Literature Overview	386
	3.3 The Decomposition Algorithm	388
	3.3.1 Calculation of a New Candidate Integer Solution	388
	3.3.2 mp-QP Solution	388
	3.3.3 Comparison Procedure	389
	4 Discussion and Concluding Remarks	390
	4.1 Size of Multi-Parametric Programming Problem and Offline Computational Effort	390
	4.2 Size of the Solution and Online Computational Effort	391
	4.3 Other Developments in Explicit MPC	392
	References	393
	Real-Time Implementation of Explicit Model Predictive Control	397
	1 Simplification of MPC Feedback Laws	397
	1.1 Preliminaries	397
	1.2 Complexity of Explicit MPC	399
	1.3 Problem Statement and Main Results	400
	2 Piecewise Affine Explicit MPC Controllers of ReducedComplexity	401
	2.1 Clipping-Based Explicit MPC	401
	2.2 Regionless Explicit MPC	404
	2.3 Piecewise Affine Approximation of Explicit MPC	407
	3 Approximation of MPC Feedback Laws for Nonlinear Systems	410
	3.1 Problem Setup	410
	3.2 A QP-Based MPC Controller	411
	3.3 Stability Verification	412
	3.3.1 Lypunov Analysis	413
	3.3.2 Sum-of-Squares Certificates	414
	3.4 Closed-Loop Performance	415
	3.5 Parameter Tuning	416
	3.5.1 First Phase: Minimization of the SOS Slack	416
	3.5.2 Second Phase: Minimization of the Performance Metric	418
	3.6 Numerical Example	418
	References	420
	Robust Optimization for MPC	423
	1 Introduction	423
	2 Problem Formulation	424
	2.1 Inf-Sup Feedback Model Predictive Control	425
	2.2 Set-Based Robust Model Predictive Control	426
	2.3 Numerical Challenges	428
	3 Convex Approximations for Robust MPC	428
	3.1 Ellipsoidal Approximation Using LMIs	429
	3.2 Affine Disturbance Feedback	431
	4 Generic Methods for Robust MPC	433
	4.1 Inf-Sup Dynamic Programming	434
	4.2 Scenario-Tree MPC	436
	4.3 Tube MPC	437
	5 Numerical Methods for Tube MPC	438
	5.1 Feedback Parametrization	438
	5.2 Affine Set-Parametrizations	439
	5.3 Tube MPC Parametrization	441
	5.4 Tube MPC Via Min-Max Differential Inequalities	441
	6 Numerical Aspects: Modern Set-Valued Computing	443
	6.1 Factorable Functions	443
	6.2 Set Arithmetics	445
	6.3 Set-Valued Integrators	447
	7 Conclusions	449
	References	450
	Scenario Optimization for MPC	454
	1 Introduction	454
	2 Stochastic MPC and the Use of the Scenario Approach	455
	3 Fundamentals of Scenario Optimization	457
	4 The Scenario Approach for Solving Stochastic MPC	460
	5 Numerical Example	465
	6 Extensions and Future Work	469
	References	470
	Nonlinear Programming Formulations for Nonlinear and Economic Model Predictive Control	473
	1 Introduction	473
	1.1 NLP Strategies for NMPC	474
	2 Properties of the NLP Subproblem	475
	2.1 NMPC Problem Reformulation	477
	3 Nominal and ISS Stability of NMPC	478
	4 Economic NMPC with Objective Regularization	480
	4.1 Regularization of Non-convex Economic Stage Costs	482
	4.2 Economic NMPC with Regularization of ReducedStates	483
	5 Economic MPC with a Stabilizing Constraint	489
	6 Case Studies	490
	6.1 Nonlinear CSTR	490
	6.2 Large-Scale Distillation System	492
	7 Conclusions	495
	References	495
	Part III Applications	498
	Automotive Applications of Model Predictive Control	499
	1 Model Predictive Control in Automotive Applications	499
	1.1 A Brief History	500
	1.2 Opportunities and Challenges	501
	1.3 Chapter Overview	504
	2 MPC for Powertrain Control, Vehicle Dynamics, and Energy Management	504
	2.1 Powertrain Control	504
	2.1.1 MPC Opportunities in Powertrain Control	508
	2.2 Control of Vehicle Dynamics	510
	2.2.1 MPC Opportunities in Vehicle Dynamics	513
	2.3 Energy Management in Hybrid Vehicles	514
	2.3.1 MPC Opportunities in Hybrid Vehicles	516
	2.4 Other Applications	517
	3 MPC Design Process in Automotive Applications	517
	3.1 Prediction Model	518
	3.2 Horizon and Constraints	521
	3.3 Cost Function, Terminal Set and Soft Constraints	522
	4 Computations and Numerical Algorithms	524
	4.1 Explicit MPC	525
	4.2 Online MPC	527
	4.3 Nonlinear MPC	528
	5 Conclusions and Future Perspectives	529
	References	529
	Applications of MPC in the Area of Health Care	534
	1 Introduction	534
	2 Is MPC Relevant to Health Problems?	535
	3 Special Characteristics of Control Problems in the Areaof Health	535
	3.1 Safety	536
	3.2 Background Knowledge	536
	3.3 Models	536
	3.4 Population Versus Personalised Models	537
	4 Specific Examples Where MPC Has Been Used in the Area of Health	537
	4.1 Ambulance Scheduling	537
	4.2 Joint Movement	539
	4.3 Type 1 Diabetes Treatment	540
	4.4 Anaesthesia	542
	4.5 HIV	543
	4.6 Cancer	545
	4.7 Inflammation	547
	5 Appraisal	548
	6 Conclusion	549
	References	550
	Model Predictive Control for Power Electronics Applications	556
	1 Introduction	556
	2 Basic Concepts	558
	2.1 System Constraints	558
	2.2 Cost Function	559
	2.3 Moving Horizon Optimization	561
	2.4 Design Parameters	562
	3 Linear Quadratic MPC for Converters with a Modulator	563
	4 Linear Quadratic Finite Control Set MPC	566
	4.1 Closed-Form Solution	567
	4.2 Design for Stability and Performance	569
	4.3 Example: Reference Tracking	571
	5 An Efficient Algorithm for Finite-Control Set MPC	575
	5.1 Modified Sphere Decoding Algorithm	576
	5.2 Simulation Study of FCS-MPC	579
	6 Conclusions	582
	References	583
	Learning-Based Fast Nonlinear Model Predictive Control for Custom-Made 3D Printed Ground and Aerial Robots	586
	1 Introduction	586
	2 Receding Horizon Control and Estimation Methods	588
	2.1 Nonlinear Model Predictive Control	588
	2.2 Nonlinear Moving Horizon Estimation	589
	3 Real-Time Applications	591
	3.1 Ultra-Compact Field Robot	591
	3.1.1 System Description	591
	3.1.2 System Model	592
	3.1.3 Control Scheme	593
	3.1.4 Implementation of NMHE	593
	3.1.5 Implementation of NMPC	594
	3.1.6 Results	595
	3.2 Tilt-Rotor Tricopter UAV	597
	3.2.1 System Description	598
	3.2.2 System Model	599
	3.2.3 Kinematic Equations	599
	3.2.4 Rigid-Body Equations	599
	3.2.5 External Forces and Moments	600
	3.2.6 Control Scheme	602
	3.2.7 Implementation of NMPC	602
	3.2.8 Implementation of NMHE	603
	3.2.9 Results	604
	3.2.10 Circular Reference Tracking	604
	4 Conclusion	608
	References	609
	Applications of MPC to Building HVAC Systems	611
	1 Introduction to Building HVAC Systems	611
	2 Problem Statement	613
	2.1 MPC	614
	3 Challenges and Opportunities	615
	3.1 Modeling	615
	3.2 Load Forecasting	616
	3.3 Discrete Decisions	617
	3.4 Large-Scale Applications	617
	3.5 Demand Charges	618
	4 Decomposition	618
	4.1 High-Level	618
	4.2 Low-Level Airside	619
	4.3 Low-Level Waterside	619
	4.4 Feedback	620
	5 Example	620
	6 Stanford University Campus	622
	6.1 SESI Project	622
	6.2 Control System	623
	6.3 Performance	624
	7 Outlook	624
	References	626
	Toward Multi-Layered MPC for Complex Electric Energy Systems	628
	1 Introduction	628
	2 Temporal and Spatial Complexities in the Changing Electric Power Industry	629
	3 Load Characterization: The Main Cause of Inter-Temporal Dependencies and Spatial Interdependencies	631
	3.1 Multi-Temporal Load Decomposition	634
	3.2 Inflexible Load Modeling	634
	4 Hierarchical Control in Today's Electric Power Systems	636
	4.1 Main Objectives of Hierarchical Control	636
	4.2 General Formulation of Main Objectives	638
	4.3 Unified Modeling Framework	639
	4.4 Assumptions and Limitations Rooted in Today's Hierarchical Control	640
	4.4.1 Tertiary Level Control	640
	4.4.2 Secondary Level Control	641
	4.4.3 Primary Level Control	641
	5 Need for Interactive Multi-Layered MPC in Changing Industry	641
	5.1 Temporal Aspect	642
	5.2 Spatial Aspect	642
	6 Temporal Lifting for Decision Making with Multi-Rate Disturbances	643
	6.1 Nested Temporal Lifting	644
	7 Spatial Lifting for Multi-Agent Decision Making	647
	7.1 Nested Spatial Lifting	648
	7.1.1 Functional Bids	650
	8 Digital Implementation	651
	9 Framework for Implementing Interactive Multi-Spatial Multi-Temporal MPC: DyMonDS	653
	10 Application of the DyMonDS Framework: One Dayin a Lifetime of Two Bus Power System	655
	10.1 Example 1: MPC for Utilizing Heterogeneous Generation Resources	655
	10.2 Example 2: MPC Spatial and Temporal Lifting in Microgrids to Support Efficient Participation of Flexible Demand	656
	10.3 Example 3: The Role of MPC in Reducing the Need for Fast Storage While Enabling Stable FeedbackResponse	658
	10.4 Example 4: The Role of MPC Spatial Lifting in Normal Operation Automatic Generation Control (AGC)	661
	11 Conclusions	663
	References	663
	Applications of MPC to Finance	667
	1 Introduction	667
	1.1 Portfolio Optimization	667
	1.2 Dynamic Option Hedging	668
	1.3 Organization of Chapter	669
	2 Modeling of Account Value Dynamics	670
	2.1 Stock Price Dynamics	672
	2.2 Control Structure of Trading Algorithms	673
	3 Portfolio Optimization Problems	673
	3.1 MPC Formulations	675
	3.1.1 Overview of MPC Literature	675
	3.1.2 Transaction Costs	677
	3.1.3 Constraints in Portfolio Optimization	678
	4 MPC in Dynamic Option Hedging	679
	4.1 European Call Option Hedging	680
	4.2 Option Replication as a Control Problem	681
	4.3 MPC Option Hedging Formulations	682
	4.3.1 Using an Option Pricing Model	683
	4.3.2 Predicting to Expiration	683
	4.4 Additional Considerations in Option Hedging	684
	5 Conclusions	685
	References	685
	Index	688