Model predictive control: theory, computation, and design
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Madison, Wisconsin
Nob Hill Publishing
October 2017
|
| Edition: | 2nd edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xlvi, 623 Seiten Diagramme |
| ISBN: | 9780975937730 |
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| _version_ | 1804178166785245184 |
|---|---|
| adam_text | This book was set in Lucida using WYjX, and printed and bound by
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free recycled paper
Cover design by Cheryl M and James B Rawlings
Copyright © 2017 by Nob Hill Publishing, LLC
All rights reserved
Nob Hill Publishing, LLC
Cheryl M Rawlings, publisher
Madison, WI 53705
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No part of this book may be reproduced, in any form or by any means,
without permission in writing from the publisher
Library of Congress Control Number: 2017909542
Printed in the United States of America
First Edition
First Printing August 2009
Electronic Download November 2013
Electronic Download (2nd) April 2014
Electronic Download (3rd) July 2014
Electronic Download (4th) October 2014
Electronic Download (5th) Second Edition February 2015 0
First Printing October 2017
FSC
www f8c org
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Model Predictive Control:
Theory, Computation, and Design
2nd Edition
James B Rawlings
Department of Chemical and Biological Engineering
University of Wisconsin
Madison, Wisconsin, USA
David Q Mayne
Department of Electrical and Electronic Engineering
Imperial College London
London, England
Moritz M Diehl
Department of Microsystems Engineering and
Department of Mathematics
University of Freiburg
Freiburg, Germany
Publishing
Madison, Wisconsin
Contents
Jm
1 Getting Started with Model Predictive Control 1
1 1 Introduction 1
1 2 Models and Modeling 1
121 Linear Dynamic Models 2
122 Input-Output Models 3
123 Distributed Models 4
124 Discrete Time Models 5
125 Constraints 6
126 Deterministic and Stochastic 9
1 3 Introductory MPC Regulator 11
131 Linear Quadratic Problem 11
132 Optimizing Multistage Functions 12
133 Dynamic Programming Solution 18
134 The Infinite Horizon LQ Problem 21
135 Controllability 23
136 Convergence of the Linear Quadratic Regulator 24
1 4 Introductory State Estimation 26
141 Linear Systems and Normal Distributions 27
142 Linear Optimal State Estimation 29
143 Least Squares Estimation 33
144 Moving Horizon Estimation 39
145 Observability 41
146 Convergence of the State Estimator 43
1 5 Tracking, Disturbances, and Zero Offset 46
151 Tracking 46
152 Disturbances and Zero Offset 49
1 6 Exercises 60
2 Model Predictive Control—Regulation 89
2 1 Introduction 89
2 2 Model Predictive Control 91
2 3 Dynamic Programming Solution 107
2 4 Stability 112
241 Introduction 112
xm
Contents
xiv
242 Stabilizing Conditions 114
243 Exponential Stability 120
244 Controllability and Observability 120
245 Time-Varying Systems 123
2 5 Examples of MPC 130
251 The Unconstrained Linear Quadratic Regulator 132
252 Unconstrained Linear Periodic Systems 133
253 Stable Linear Systems with Control Constraints 134
254 Linear Systems with Control and State Constraints 136
255 Constrained Nonlinear Systems 139
256 Constrained Nonlinear Time-Varying Systems 141
2 6 Is a Terminal Constraint Set X/ Necessary? 144
2 7 Suboptimal MPC 147
271 Extended State 150
272 Asymptotic Stability of Difference Inclusions 150
2 8 Economic Model Predictive Control 153
281 Asymptotic Average Performance 155
282 Dissipativity and Asymptotic Stability 156
2 9 Discrete Actuators 160
2 10 Concluding Comments 163
2 11 Notes 166
2 12 Exercises 172
3 Robust and Stochastic Model Predictive Control 193
3 1 Introduction 193
311 Types of Uncertainty 193
312 Feedback Versus Open-Loop Control 195
313 Robust and Stochastic MPC 200
314 Tubes 202
315 Difference Inclusion Description of Uncertain Sys-
tems 203
3 2 Nominal (Inherent) Robustness 204
321 Introduction 204
322 Difference Inclusion Description of Discontinu-
ous Systems 206
323 When Is Nominal MPC Robust? 207
324 Robustness of Nominal MPC 209
3 3 Min-Max Optimal Control: Dynamic Programming Solution 214
331 Introduction 214
332 Properties of the Dynamic Programming Solution 216
Contents xv
3 4 Robust Min-Max MPC 220
,35 Tube-Based Robust MPC 223
351 Introduction 223
352 Outer-Bounding Tube for a Linear System with
Additive Disturbance 224
353 Tube-Based MPC of Linear Systems with Additive
Disturbances 228
354 Improved Tube-Based MPC of Linear Systems with
Additive Disturbances 234
3 6 Tube-Based MPC of Nonlinear Systems 236
361 The Nominal Trajectory 238
362 Model Predictive Controller 238
363 Choosing the Nominal Constraint Sets Ü and X 242
3 7 Stochastic MPC 246
371 Introduction 246
372 Stabilizing Conditions 248
373 Stochastic Optimization 248
374 Tube-Based Stochastic MPC for Linear Constrained
Systems 249
3 8 Notes 257
3 9 Exercises 262
4 State Estimation 269
4 1 Introduction 269
4 2 Full Information Estimation 269
421 State Estimation as Optimal Control of Estimate
Error 278
422 Duality of Linear Estimation and Regulation 281
4 3 Moving Horizon Estimation 283
431 Zero Prior Weighting 283
432 Nonzero Prior Weighting 287
433 Constrained Estimation 294
434 Smoothing and Filtering Update 295
4 4 Bounded Disturbances 300
4 5 Other Nonlinear State Estimators 308
451 Particle Filtering 308
452 Extended Kalman Filtering 309
453 Unscented Kalman Filtering 310
454 EKF, UKF, and MHE Comparison 312
4 6 On combining MHE and MPC 318
XVI
Contents
4 7 Notes 325
4 8 Exercises 327
5 Output Model Predictive Control 339
5 1 Introduction 339
52A Method for Output MPC 341
5 3 Linear Constrained Systems: Time-Invariant Case 344
531 Introduction 344
532 State Estimator 344
533 Controlling x 346
534 Output MPC 348
535 Computing the Tightened Constraints 352
5 4 Linear Constrained Systems: Time-Varying Case 353
5 5 Offset-Free MPC 353
551 Estimation 355
552 Control 356
553 Convergence Analysis 360
5 6 Nonlinear Constrained Systems 363
5 7 Notes 363
5 8 Exercises 366
6 Distributed Model Predictive Control 369
6 1 Introduction and Preliminary Results 369
611 Least Squares Solution 370
612 Stability of Suboptimal MPC 375
6 2 Unconstrained Two-Player Game 380
621 Centralized Control 382
622 Decentralized Control 383
623 Noncooperative Game 384
624 Cooperative Game 392
625 Tracking Nonzero Setpoints 398
626 State Estimation 405
6 3 Constrained Two-Player Game 406
631 Uncoupled Input Constraints 408
632 Coupled Input Constraints 411
633 Exponential Convergence with Estimate Error 413
634 Disturbance Models and Zero Offset 415
6 4 Constrained M-Player Game 419
6 5 Nonlinear Distributed MPC 421
651 Nonconvexity 421
652 Distributed Algorithm for Nonconvex Functions 423
Contents xvii
653 Distributed Nonlinear Cooperative Control 425
654 Stability 428
6 6 Notes 430
6 7 Exercises 435
7 Explicit Control Laws for Constrained Linear Systems 451
7 1 Introduction 451
7 2 Parametric Programming 452
7 3 Parametric Quadratic Programming 457
731 Preliminaries 457
732 Preview 458
733 Optimality Condition for a Convex Program 459
734 Solution of the Parametric Quadratic Program 462
735 Continuity of V°(■) and u°(■) 466
7 4 Constrained Linear Quadratic Control 467
7 5 Parametric Piecewise Quadratic Programming 469
7 6 DP Solution of the Constrained LQ Control Problem 475
7 7 Parametric Linear Programming 476
771 Preliminaries 476
772 Minimizer u°(x) is Unique for all xeX 478
7 8 Constrained Linear Control 481
7 9 Computation 482
7 10 Notes 483
7 11 Exercises 484
8 Numerical Optimal Control 491
8 1 Introduction 491
811 Discrete Time Optimal Control Problem 492
812 Convex Versus Nonconvex Optimization 493
813 Simultaneous Versus Sequential Optimal Control 496
814 Continuous Time Optimal Control Problem 498
8 2 Numerical Simulation 501
821 Explicit Runge-Kutta Methods 502
822 Stiff Equations and Implicit Integrators 506
823 Implicit Runge-Kutta and Collocation Methods 507
824 Differential Algebraic Equations 511
825 Integrator Adaptivity 513
8 3 Solving Nonlinear Equation Systems 513
831 Linear Systems 513
832 Nonlinear Root-Finding Problems 514
833 Local Convergence of Newton-Type Methods 517
xviii Contents
834 Affine Invariance 519
,835 Globalization for Newton-Type Methods 519
8 4 Computing Derivatives 520
841 Numerical Differentiation 521
842 Algorithmic Differentiation 522
843 Implicit Function Interpretation 523
844 Algorithmic Differentiation in Forward Mode 526
845 Algorithmic Differentiation in Reverse Mode 528
846 Differentiation of Simulation Routines 531
847 Algorithmic and Symbolic Differentiation Software 533
848 CasADi for Optimization 533
8 5 Direct Optimal Control Parameterizations 536
851 Direct Single Shooting 538
852 Direct Multiple Shooting 540
853 Direct Transcription and Collocation Methods 544
8 6 Nonlinear Optimization 548
861 Optimality Conditions and Perturbation Analysis 549
862 Nonlinear Optimization with Equalities 552
863 Hessian Approximations 553
8 7 Newton-Type Optimization with Inequalities 556
871 Sequential Quadratic Programming 557
872 Nonlinear Interior Point Methods 558
873 Comparison of SQP and Nonlinear IP Methods 560
8 8 Structure in Discrete Time Optimal Control 561
881 Simultaneous Approach 562
882 Linear Quadratic Problems (LQP) 564
883 LQP Solution by Riccati Recursion 564
884 LQP Solution by Condensing 566
885 Sequential Approaches and Sparsity Exploitation 568
886 Differential Dynamic Programming 570
887 Additional Constraints in Optimal Control 572
8 9 Online Optimization Algorithms 573
891 General Algorithmic Considerations 574
892 Continuation Methods and Real-Time Iterations 577
8 10 Notes 580
8 11 Exercises 583
Author Index 601
Citation Index
608
Contents
XIX
Subject Index 614
A Mathematical Background 624
A l Introduction 624
A 2 Vector Spaces 624
A 3 Range and Nullspace of Matrices 624
A4 Linear Equations — Existence and Uniqueness 625
A 5 Pseudo-Inverse 625
A 6 Partitioned Matrix Inversion Theorem 628
A 7 Quadratic Forms 629
A 8 Norms in IRn 631
A 9 Sets in IRn 631
A 10 Sequences 632
A 11 Continuity 633
A 12Derivatives 636
A 13 Convex Sets and Functions 641
A 13 1 Convex Sets 641
A 13 2 Convex Functions 646
A 14Differential Equations 648
A 15 Random Variables and the Probability Density 654
A 16Multivariate Density Functions 659
A 16 1 Statistical Independence and Correlation 668
A 17Conditional Probability and Bayes’s Theorem 672
A 18 Exercises 678
B Stability Theory 693
B l Introduction 693
B 2 Stability and Asymptotic Stability 696
B 3 Lyapunov Stability Theory 700
B31 Time-Invariant Systems 700
B32 Time-Varying, Constrained Systems 707
B33 Upper bounding X functions 709
B 4 Robust Stability 709
B41 Nominal Robustness 709
B42 Robustness 711
B 5 Control Lyapunov Functions 713
B 6 Input-to-State Stability 717
B 7 Output-to-State Stability and Detectability 719
B 8 Input/Output-to-State Stability 720
B 9 Incremental-Input/Output-to-State Stability 722
B 10 Observability 722
XX
Contents
B ll Exercises 724
C Optimization 729
C l Dynamic Programming 729
Cll Optimal Control Problem 731
C12 Dynamic Programming 733
C 2 Optimality Conditions 737
C21 Tangent and Normal Cones 737
C22 Convex Optimization Problems 741
C23 Convex Problems: Polyhedral Constraint Set 743
C24 Nonconvex Problems 745
C25 Tangent and Normal Cones 746
C26 Constraint Set Defined by Inequalities 750
C27 Constraint Set; Equalities and Inequalities 753
C 3 Set-Valued Functions and Continuity of Value Function 755
C31 Outer and Inner Semicontinuity 757
C32 Continuity of the Value Function 759
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| spelling | Rawlings, James Blake Verfasser aut Model predictive control theory, computation, and design James B. Rawlings, David Q. Mayne, Moritz M. Diehl 2nd edition Madison, Wisconsin Nob Hill Publishing October 2017 xlvi, 623 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Prädiktive Regelung (DE-588)4271836-3 gnd rswk-swf Prädiktive Regelung (DE-588)4271836-3 s DE-604 Mayne, David Q. Verfasser aut Diehl, Moritz 1971- Verfasser (DE-588)1045085804 aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030095384&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rawlings, James Blake Mayne, David Q. Diehl, Moritz 1971- Model predictive control theory, computation, and design Prädiktive Regelung (DE-588)4271836-3 gnd |
| subject_GND | (DE-588)4271836-3 |
| title | Model predictive control theory, computation, and design |
| title_auth | Model predictive control theory, computation, and design |
| title_exact_search | Model predictive control theory, computation, and design |
| title_full | Model predictive control theory, computation, and design James B. Rawlings, David Q. Mayne, Moritz M. Diehl |
| title_fullStr | Model predictive control theory, computation, and design James B. Rawlings, David Q. Mayne, Moritz M. Diehl |
| title_full_unstemmed | Model predictive control theory, computation, and design James B. Rawlings, David Q. Mayne, Moritz M. Diehl |
| title_short | Model predictive control |
| title_sort | model predictive control theory computation and design |
| title_sub | theory, computation, and design |
| topic | Prädiktive Regelung (DE-588)4271836-3 gnd |
| topic_facet | Prädiktive Regelung |
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