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Model predictive control: theory, computation, and design

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Bibliographische Detailangaben
Beteiligte Personen:	Rawlings, James Blake (VerfasserIn), Mayne, David Q. (VerfasserIn), Diehl, Moritz 1971- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Madison, Wisconsin Nob Hill Publishing October 2017
Ausgabe:	2nd edition
Schlagwörter:	Prädiktive Regelung
Links:	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
Umfang:	xlvi, 623 Seiten Diagramme
ISBN:	9780975937730

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adam_text	This book was set in Lucida using WYjX, and printed and bound by Worzalla It was printed on Forest Stewardship Council® certified acid- 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 orders@nobhi11publishing com http://www nobhi11publishing com 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 MIX Paper from responsible sources FSC* C002589 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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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
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