Verfügbarkeit: Model predictive control | Technische Universität München

Model predictive control: theory and design

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Bibliographische Detailangaben
Beteiligte Personen:	Rawlings, James Blake (VerfasserIn), Mayne, David Q. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Madison, Wis. Nob Hill Publ. 2009
Ausgabe:	1. printing
Schlagwörter:	Control theory Feedback control systems Predictive control Prädiktive Regelung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017726739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XLI, 533 S. graph. Darst.
ISBN:	9780975937709

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Datensatz im Suchindex

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adam_text	Contents 1 Getting Started with Model Predictive Control 1 1.1 Introduction ............................ 1 1.2 Models and Modeling ...................... 1 1.2.1 Linear Dynamic Models ................. 2 1.2.2 Input-Output Models .................. 3 1.2.3 Distributed Models ................... 4 1.2.4 Discrete Time Models .................. 5 1.2.5 Constraints ........................ 6 1.2.6 Deterministic and Stochastic ............. 8 1.3 Introductory MPC Regulator .................. 9 1.3.1 Linear Quadratic Problem ............... 9 1.3.2 Optimizing Multistage Functions ........... 11 1.3.3 Dynamic Programming Solution ........... 17 1.3.4 The Infinite Horizon LQ Problem ........... 20 1.3.5 Controllability ...................... 22 1.3.6 Convergence of the Linear Quadratic Regulator . . 23 1.4 Introductory State Estimation ................. 25 1.4.1 Linear Systems and Normal Distributions ..... 26 1.4.2 Linear Optimal State Estimation ........... 28 1.4.3 Least Squares Estimation ............... 32 1.4.4 Moving Horizon Estimation .............. 37 1.4.5 Observability ....................... 40 1.4.6 Convergence of the State Estimator ......... 41 1.5 Tracking, Disturbances, and Zero Offset .......... 45 1.5.1 Tracking .......................... 45 1.5.2 Disturbances and Zero Offset ............. 47 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 2.4.1 Introduction ....................... 112 xi xii Contents 2.4.2 Stabilizing Conditions: No State Constraints ... 113 2.4.3 Stabilizing Conditions: Constrained Problems .. 115 2.4.4 Monotonicity of the Value Function ......... 116 2.4.5 Further Properties of the Value Function V^(-) .. 118 2.4.6 Summary ......................... 123 2.4.7 Controllability and Observability ........... 125 2.4.8 Time-Varying Systems ................. 126 2.5 Examples of MPC ......................... 131 2.5.1 Unconstrained Systems ................ 132 2.5.1.1 Linear Time-Invariant Systems ....... 132 2.5.1.2 Linear Time-Varying Systems ........ 134 2.5.1.3 Nonlinear Systems .............. 134 2.5.2 Systems with Control Constraints .......... 138 2.5.2.1 Linear Stable Systems ............ 138 2.5.2.2 Neutrally Stable Systems .......... 139 2.5.3 Systems with Control and State Constraints .... 142 2.5.3.1 Linear Systems ................ 142 2.5.3.2 Nonlinear Systems .............. 145 2.6 Is a Terminal Constraint Set X/ Necessary? ........ 147 2.6.1 Replacing the Terminal Constraint by a Terminal Cost ............................ 147 2.6.2 Omitting the Terminal Constraint .......... 149 2.7 Stage Cost A·) not Positive Definite ............. 153 2.8 Suboptimal MPC......................... 155 2.9 Tracking .............................. 159 2.9.1 No Uncertainty ...................... 159 2.9.2 Offset-Free MPC ..................... 160 2.9.3 Unreachable Setpoints................. 162 2.10 Concluding Comments ..................... 167 2.11 Notes ................................ 169 2.12 Exercises .............................. 172 Robust Model Predictive Control 187 3.1 Introduction ............................ 187 3.1.1 Types of Uncertainty .................. 187 3.1.2 Feedback Versus Open-Loop Control ........ 188 3.1.3 Robust MPC ........................ 193 3.1.4 Tubes ............................ 196 3.1.5 Difference Inclusion Description of Uncertain Sys¬ tems ............................ 196 Contents xiii 3.2 Nominal (Inherent) Robustness ................ 198 3.2.1 Introduction ....................... 198 3.2.2 Difference Inclusion Description of Discontinu¬ ous Systems ....................... 199 3.2.3 When Is Nominal MPC Robust? ............ 200 3.2.4 Input-to-State Stability ................. 203 3.3 Dynamic Programming Solution ............... 207 3.3.1 Introduction ....................... 207 3.3.2 Preliminary Results ................... 209 3.3.3 Stability of Min-Max RHC ................ 213 3.3.4 Feedback MPC ..................... 218 3.4 Tube-Based Robust MPC .................... 220 3.4.1 Introduction ....................... 220 3.4.2 Outer-Bounding Tubes for Linear Systems with Additive Disturbances ................. 221 3.4.3 Tube-Based MPC of Linear Systems with Additive Disturbances ....................... 226 3.4.4 Improved Tube-Based MPC of Linear Systems with Additive Disturbances ................. 234 3.5 Tube-Based MPC of Systems with Parametric Uncertainty 237 3.6 Tube-Based MPC of Nonlinear Systems ........... 242 3.6.1 The Central Path ..................... 243 3.6.2 Ancillary Controller ................... 245 3.6.3 Controller Algorithm .................. 248 3.6.4 Analysis .......................... 249 3.6.5 Choosing Z and V .................... 250 3.7 Notes ................................ 255 3.8 Exercises .............................. 258 State Estimation 265 4.1 Introduction ............................ 265 4.2 Full Information Estimation .................. 265 4.2.1 State Estimation as Optimal Control of Estimate Error ............................ 272 4.2.2 Duality of Linear Estimation and Regulation .... 275 4.3 Moving Horizon Estimation .................. 277 4.3.1 Zero Prior Weighting .................. 278 4.3.2 Nonzero Prior Weighting ................ 280 4.3.3 Constrained Estimation ................ 287 4.3.4 Smoothing and Filtering Update ........... 289 xiv Contents 4.4 Extended Kalman Filtering ................... 292 4.5 Unscented Kalman Filtering .................. 294 4.6 Interlude: EKF, UKF, and МНЕ Comparison ......... 296 4.7 Particle Filtering ......................... 301 4.7.1 The Sampled Density of a Transformed Random Variable .......................... 304 4.7.2 Sampling and Importance Sampling ......... 307 4.7.3 Resampling ........................ 324 4.7.4 The Simplest Particle Filter .............. 329 4.7.5 A Particle Filter Based on Importance Sampling . . 338 4.7.6 Optimal Importance Function ............. 343 4.8 Combined MHE/Particle Filtering ............... 348 4.9 Notes ................................ 356 4.10 Exercises .............................. 358 Output Model Predictive Control 371 5.1 Introduction ............................ 371 5.2 A Method for Output MPC ................... 373 5.3 Linear Constrained Systems: Time-Invariant Case .... 376 5.3.1 Introduction ....................... 376 5.3.2 State Estimator ...................... 377 5.3.3 Controlling χ ....................... 378 5.3.4 Output MPC ........................ 380 5.4 Linear Constrained Systems: Time-Varying Case ..... 384 5.4.1 Introduction ....................... 384 5.4.2 State Estimator ...................... 385 5.4.3 Controlling χ ....................... 385 5.4.4 Control of the Nominal System ............ 388 5.4.5 Control of the State Estimator ............ 390 5.5 Offset-Free MPC ......................... 391 5.5.1 Estimation ......................... 392 5.5.2 Control ........................... 394 5.5.3 Stability Analysis .................... 397 5.6 Nonlinear Constrained Systems ................ 399 5.6.1 Introduction ....................... 399 5.6.2 State Estimator ...................... 399 5.6.3 Nominal MPC ....................... 400 5.6.4 Tube-Based Output MPC ................ 401 5.6.5 Choosing 1 and V .................... 403 5.7 Notes ................................ 403 Contents xv 5.8 Exercises .............................. 406 Distributed Model Predictive Control 409 6.1 Introduction and Preliminary Results ............ 409 6.1.1 Least Squares Solution ................. 410 6.1.2 Stability of Suboptimal MPC.............. 415 6.2 Unconstrained Two-Player Game ............... 421 6.2.1 Centralized Control ................... 422 6.2.2 Decentralized Control ................. 423 6.2.3 Noncooperative Game ................. 424 6.2.4 Cooperative Game .................... 433 6.2.5 Tracking Nonzero Setpoints .............. 438 6.2.6 State Estimation ..................... 445 6.3 Constrained Two-Player Game ................ 446 6.3.1 Uncoupled Input Constraints ............. 448 6.3.2 Coupled Input Constraints .............. 451 6.3.3 Exponential Stability with Estimate Error ...... 453 6.3.4 Disturbance Models and Zero Offset ........ 455 6.4 Constrained M-Player Game .................. 459 6.5 Nonlinear Distributed MPC ................... 461 6.6 Notes ................................ 463 6.7 Exercises .............................. 467 Explicit Control Laws for Constrained Linear Systems 483 7.1 Introduction ............................ 483 7.2 Parametric Programming .................... 484 7.3 Parametric Quadratic Programming ............. 489 7.3.1 Preliminaries ....................... 489 7.3.2 Preview .......................... 490 7.3.3 Optimality Condition for a Convex Program .... 491 7.3.4 Solution of the Parametric Quadratic Program . . 494 7.3.5 Continuity of V°(-) andu°(-) ............ 498 7.4 Constrained Linear Quadratic Control ............ 499 7.5 Parametric Piecewise Quadratic Programming ....... 501 7.6 DP Solution of the Constrained LQ Control Problem ... 507 7.7 Parametric Linear Programming ............... 508 7.7.1 Preliminaries ....................... 508 7.7.2 Minimizer u°(x) is Unique for all χ є X ...... 510 7.8 Constrained Linear Control .................. 513 7.9 Computation ........................... 514 7.10Notes ................................ 514 xv¡ Contents 7.11 Exercises .............................. 516 Author Index 520 Citation Index 525 Subject Index 530 A Mathematical Background 534 A.1 Introduction ............................ 534 A.2 Vector Spaces ........................... 534 A.3 Range and Nullspace of Matrices ............... 534 A.4 Linear Equations — Existence and Uniqueness ...... 535 A.5 Pseudo-Inverse .......................... 535 A.6 Partitioned Matrix Inversion Theorem ............ 538 A.7 Quadratic Forms ......................... 539 A.8 Norms in Kn ........................... 540 A.9 Sets in R ............................. 541 A-lOSequences ............................. 542 A-llContinuity ............................. 543 A. 12 Derivatives ............................ 546 A.13Convex Sets and Functions ................... 550 A. 13.1 Convex Sets ........................ 551 A. 13.2 Convex Functions .................... 556 A. 14 Differential Equations ...................... 558 A. 15 Random Variables and the Probability Density ...... 564 A-löMultivariate Density Functions ................ 569 A.16.1 Statistical Independence and Correlation ...... 578 A. 17 Conditional Probability and Bayes s Theorem ....... 582 A-ieExercises .............................. 588 В Stability Theory 603 B.I Introduction ............................ 603 B.2 Stability and Asymptotic Stability .............. 605 B.3 Lyapunov Stability Theory ................... 608 B.3.1 Lyapunov Function for Linear Systems ....... 611 B.4 Robust Stability ......................... 611 B.4.1 Nominal Robustness .................. 612 B.4.2 Robustness ........................ 613 B.5 Control-Lyapunov Functions .................. 615 B.6 Input-to-State Stability ..................... 618 Contents xvii B.7 Output-to-State Stability and Detectability ......... 620 B.8 Input/Output-to-State Stability................ 621 В. 9 Incremental-Input/Output-to-State Stability ........ 622 B.IO Observability ........................... 622 B.ll Exercises .............................. 624 Optimization 627 C.I Dynamic Programming ..................... 627 C.I.I Optimal Control Problem ............... 629 C.1.2 Dynamic Programming ................. 631 C.2 Optimality Conditions ..................... 635 C.2.1 Tangent and Normal Cones .............. 635 C.2. 2 Convex Optimization Problems ............ 639 C.2.3 Convex Problems: Polyhedral Constraint Set ... 641 C.2.4 Nonconvex Problems .................. 643 C.2. 5 Tangent and Normal Cones .............. 644 C.2.6 Constraint Set Defined by Inequalities ....... 648 C.2. 7 Constraint Set; Equalities and Inequalities ..... 651 C.3 Set-Valued Functions and Continuity of Value Function . 653 C.3.1 Outer and Inner Semicontinuity ........... 655 C.3. 2 Continuity of the Value Function ........... 657 C.4 Exercises .............................. 665
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title	Model predictive control theory and design
title_auth	Model predictive control theory and design
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title_full	Model predictive control theory and design James B. Rawlings ; David Q. Mayne
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