Model predictive control: theory and design
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Madison, Wis.
Nob Hill Publ.
2009
|
| Edition: | 1. printing |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XLI, 533 S. graph. Darst. |
| ISBN: | 9780975937709 |
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MARC
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| 100 | 1 | |a Rawlings, James Blake |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Model predictive control |b theory and design |c James B. Rawlings ; David Q. Mayne |
| 250 | |a 1. printing | ||
| 264 | 1 | |a Madison, Wis. |b Nob Hill Publ. |c 2009 | |
| 300 | |a XLI, 533 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Feedback control systems | |
| 650 | 4 | |a Predictive control | |
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| 700 | 1 | |a Mayne, David Q. |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017726739 | ||
Record in the Search Index
| _version_ | 1804139368727707648 |
|---|---|
| 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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| id | DE-604.BV035672485 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:42:59Z |
| institution | BVB |
| isbn | 9780975937709 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017726739 |
| oclc_num | 430536884 |
| open_access_boolean | |
| owner | DE-703 DE-91 DE-BY-TUM DE-706 |
| owner_facet | DE-703 DE-91 DE-BY-TUM DE-706 |
| physical | XLI, 533 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Nob Hill Publ. |
| record_format | marc |
| spelling | Rawlings, James Blake Verfasser aut Model predictive control theory and design James B. Rawlings ; David Q. Mayne 1. printing Madison, Wis. Nob Hill Publ. 2009 XLI, 533 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Control theory Feedback control systems Predictive control Prädiktive Regelung (DE-588)4271836-3 gnd rswk-swf Prädiktive Regelung (DE-588)4271836-3 s DE-604 Mayne, David Q. Verfasser aut Digitalisierung UB Bayreuth application/pdf 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 Inhaltsverzeichnis |
| spellingShingle | Rawlings, James Blake Mayne, David Q. Model predictive control theory and design Control theory Feedback control systems Predictive control Prädiktive Regelung (DE-588)4271836-3 gnd |
| subject_GND | (DE-588)4271836-3 |
| title | Model predictive control theory and design |
| title_auth | Model predictive control theory and design |
| title_exact_search | Model predictive control theory and design |
| title_full | Model predictive control theory and design James B. Rawlings ; David Q. Mayne |
| title_fullStr | Model predictive control theory and design James B. Rawlings ; David Q. Mayne |
| title_full_unstemmed | Model predictive control theory and design James B. Rawlings ; David Q. Mayne |
| title_short | Model predictive control |
| title_sort | model predictive control theory and design |
| title_sub | theory and design |
| topic | Control theory Feedback control systems Predictive control Prädiktive Regelung (DE-588)4271836-3 gnd |
| topic_facet | Control theory Feedback control systems Predictive control Prädiktive Regelung |
| url | 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 |
| work_keys_str_mv | AT rawlingsjamesblake modelpredictivecontroltheoryanddesign AT maynedavidq modelpredictivecontroltheoryanddesign |