The dynamics of control:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2012
|
| Edition: | [softcover repr. of the original 1. ed. 2000] |
| Series: | Systems & control: foundations & applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 629 S. graph. Darst. |
| ISBN: | 9781461271079 |
Staff View
MARC
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| 100 | 1 | |a Colonius, Fritz |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The dynamics of control |c Fritz Colonius ; Wolfgang Kliemann |
| 250 | |a [softcover repr. of the original 1. ed. 2000] | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2012 | |
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Systems & control: foundations & applications | |
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Record in the Search Index
| _version_ | 1804152929642348544 |
|---|---|
| adam_text | Contents
Preface
xi
1
Introduction
1
2
Dynamics, Perturbations, and
Control
7
2.1
Perturbations
of Complex Behavior
................. 9
2.2
Approximation
of Complex Systems
................ 15
2.3
Generic Behavior of Perturbations
................. 19
2.4
Stability Boundaries and Multistability
............... 23
2.5
Reachability in Control Systems
.................. 25
2.6
Linear and Nonlinear Stability Radii
................ 29
2.7
Stabilization of Bilinear Systems
.................. 34
2.8
The Lyapunov Spectrum of Matrices
................ 37
I Global Theory
45
3
Control Sets
47
3.1
Problem Formulation and Main Results
.............. 47
3.2
Control Sets
............................. 53
3.3
Relative
Invariance
and Multistability
............... 69
3.4
Chain Control Sets
.......................... 79
3.5
Notes
................................. 87
4
Control Flows and Limit Behavior
89
4.1
Problem Formulation and Main Results
....,,,,..,.,. 90
4.2
The Shift Space
............................ 95
4.3
The Control Flow
........................... 99
4.4
Recurrence and Ergodic Theory
................... 109
4.5
Chain Controllability and Inner Pairs
............... 113
4.6
Genericity
............................... 123
4.7
Perturbations and Order
....................... 126
4.8
Notes
................................. 134
vii
viii CONTENTS
II Linearization Theory
137
5
Linear Flows on Vector Bundles
139
5.1
Problem Formulation and Main Results
.............. 139
5.2
Morse Decompositions
........................ 148
5.3
The Morse Spectrum
......................... 159
5.4
Morse Spectrum and Lyapunov Spectrum
............. 168
5.5
Relations to Other Spectra
..................... 183
5.6
Invariant and Stable Manifolds
.................. . 196
5.7
Notes
................................. 208
6
Bilinear Systems on Vector Bundles
209
6.1
Problem Formulation and Main Results
.............. 209
6.2
Floquet and Morse Spectrum
.................... 221
6.3
The Lyapunov Spectrum
.......................237
6.4
Invariant and Stable Manifolds
...................242
6.5
Notes
.................................252
7
Linearization at a Singular Point
255
7.1
Problem Formulation and Main Results
.............. 256
7.2
Semigroups and Lyapunov Exponents
...............265
7.3
Control Sets and Spectra
......................281
7.4
Invariant and Stable Manifolds
...................302
7.5
Notes
.................................307
III Applications
309
8
One-Dimensional Control Systems
311
8.1
Problem Formulation and Main Results
..............312
8.2
Global Structure and Bifurcation
..................318
8.3
Linearization and Bifurcation
.................... 329
8.4
Feedback Control and Stabilization
................. 340
8.5
Notes
................................. 352
9
Examples for Global Behavior
353
9.1
Stirred Tank Reactor: Global Behavior
...............354
9.2
Stirred Tank Reactor: Bifurcation
.................. 360
9.3
A Bacterial Respiration Model
................... 365
9.4
The Takens-Bogdanov System
.................. . 367
9.5
Notes
.................................375
10
Examples for the Spectrum
377
10.1
Spectrum in Dimension Two
....................377
10.2
Numerically Computed Spectra
...................393
10.3
Notes
................................. 405
CONTENTS ix
11
Stability Radii and Robust Stability
407
11.1
Stability Radii of Linear Systems
..................408
11.2
Stability Radii of Nonlinear Systems
................416
11.3
Robust Stabilization of Linear Systems
..............423
11.4
Notes
.................................432
12
Open and Closed Loop Stabilization
433
12.1
Feedback Stabilization of Regular Systems
.............434
12.2
Open Loop Stabilization: The Singular Case
............449
12.3
Feedback Stabilization: The Singular Case
............ . 461
12.4
Notes
.................................473
13
Dynamics of Perturbations
477
13.1
Persistence of Attractors and Spectra
................478
13.2
The
Lorenz
Equation
.........................484
13.3
A Model for Ship Roll Motion
.................... 489
13.4
Notes
................................. 497
IV Appendices
499
A Geometric Control Theory
501
А Л
Differentiable Manifolds and Vector Fields
............. 502
A.
2
Basic Definitions for Control Systems
................505
A.3 The Orbit Theorem
.........................508
A.
4
Local Accessibility
..........................525
A.5 Notes
.................................530
В
Dynamical Systems
531
B.I Vector Bundles
............................531
B.2 Morse Decompositions, Attractors, Chains
............. 539
B.3 Ergodic Theory
............................ 551
B.4 Notes
................................. 554
С
Numerical Computation of Orbits
555
C.I Orbits and Approximately Invariant Sets
.............. 555
C.2 Computing Approximately Invariant Sets
............. 561
C.3 Computation via Time Optimal Control
.............. 565
C.4 Notes
.................................
56V
D
Computation of the Spectrum by
Lars Grüne 569
D.I Problem Formulation and Main Results
.............. 569
D.2 Discounted and Average Functionals
................ 573
D.3 Approximation of the Spectrum
................... 578
D.4 The Hamilton-Jacobi-Bellman Equation
.............. 583
D.5 Discounted Optimal Control Problems
............... 587
D.6 Notes
................................. 595
χ
CONTENTS
Bibliography
597
Index
621
|
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| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | [softcover repr. of the original 1. ed. 2000] |
| format | Book |
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| language | English |
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| spelling | Colonius, Fritz Verfasser aut The dynamics of control Fritz Colonius ; Wolfgang Kliemann [softcover repr. of the original 1. ed. 2000] Boston [u.a.] Birkhäuser 2012 XII, 629 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Systems & control: foundations & applications Automatic control Dynamics Komplexes System (DE-588)4114261-5 gnd rswk-swf Regelungssystem (DE-588)4134712-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Komplexes System (DE-588)4114261-5 s Regelungssystem (DE-588)4134712-2 s Dynamisches System (DE-588)4013396-5 s Kontrolltheorie (DE-588)4032317-1 s Störungstheorie (DE-588)4128420-3 s DE-604 Kliemann, Wolfgang Verfasser aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027763828&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Colonius, Fritz Kliemann, Wolfgang The dynamics of control Automatic control Dynamics Komplexes System (DE-588)4114261-5 gnd Regelungssystem (DE-588)4134712-2 gnd Dynamisches System (DE-588)4013396-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Störungstheorie (DE-588)4128420-3 gnd |
| subject_GND | (DE-588)4114261-5 (DE-588)4134712-2 (DE-588)4013396-5 (DE-588)4032317-1 (DE-588)4128420-3 |
| title | The dynamics of control |
| title_auth | The dynamics of control |
| title_exact_search | The dynamics of control |
| title_full | The dynamics of control Fritz Colonius ; Wolfgang Kliemann |
| title_fullStr | The dynamics of control Fritz Colonius ; Wolfgang Kliemann |
| title_full_unstemmed | The dynamics of control Fritz Colonius ; Wolfgang Kliemann |
| title_short | The dynamics of control |
| title_sort | the dynamics of control |
| topic | Automatic control Dynamics Komplexes System (DE-588)4114261-5 gnd Regelungssystem (DE-588)4134712-2 gnd Dynamisches System (DE-588)4013396-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Störungstheorie (DE-588)4128420-3 gnd |
| topic_facet | Automatic control Dynamics Komplexes System Regelungssystem Dynamisches System Kontrolltheorie Störungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027763828&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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