Boundary control of PDEs: a course on backstepping designs
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, PA
Society for Industrial and Applied Mathematics
2008
|
| Series: | Advances in design and control
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 177-190) and index |
| Physical Description: | X, 192 S. Ill., graph. Darst. 27 cm |
| ISBN: | 9780898716504 0898716500 |
Staff View
MARC
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| 100 | 1 | |a Krstic, Miroslav |d 1964- |e Verfasser |0 (DE-588)118153315 |4 aut | |
| 245 | 1 | 0 | |a Boundary control of PDEs |b a course on backstepping designs |c Miroslav Krstic ; Andrey Smyshlyaev |
| 264 | 1 | |a Philadelphia, PA |b Society for Industrial and Applied Mathematics |c 2008 | |
| 300 | |a X, 192 S. |b Ill., graph. Darst. |c 27 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Advances in design and control |v 16 | |
| 500 | |a Includes bibliographical references (p. 177-190) and index | ||
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 4 | |a Théorie de la commande - Mathématiques | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Boundary layer | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Advances in design and control |v 16 |w (DE-604)BV021715022 |9 16 | |
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Record in the Search Index
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| adam_text | Contents
Preface
Introduction
1
. 1
Boundary Control
............................ 1
.2
Backstepping
............................... 2
.3
A Short List of Existing Books on Control of PDEs
.......... 2
.4
No Model Reduction in This Book
................... 3
.5
Control Objectives for PDE Systems
.................. 3
.6
Classes of PDEs and Benchmark PDEs Dealt with in This Book
.... 3
.7
Choices of Boundary Controls
...................... 4
.8
The Domain Dimension:
1
D, 2D, and
3D
Problems
.......... 5
.9
Observers
................................ 6
.10
Adaptive Control of PDEs
........................ 6
.11
Nonlinear PDEs
............................. 6
.12
Organization of the Book
........................ 6
.13
Why We Don t State Theorems
..................... 8
.14
Focus on Unstable PDEs and Feedback Design Difficulties
...... 9
.15
The Main Idea of Backstepping Control
................ 9
. 16
Emphasis on Problems in One Dimension
............... 11
.17
Unique to This Book: Elements of Adaptive and Nonlinear Designs
for PDEs
................................. 11
1.18
How to Teach from This Book
...................... 11
Lyapunov Stability
13
2.1
A Basic PDE Model
........................... 14
2.2
Lyapunov Analysis for a Heat Equation in Terms
oí
¿.τ
Energy
... 16
2.3
Pointwise-in-Space Boundedness and Stability in Higher Norms
... 19
2.4
Notes and References
.......................... 22
Exercises
..................................... 22
Exact Solutions to PDEs
23
3.1
Separation of Variables
......................... 23
3.2
Notes and References
.......................... 27
Exercises
..................................... 27
v¡
Contents
4
Parabolic PDEs: Reaction-Advection-Diffusion and Other Equations
29
4.1
Backstepping: The Main Idea
...................... 30
4.2
Gain Kernel PDE
............................ 31
4.3
Converting the Gain Kernel PDE into an Integral Equation
...... 33
4.4
Method of Successive Approximations
................. 34
4.5
Inverse
Transformation
......................... 35
4.6
Neumann Actuation
........................... 41
4.7
Reaction-Advection-Diffusion Equation
................ 42
4.8
Reaction-Advection-Diffusion Systems with Spatially Varying
Coefficients
............................... 44
4.9
Other Spatially Causal Plants
...................... 46
4.10
Comparison with ODE Backstepping
.................. 47
4.11
Notes and References
.......................... 50
Exercises
..................................... 50
5
Observer Design
53
5.1
Observer Design for PDEs
........................ 53
5.2
Output Feedback
............................. 56
5.3
Observer Design for Collocated Sensor and Actuator
.......... 57
5.4
Compensator Transfer Function
..................... 60
5.5
Notes and References
.......................... 63
Exercises
..................................... 63
6
Complex-Valued PDEs:
Schrödinger
and Ginzburg-Landau Equations
65
6.1 Schrödinger
Equation
.......................... 65
6.2
Ginzburg-Landau Equation
....................... 67
6.3
Notes and References
.......................... 75
Exercises
..................................... 76
7
Hyperbolic PDEs: Wave Equations
79
7.1
Classical Boundary Damping/Passive Absorber Control
........ 80
7.2
Backstepping Design: A String with One Free End and Actuation on
the Other End
.............................. 83
7.3
Wave Equation with Kelvin-
Voigt
Damping
.............. 85
7.4
Notes and References
.......................... 87
Exercises
..................................... 88
8
Beam Equations
89
8.1
Shear Beam
............................... 91
8.2
Euler-Bernoulli Beam
.......................... 95
8.3
Notes and References
.......................... 101
Exercises
..................................... 105
9
First-Order Hyperbolic PDEs and Delay Equations
109
9.1
First-Order Hyperbolic PDEs
...................... 109
9.2
ODE Systems with Actuator Delay
...................
Ill
9.3
Notes and References
.......................... 113
Exercises
........................ 114
Contents
vii
10 Kuramoto-Sivashinsky, Korteweg-de
Vries,
and Other Exotic
Equations
115
10.1
Kuramoto-Sivashinsky Equation
....................
П6
10.2
Korteweg-de
Vries
Equation
......................117
10.3
Notes and References
..........................118
Exercises
.....................................118
11
Navier-Stokes Equations
119
11.1
Channel Flow PDEs and Their Linearization
.............. 119
11.2
From Physical Space to Wavenumber Space
.............. 121
11.3
Control Design for Orr-Sommerfeld and Squire Subsystems
...... 122
11.4
Notes and References
.......................... 127
Exercises
..................................... 128
12
Motion Planning for PDEs
131
12.1
Trajectory Generation
.......................... 132
12.2
Trajectory Tracking
........................... 139
12.3
Notes and References
.......................... 141
Exercises
..................................... 141
13
Adaptive Control for PDEs
145
13.1
State-Feedback Design with Passive ldentilier
.............146
13.2
Output-Feedback Design with Swapping Identifier
...........151
13.3
Notes and References
..........................157
Exercises
.....................................158
14
Towards Nonlinear PDEs
161
14.1
The Nonlinear Optimal Control Alternative
............... 162
14.2
Feedback Linearization for a Nonlinear PDE: Transformation in Two
Stages
.................................. 163
14.3
PDEs for the Kernels of the Spatial Volterra Series in the Nonlinear
Feedback Operator
............................ 165
14.4
Numerical Results
............................ 167
14.5
What Class of Nonlinear PDEs Can This Approach Be Applied to in
General?
................................. 167
14.6
Notes and References
.......................... 170
Exercise
...................................... 171
Appendix Bessel Functions
173
A.I Bessel Function JH
............................173
A.2 Modified Bessel Function
/„.......................174
Bibliography
177
Index
191
|
| adam_txt |
Contents
Preface
Introduction
1
. 1
Boundary Control
. 1
.2
Backstepping
. 2
.3
A Short List of Existing Books on Control of PDEs
. 2
.4
No Model Reduction in This Book
. 3
.5
Control Objectives for PDE Systems
. 3
.6
Classes of PDEs and Benchmark PDEs Dealt with in This Book
. 3
.7
Choices of Boundary Controls
. 4
.8
The Domain Dimension:
1
D, 2D, and
3D
Problems
. 5
.9
Observers
. 6
.10
Adaptive Control of PDEs
. 6
.11
Nonlinear PDEs
. 6
.12
Organization of the Book
. 6
.13
Why We Don't State Theorems
. 8
.14
Focus on Unstable PDEs and Feedback Design Difficulties
. 9
.15
The Main Idea of Backstepping Control
. 9
. 16
Emphasis on Problems in One Dimension
. 11
.17
Unique to This Book: Elements of Adaptive and Nonlinear Designs
for PDEs
. 11
1.18
How to Teach from This Book
. 11
Lyapunov Stability
13
2.1
A Basic PDE Model
. 14
2.2
Lyapunov Analysis for a Heat Equation in Terms
oí
"'¿.τ
Energy"
. 16
2.3
Pointwise-in-Space Boundedness and Stability in Higher Norms
. 19
2.4
Notes and References
. 22
Exercises
. 22
Exact Solutions to PDEs
23
3.1
Separation of Variables
. 23
3.2
Notes and References
. 27
Exercises
. 27
v¡
Contents
4
Parabolic PDEs: Reaction-Advection-Diffusion and Other Equations
29
4.1
Backstepping: The Main Idea
. 30
4.2
Gain Kernel PDE
. 31
4.3
Converting the Gain Kernel PDE into an Integral Equation
. 33
4.4
Method of Successive Approximations
. 34
4.5
Inverse
Transformation
. 35
4.6
Neumann Actuation
. 41
4.7
Reaction-Advection-Diffusion Equation
. 42
4.8
Reaction-Advection-Diffusion Systems with Spatially Varying
Coefficients
. 44
4.9
Other Spatially Causal Plants
. 46
4.10
Comparison with ODE Backstepping
. 47
4.11
Notes and References
. 50
Exercises
. 50
5
Observer Design
53
5.1
Observer Design for PDEs
. 53
5.2
Output Feedback
. 56
5.3
Observer Design for Collocated Sensor and Actuator
. 57
5.4
Compensator Transfer Function
. 60
5.5
Notes and References
. 63
Exercises
. 63
6
Complex-Valued PDEs:
Schrödinger
and Ginzburg-Landau Equations
65
6.1 Schrödinger
Equation
. 65
6.2
Ginzburg-Landau Equation
. 67
6.3
Notes and References
. 75
Exercises
. 76
7
Hyperbolic PDEs: Wave Equations
79
7.1
Classical Boundary Damping/Passive Absorber Control
. 80
7.2
Backstepping Design: A String with One Free End and Actuation on
the Other End
. 83
7.3
Wave Equation with Kelvin-
Voigt
Damping
. 85
7.4
Notes and References
. 87
Exercises
. 88
8
Beam Equations
89
8.1
Shear Beam
. 91
8.2
Euler-Bernoulli Beam
. 95
8.3
Notes and References
. 101
Exercises
. 105
9
First-Order Hyperbolic PDEs and Delay Equations
109
9.1
First-Order Hyperbolic PDEs
. 109
9.2
ODE Systems with Actuator Delay
.
Ill
9.3
Notes and References
. 113
Exercises
. 114
Contents
vii
10 Kuramoto-Sivashinsky, Korteweg-de
Vries,
and Other "Exotic"
Equations
115
10.1
Kuramoto-Sivashinsky Equation
.
П6
10.2
Korteweg-de
Vries
Equation
.117
10.3
Notes and References
.118
Exercises
.118
11
Navier-Stokes Equations
119
11.1
Channel Flow PDEs and Their Linearization
. 119
11.2
From Physical Space to Wavenumber Space
. 121
11.3
Control Design for Orr-Sommerfeld and Squire Subsystems
. 122
11.4
Notes and References
. 127
Exercises
. 128
12
Motion Planning for PDEs
131
12.1
Trajectory Generation
. 132
12.2
Trajectory Tracking
. 139
12.3
Notes and References
. 141
Exercises
. 141
13
Adaptive Control for PDEs
145
13.1
State-Feedback Design with Passive ldentilier
.146
13.2
Output-Feedback Design with Swapping Identifier
.151
13.3
Notes and References
.157
Exercises
.158
14
Towards Nonlinear PDEs
161
14.1
The Nonlinear Optimal Control Alternative
. 162
14.2
Feedback Linearization for a Nonlinear PDE: Transformation in Two
Stages
. 163
14.3
PDEs for the Kernels of the Spatial Volterra Series in the Nonlinear
Feedback Operator
. 165
14.4
Numerical Results
. 167
14.5
What Class of Nonlinear PDEs Can This Approach Be Applied to in
General?
. 167
14.6
Notes and References
. 170
Exercise
. 171
Appendix Bessel Functions
173
A.I Bessel Function JH
.173
A.2 Modified Bessel Function
/„.174
Bibliography
177
Index
191 |
| any_adam_object | 1 |
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| author | Krstic, Miroslav 1964- Smyshlyaev, Andrey |
| author_GND | (DE-588)118153315 |
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| ctrlnum | (OCoLC)199456142 (DE-599)BVBBV035069742 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV035069742 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:03:44Z |
| indexdate | 2024-07-09T21:21:30Z |
| institution | BVB |
| isbn | 9780898716504 0898716500 |
| language | English |
| lccn | 2008006666 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016738139 |
| oclc_num | 199456142 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-91G DE-BY-TUM DE-703 DE-83 DE-11 DE-739 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-91G DE-BY-TUM DE-703 DE-83 DE-11 DE-739 |
| physical | X, 192 S. Ill., graph. Darst. 27 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | Advances in design and control |
| series2 | Advances in design and control |
| spelling | Krstic, Miroslav 1964- Verfasser (DE-588)118153315 aut Boundary control of PDEs a course on backstepping designs Miroslav Krstic ; Andrey Smyshlyaev Philadelphia, PA Society for Industrial and Applied Mathematics 2008 X, 192 S. Ill., graph. Darst. 27 cm txt rdacontent n rdamedia nc rdacarrier Advances in design and control 16 Includes bibliographical references (p. 177-190) and index Problèmes aux limites Théorie de la commande - Mathématiques Équations aux dérivées partielles Control theory Boundary layer Differential equations, Partial Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Nichtlineare Regelung (DE-588)4132964-8 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Randwertproblem (DE-588)4048395-2 s Kontrolltheorie (DE-588)4032317-1 s Nichtlineare Regelung (DE-588)4132964-8 s DE-604 Smyshlyaev, Andrey Verfasser aut Advances in design and control 16 (DE-604)BV021715022 16 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016738139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krstic, Miroslav 1964- Smyshlyaev, Andrey Boundary control of PDEs a course on backstepping designs Advances in design and control Problèmes aux limites Théorie de la commande - Mathématiques Équations aux dérivées partielles Control theory Boundary layer Differential equations, Partial Kontrolltheorie (DE-588)4032317-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare Regelung (DE-588)4132964-8 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4044779-0 (DE-588)4132964-8 (DE-588)4048395-2 |
| title | Boundary control of PDEs a course on backstepping designs |
| title_auth | Boundary control of PDEs a course on backstepping designs |
| title_exact_search | Boundary control of PDEs a course on backstepping designs |
| title_exact_search_txtP | Boundary control of PDEs a course on backstepping designs |
| title_full | Boundary control of PDEs a course on backstepping designs Miroslav Krstic ; Andrey Smyshlyaev |
| title_fullStr | Boundary control of PDEs a course on backstepping designs Miroslav Krstic ; Andrey Smyshlyaev |
| title_full_unstemmed | Boundary control of PDEs a course on backstepping designs Miroslav Krstic ; Andrey Smyshlyaev |
| title_short | Boundary control of PDEs |
| title_sort | boundary control of pdes a course on backstepping designs |
| title_sub | a course on backstepping designs |
| topic | Problèmes aux limites Théorie de la commande - Mathématiques Équations aux dérivées partielles Control theory Boundary layer Differential equations, Partial Kontrolltheorie (DE-588)4032317-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare Regelung (DE-588)4132964-8 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Problèmes aux limites Théorie de la commande - Mathématiques Équations aux dérivées partielles Control theory Boundary layer Differential equations, Partial Kontrolltheorie Partielle Differentialgleichung Nichtlineare Regelung Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016738139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021715022 |
| work_keys_str_mv | AT krsticmiroslav boundarycontrolofpdesacourseonbacksteppingdesigns AT smyshlyaevandrey boundarycontrolofpdesacourseonbacksteppingdesigns |