Control of higher-dimensional PDEs: flatness and backstepping designs
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Communications and control engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIX, 366 S. |
| ISBN: | 9783642300141 9783642435096 |
Internformat
MARC
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| 020 | |a 9783642435096 |c Pb. : EUR 101.60 (DE) (freier Pr.), EUR 104.45 (AT) (freier Pr.), sfr 126.50 (freier Pr.) |9 978-3-642-43509-6 | ||
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| 100 | 1 | |a Meurer, Thomas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Control of higher-dimensional PDEs |b flatness and backstepping designs |c Thomas Meurer |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XIX, 366 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Communications and control engineering | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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Datensatz im Suchindex
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Contents
List of Symbols
.
XV
Part I Introduction and Survey
1
Introduction
.3
1.1
Feedback Stabilization of PDE Systems
. 4
1.2
Trajectory Planning and Tracking Control for PDE Systems
. 6
1.3
Objectives of this Book
. 9
1.4
Outline and Structure
. 11
References
. 13
Part II Modeling and Application Examples
2
Model Equations for Non-Convective and Convective Heat
Transfer
. 23
2.
l
Non—
Convective Heat Transfer
. 23
2.2
Convective Heat Transfer in Single Phase Flow
. 26
2.3
Selected Applications and Control Problems
. 31
2.3.
1 Thermal Battery Management
. 31
2.3.2
Building Climate Control
. 33
2.3.3
Medical Applications
. 34
References
. 34
3
Model Equations for
Multi—
Agent Networks
. 37
3.1
Distributed—Parameter Modeling of Networks of Mobile Agents
. 38
3.1.1
Agent Models
—
Discrete and Continuous Formulations
. . . 38
3.1.2
Communication Topology by Discretization
. 44
3.2
Selected Applications and Control Problems
. 46
3.2.1
Consensus and Stabilization
. 46
3.2.2
Leader-Enabled Formation Deployment
. 47
References
. 48
χ
Contents
4
Model Equations for Flexible Structures with Piezoelectric
Actuation
. 51
4.1
Continuum Mechanical Preliminaries
. 51
4.2
Flexible Plate with Distributed MFC Actuators
. 58
4.2.1
Preparations
. 60
4.2.2
Potential Energy, Kinetic Energy, and Virtual Work
of
Non—
Conservative Forces
. 62
4.2.3
Strong Form of the Equations of Motion
. 66
4.2.4
Weak or Variational form of the Equations of Motion
. 69
4.3
Selected Applications and Control Problems
. 72
4.3.1
Motion Planning and Transient Elastic Shaping
of Structures
. 72
4.3.2
Vibration Suppression and Elastic Motion Tracking
. 73
References
. 74
5
Mathematical Problem Formulation
. 77
5.1
General System Setting
. 77
5.2
Trajectory Planning and Tracking Control
. 79
References
. 80
Part III Trajectory Planning and Feedforward Control
6
Spectral Approach for Time-Invariant Systems with General
Spatial Domain
. 83
6.1
Abstract Formulation and Spectral Analysis
. 85
6.1.1
Admissible Control and Observation Operators
. 86
6.1.2
Abstract Boundary Control Systems
. 87
6.1.3
Bases of Hilbert Spaces, Riesz Bases, and Spectral
Operators
. 91
6.2
Formal Parametrization of Riesz Spectral Systems
. 98
6.2.1
Finite—Dimensional In—Domain and Boundary Control
. 99
6.2.2
Infinite—Dimensional In—Domain and Boundary Control
. 103
6.3
Convergence in Gevrey Classes
.109
6.3.1
Operational Convergence
.110
6.3.2
Convergence of the Parametrized Fourier Series
.115
6.4
Admissible Trajectory Assignment for the Basic Output
.118
6.4.1
Finite Time Transitions between Stationary States
. 118
6.4.2
Finite Time Transitions between
Non—
stationary States
. 123
6.5
Application Examples and Simulation Results
. 127
6.5.
í
Heat and Wave Equation on
1—
Dimensional Domain
.
і
27
6.5.2
Boundary Controlled Linear Diffusion—Reaction
Equation on r—Dimensional Riemannian Manifold
.133
6.5.3
Boundary Controlled Linear
Diffusion—Convection—Reaction Equation
on Parallelepiped Domain
.143
Contents Xl
6.6
Experimental
Validation
for a Flexible Plate with Distributed
MFC Actuators
.166
6.6.
1 Spectral Properties and Spectral System Representation
. 166
6.6.2
Formal State and input Parametrization
.170
6.6.3
Convergence Analysis for Special Plate Configurations
. 171
6.6.4
Semi—Numeric Finite—Dimensional Realization and
Numerical Convergence Indicator
.1 73
6.6.5
Experimental Results for Feedforward and Closed—Loop
Tracking Control
.175
References
.1 85
7
Formal Integration Approach for Time Varying Systems
.189
7.1
Trajectory Planning Problem
.1 90
7.1.1
Transformation into Standard Form
.
і
9
і
7.1.2
Boundary Control Problem
.
І
93
7.2
Formal State and Input Parametrization
.194
7.2.1
Construction of a Basic Output
.1 95
7'.2.2
Uniform Series Convergence in Gevrey Classes
.196
7.3
Admissible Trajectory Assignment for the Basic Output
.204
7.3.1
Stationary Profiles
.704
7.3.2
Admissible Trajectories for the Basic Output
.20:5
7.3.3
Construction of Admissible Trajectories for the Basic
Output
.206
7.4
Extension to Multiple Input Configurations
.210
7.5
Application Examples and Simulation Results
.213
7.5.1
Isotropie
Diffusion and Reaction
.215
7.5.2
Orthotropic Diffusion and Reaction
.216
References
.219
Part IV Feedback Stabilization, Observer Design, and Tracking Control
8
Backstepping for Linear Diffusion—Convection—Reaction Systems
with Varying Parameters on
1—
Dimensional Domains
.223
8.1
Stabilization and Tracking Control Problem
.224
8.2
Exponentially Stabilizing State—Feedback Control
.227
8.2.1
Selection of the Target System
.227
8.2.2
Determination of the Kernel-PDE
.230
8.2.3
Solution of the Kernel-PDE
.,.232
8.2.4
Backstepping—Based State—Feedback Control
{er.240
8.2.5
Inverse? Backstepping—Transformation and Exponential
Stability of the Closed-Loop System
.241
8.3
State—Observer with Exponentially Stable Error Dynamics
.244
8.3.1
Selection of the Target System
.245
8.3.2
Determination of the Kernel—PDE
and the Observer Gains
.246
XII Contents
8.3.3
Solution
of the Kernel-PDE
.248
8.3.4
Inverse
Backstepping—
Transformation and Exponential
Stability of the Observer Error Dynamics
.25 1
8.3.5
Separation Principle and Exponential Stability
of the Closed—Loop System
.253
8.4
Tracking Control Using Backstepping and Differential Flatness
. 255
8.4.1
Flatness—Based Trajectory Planning
.255
8.4.2
Trajectory Assignment in Gevrey Classes Using
the Backstepping Transformation
.258
8.4.3
Combining Backstepping and Differential Flatness
for Exponentially Stabilizing Tracking Control
.260
8.5
Application Examples and Simulation Results
.261
8.5.1
Trajectory Planning
.263
8.5.2
Stabilization and Tracking
.263
References
.266
9
Backstepping for Linear Diffusion—Convection—Reaction Systems
with Varying Parameters on Parallelepiped Domains
.269
9.1
Stabilization and Tracking Control Problem
.270
9.1.1
Transformation into Standard Form
.272
9.1.2
Boundary Control Problem
.273
9.2
Exponentially Stabilizing State—Feedback Control
—
The Single Input Case
.274
9.2.1
Determination of the Kernel—PDE and Selection
of the Target System
.274
9.2.2
Solution of the Kernel-PDE
.279
9.2.3
Backstepping-Based State-Feedback Controller
.280
9.2.4
Inverse Backstepping—Transformation and Exponential
Stability of the Closed-Loop System
.28 1
9.2.5
Approximate Finite—Dimensional Realization of
Backstepping—Based State—Feedback Control
.283
9.3
State—Observer with Exponentially Stable Error Dynamics
—
The Single Output Case
.284
9.3.1
Selection of the Target System
.286
9.3.2
Determination of the Kernel—PDE and the Observer
Gains
.287
9.3.3
Solution of the Kernel-PDE
.289
9.3.4
Inverse Backstepping—Transformation and Exponential
Stability of the Observer Error Dynamics
.290
9.3.5
Separation Principle and Exponential Stability
of the Closed—Loop System
.29 1
9.3.6
Approximate Realization of the State-Observer
by means of Spatial Output Interpolation
.294
9.4
Tracking Control
—
The Single Input and Output Case
.296
Contents
ХШ
9.5
Exponentially Stabilizing State—Feedback Control
—
The
Multiple Input Case
.298
9.5.1
Multi—
linear Backstepping—Transformation
.299
9.5.2
Determination and Solution of the Kernel-PDEs
.300
9.5.3
Backstepping—Based State—Feedback Controller
.303
9.5.4
Inverse
Multi—
linear Backstepping—Transformation and
Exponential Stability of the Closed—Loop System
.305
9.5.5
Approximate Finite—Dimensional Realization of
Backstepping—Based State—Feedback Control
.306
9.6
State—Observer with Exponentially Stable Error Dynamics
—
The Multiple Output Case
.307
9.6.1
Multi—
linear Backstepping—Transformation
.309
9.6.2
Determination of the Kernel-PDEs and the Observer
Gains
.310
9.6.3
Solution of the Kernel-PDEs
.319
9.6.4
Inverse Backstepping—Transformation and Exponential
Stability of the Observer Error Dynamics
.3 19
9.6.5
Separation Principle and Exponential Stability
of the Closed—Loop System
.320
9.6.6
Approximate Realization of the State—Observer
by means of Spatial Output Interpolation
.327
9.7
Tracking Control
—
The Multiple Input and Output Case
.328
9.8
Application Examples and Simulation Results
.329
9.8.1
Exponential Feedback Stabilization and State
Estimation for an Unstable Time Varying
Diffusion—Reaction System
.329
9.8.2
Synchronization of Large Scale
Multi—
Agent Network
.334
References
.346
Part V Appendix
A Notation
.349
A.
1
Einstein Summation Convention
.349
A.
2
Multi-Index Notation
.350
References
.350
В
Mathematical Background
.351
B. I Complex Analysis
.35 1
B.2 Entire Functions
.35?.
B.2.
]
Fundamenta}
Notions
.352
B.2.
2
Weierstrass
Canonical Products and the
Hadamard
Theorem
.354
B.3 Functional Analysis
.356
B.3.
1
Fundamental Notions and Definitions
.356
B.3.
2
Duality and Pivot Spaces
.357
XIV Contents
В.
3.3
The Spaces
Χι
and
Χ^γ
.358
В.
3.4
Sesquiiinear Forms and the Lax—
M
i Igram
Theorem
.359
В.
4
Auxiliary Theorems and Lemmas
.360
References
.360
Index
.363
Communications
and Control Engineering
Thomas Meurer
Control of Higher-Dimensional PDEs
flatness and Backs.tepping Designs
í
his monograph presents new model-based design methods for trajectory planning,
feedback stabilization, stale estimation, and tracking control of distributed-parameter
systems governed by partial differentia! equations (PDEs). Flatness and backstepping
techniques and their generalization to PDEs with higher-dimensional spatial domain
lie at the core of this treatise, 'ibis includes the development of systematic late lumping
design procedures and the deduction of semi numerical approaches using suitable ap¬
proximation methods. Theoretical developments are combined with both simulation
examples and experimental results to bridge the gap between mathematical theory and
control engineering practice in the rapidly evolving
PDĽ
control area.
'flic text is divided into live parts featuring:
•
a literature survey of paradigms and control design methods for PDE systems
•
the first principle mathematical modeling o{ applications arising in heal and mass
transfer, interconnected multi-agent systems, and piezo-actuated smart elastic
structures
•
the generalization of flatness-based trajectory planning and feedforward control to
parabolic and biharmonic PDE systems defined on general higher-dimensional
domains
•
an extension of the baekstepping approach to the feedback control and observer design
for parabolic PDEs with parallelepiped domain and spatially and time varying parameters
•
the development of design techniques to realize exponentially stabilizing tracking
control
•
the evaluation in simulations and experiments
Control of Higher-Dimensional PDEs
—
Flatness and Baekstepping Designs is an ad¬
vanced research monograph for graduate students in applied mathematics, control
theory, and related fields.
Tlie
book may serve as a reference to recent developments
lor researchers and control engineers interested in the analysis and control of systems
governed by PDEs. |
| any_adam_object | 1 |
| author | Meurer, Thomas |
| author_facet | Meurer, Thomas |
| author_role | aut |
| author_sort | Meurer, Thomas |
| author_variant | t m tm |
| building | Verbundindex |
| bvnumber | BV040410365 |
| classification_rvk | SK 540 SK 880 |
| classification_tum | MAT 354f |
| ctrlnum | (OCoLC)812264547 (DE-599)DNB102159847X |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV040410365 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-21T00:09:20Z |
| institution | BVB |
| isbn | 9783642300141 9783642435096 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025263341 |
| oclc_num | 812264547 |
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| owner_facet | DE-384 DE-355 DE-BY-UBR DE-29T DE-739 DE-91 DE-BY-TUM |
| physical | XIX, 366 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Communications and control engineering |
| spelling | Meurer, Thomas Verfasser aut Control of higher-dimensional PDEs flatness and backstepping designs Thomas Meurer Berlin [u.a.] Springer 2013 XIX, 366 S. txt rdacontent n rdamedia nc rdacarrier Communications and control engineering Hier auch später erschienene, unveränderte Nachdrucke Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Kontrolltheorie (DE-588)4032317-1 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4012765&prov=M&dok_var=1&dok_ext=htm Inhaltstext 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=025263341&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=025263341&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Meurer, Thomas Control of higher-dimensional PDEs flatness and backstepping designs Kontrolltheorie (DE-588)4032317-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4044779-0 |
| title | Control of higher-dimensional PDEs flatness and backstepping designs |
| title_auth | Control of higher-dimensional PDEs flatness and backstepping designs |
| title_exact_search | Control of higher-dimensional PDEs flatness and backstepping designs |
| title_full | Control of higher-dimensional PDEs flatness and backstepping designs Thomas Meurer |
| title_fullStr | Control of higher-dimensional PDEs flatness and backstepping designs Thomas Meurer |
| title_full_unstemmed | Control of higher-dimensional PDEs flatness and backstepping designs Thomas Meurer |
| title_short | Control of higher-dimensional PDEs |
| title_sort | control of higher dimensional pdes flatness and backstepping designs |
| title_sub | flatness and backstepping designs |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Kontrolltheorie Partielle Differentialgleichung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4012765&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025263341&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025263341&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT meurerthomas controlofhigherdimensionalpdesflatnessandbacksteppingdesigns |