Control of higher–dimensional PDEs: flatness and backstepping designs
<p>This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to...
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Format: | Elektronisch E-Book |
Sprache: | English |
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Berlin [u.a.]
Springer
2013
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Schriftenreihe: | Communications and control engineering
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Online-Zugang: | BTU01 FHA01 FHI01 FHN01 FHR01 FKE01 FWS01 UBY01 Volltext Inhaltsverzeichnis Abstract |
Zusammenfassung: | <p>This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation 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 PDE control area.</p><p>The text is divided into five parts featuring:</p><p><p>- a literature survey of paradigms and control design methods for PDE systems</p><p>- the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures</p><p>- the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains</p><p>- an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters</p><p>- the development of design techniques to realize exponentially stabilizing tracking control</p><p>- the evaluation in simulations and experiments</p><p><i>Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs </i>is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.</p> |
Beschreibung: | <p>Model equations for multi–agent networks -- Model equations for flexible structures with piezoelectric actuation -- Mathematical problem formulation -- Spectral approach for time–invariant systems with general spatial domain -- Formal integration approach for time varying systems -- Backstepping for linear diffusion–convection–reaction systems with varying parameters on 1–dimensional domains -- Backstepping for linear diffusion–convection–reaction systems with varying parameters on parallelepiped domains.</p> |
Beschreibung: | 1 Online-Ressource (XX, 368 p. 53 illus) |
ISBN: | 9783642300158 |
DOI: | 10.1007/978-3-642-30015-8 |
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adam_text | CONTROL OF HIGHER–DIMENSIONAL PDES
/ MEURER, THOMAS
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
MODEL EQUATIONS FOR MULTI–AGENT NETWORKS
MODEL EQUATIONS FOR FLEXIBLE STRUCTURES WITH PIEZOELECTRIC ACTUATION
MATHEMATICAL PROBLEM FORMULATION
SPECTRAL APPROACH FOR TIME–INVARIANT SYSTEMS WITH GENERAL SPATIAL
DOMAIN
FORMAL INTEGRATION APPROACH FOR TIME VARYING SYSTEMS
BACKSTEPPING FOR LINEAR DIFFUSION–CONVECTION–REACTION SYSTEMS WITH
VARYING PARAMETERS ON 1–DIMENSIONAL DOMAINS
BACKSTEPPING FOR LINEAR DIFFUSION–CONVECTION–REACTION SYSTEMS WITH
VARYING PARAMETERS ON PARALLELEPIPED DOMAINS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
CONTROL OF HIGHER–DIMENSIONAL PDES
/ MEURER, THOMAS
: 2013
ABSTRACT / INHALTSTEXT
THIS MONOGRAPH PRESENTS NEW MODEL-BASED DESIGN METHODS FOR TRAJECTORY
PLANNING, FEEDBACK STABILIZATION, STATE ESTIMATION, AND TRACKING CONTROL
OF DISTRIBUTED-PARAMETER SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL
EQUATIONS (PDES). FLATNESS AND BACKSTEPPING TECHNIQUES AND THEIR
GENERALIZATION TO PDES WITH HIGHER-DIMENSIONAL SPATIAL DOMAIN LIE AT THE
CORE OF THIS TREATISE. THIS INCLUDES THE DEVELOPMENT OF SYSTEMATIC LATE
LUMPING DESIGN PROCEDURES AND THE DEDUCTION OF SEMI-NUMERICAL APPROACHES
USING SUITABLE APPROXIMATION 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 PDE CONTROL AREA. THE TEXT IS DIVIDED
INTO FIVE PARTS FEATURING: - A LITERATURE SURVEY OF PARADIGMS AND
CONTROL DESIGN METHODS FOR PDE SYSTEMS -THE FIRST PRINCIPLE
MATHEMATICAL MODELING OF APPLICATIONS ARISING IN HEAT 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
BACKSTEPPING 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 BACKSTEPPING DESIGNS IS AN ADVANCED RESEARCH MONOGRAPH FOR
GRADUATE STUDENTS IN APPLIED MATHEMATICS, CONTROL THEORY, AND RELATED
FIELDS. THE BOOK MAY SERVE AS A REFERENCE TO RECENT DEVELOPMENTS FOR
RESEARCHERS AND CONTROL ENGINEERS INTERESTED IN THE ANALYSIS AND CONTROL
OF SYSTEMS GOVERNED BY PDES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
any_adam_object | 1 |
author | Meurer, Thomas |
author_facet | Meurer, Thomas |
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discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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id | DE-604.BV040806087 |
illustrated | Not Illustrated |
indexdate | 2024-08-01T16:14:46Z |
institution | BVB |
isbn | 9783642300158 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025786086 |
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physical | 1 Online-Ressource (XX, 368 p. 53 illus) |
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publishDate | 2013 |
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spellingShingle | Meurer, Thomas Control of higher–dimensional PDEs flatness and backstepping designs Ingenieurwissenschaften Engineering Systems theory Partielle Differentialgleichung (DE-588)4044779-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
subject_GND | (DE-588)4044779-0 (DE-588)4032317-1 |
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 | Ingenieurwissenschaften Engineering Systems theory Partielle Differentialgleichung (DE-588)4044779-0 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
topic_facet | Ingenieurwissenschaften Engineering Systems theory Partielle Differentialgleichung Kontrolltheorie |
url | https://doi.org/10.1007/978-3-642-30015-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025786086&sequence=000001&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=025786086&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT meurerthomas controlofhigherdimensionalpdesflatnessandbacksteppingdesigns |