Numerical methods for distributed parameter port-Hamiltonian systems: structure-preserving approaches for simulation and control
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
München
TUM.University Press
[2019]
|
| Schriftenreihe: | THESES
|
| Schlagworte: | |
| Online-Zugang: | Volltext Inhaltsverzeichnis |
| Beschreibung: | Auf dem Umschlag: Maschinenbau. - Im Vorwort: "This monograph is a slightly edited version of the submitted habilitation". |
| Beschreibung: | xi, 187 Seiten Diagramme |
| ISBN: | 9783958840287 3958840280 |
| DOI: | 10.14459/2019md1510230 |
Internformat
MARC
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| 016 | 7 | |a 1197823387 |2 DE-101 | |
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| 035 | |a (OCoLC)1137812484 | ||
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| 100 | 1 | |a Kotyczka, Paul |d 1979- |e Verfasser |0 (DE-588)143631098 |4 aut | |
| 245 | 1 | 0 | |a Numerical methods for distributed parameter port-Hamiltonian systems |b structure-preserving approaches for simulation and control |c Paul Kotyczka |
| 264 | 1 | |a München |b TUM.University Press |c [2019] | |
| 300 | |a xi, 187 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a THESES | |
| 500 | |a Auf dem Umschlag: Maschinenbau. - Im Vorwort: "This monograph is a slightly edited version of the submitted habilitation". | ||
| 653 | |a Paperback / softback | ||
| 653 | |a Conservation Laws | ||
| 653 | |a Discrete Exterior Calculus | ||
| 653 | |a Discrete-time Systems | ||
| 653 | |a Distributed Parameter Systems | ||
| 653 | |a Feedforward Control | ||
| 653 | |a Flatness-based Control | ||
| 653 | |a Geometric Integration | ||
| 653 | |a Mixed Finite Elements | ||
| 653 | |a Numerical Methods | ||
| 653 | |a Partial Differentail Equations | ||
| 653 | |a Port-Hamiltonian Systems | ||
| 653 | |a Structure-Preserving Discretization | ||
| 653 | |a 2682: Taschenbuch / Technik/Maschinenbau, Fertigungstechnik | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 710 | 2 | |a Universitätsbibliothek (Technische Universität München) |0 (DE-588)2024930-5 |4 pbl | |
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| 912 | |a ebook |a ebook | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-031726718 | ||
Datensatz im Suchindex
| _version_ | 1804180855986323456 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 1
1.1 PORT-HAMILTONIAN MODELING AND CONTROL. 1
1.2 STRUCTURE-PRESERVING DISCRETIZATION. 6
1.3 OBJECTIVES OF THE BOOK. 10
1.4 OUTLINE. 12
2 STRUCTURED REPRESENTATION OF CONSERVATION LAWS 15
2.1 FINITE-DIMENSIONAL PORT-HAMILTONIAN SYSTEMS .. 15
2.1.1 DIRAC STRUCTURES. 15
2.1.2 STATE SPACE REPRESENTATION. . 18
2.2 SYSTEMS OF CONSERVATION LAWS. 19
2.2.1 THE STOKES-DIRAC STRUCTURE. . 20
2.2.2 NON-UNIFORM BOUNDARY CAUSALITY . 22
2.2.3 PORT-HAMILTONIAN REPRESENTATION. 25
2.3 EXAMPLES. 27
2.3.1 WAVE EQUATION. 28
2.3.2 2D SHALLOW WATER EQUATIONS. . 31
2.3.3 HEAT EQUATION. . 34
3 DISCRETE PH FORMULATION OF CONSERVATION LAWS 37
3.1 DISCRETE REPRESENTATION OF CONSERVATION LAWS .. 38
3.2 PRELIMINARIES FROM DISCRETE EXTERIOR CALCULUS. 39
3.2.1 ORIENTED DISCRETIZATION MESH. 39
3.2.2 CELLS, CHAINS AND COCHAINS. 39
3.2.3 BOUNDARY MAPS AND PRIMAL CHAIN COMPLEX. 41
3.2.4 COBOUNDARY MAPS AND COCHAIN COMPLEX . .. 41
3.2.5 TVACE OPERATORS .. 42
3.2.6 THE DUAL N-COMPLEX. 42
3.2.7 DUALITY RELATIONS OF THE CO-INCIDENCE MATRICES. 43
3.3 DISCRETE CONSERVATION LAWS ON N-COMPLEXES. 43
3.3.1 NON-UNIFORM BOUNDARY INPUTS. 43
3.3.2 CONSTRUCTION OF THE DUAL COMPLEXES . .. 44
3.3.3 DISCRETE PH REPRESENTATION. 48
3.4 NUMERICAL APPROXIMATION .. 50
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1197823387
X
CONTENTS
3.4.1 EXAMPLE: IRROTATIONAL 2D SHALLOW WATER EQUATIONS ... 51
3.4.2 FINITE-DIMENSIONAL PORT-HAMILTONIAN MODEL....... 52
3.4.3 REMARKS........................... 56
3.5 CONCLUSIONS ............................. 57
4 MIXED GALERKIN DISCRETIZATION 59
4.1 WEAK FORM OF THE STOKES-DIRAC STRUCTURE .. 61
4.2 APPROXIMATION OF THE STOKES-DIRAC STRUCTURE . . . ...... . 63
4.2.1 WEAK IMPOSITION OF BOUNDARY CONDITIONS. 63
4.2.2 APPROXIMATION PROBLEM AND COMPATIBILITY CONDITION . 64
4.2.3 DISCRETIZED STRUCTURE EQUATIONS .............. 66
4.2.4 DISCRETE BOUNDARY PORT VARIABLES . 68
4.2.5 POWER BALANCE ON THE DISCRETE BOND SPACE ....... 70
4.2.6 DISCRETE CONSERVATION LAWS ................ 71
4.3 POWER-PRESERVING MAPPINGS AND DIRAC STRUCTURE ........ 72
4.3.1 MINIMAL DISCRETE BOND VARIABLES ............. 73
4.3.2 DIRAC STRUCTURE. 74
4.4 FINITE-DIMENSIONAL PORT-HAMILTONIAN MODEL. 75
4.5 WHITNEY FINITE ELEMENTS . 77
4.6 ONE-DIMENSIONAL EXAMPLES .. 78
4.6.1 DISCRETIZATION OF THE STRUCTURE EQUATIONS.. . 79
4.6.2 POWER-PRESERVING MAPPINGS .. 80
4.6.3 CONSTITUTIVE EQUATIONS ................... 81
4.6.4 INTERPRETATION OF THE MAPPING PARAMETER ........ 83
4.6.5 WAVE EQUATION ....................... 84
4.6.6 HEAT EQUATION ....................... 91
4.7 TWO-DIMENSIONAL WAVE EQUATION ................. 98
4.7.1 MESH, MATRICES AND DIMENSIONS . .. 98
4.7.2 POWER-PRESERVING MAPPINGS, DISCRETE IN- AND OUTPUTS . 99
4.7.3 GENERALIZATION TOIVXM MESHES AND REMARKS ..... 107
4.7.4 DISCRETE CONSTITUTIVE EQUATIONS .. . 109
4.7.5 SIMULATION: WAVE PROPAGATION ON A SQUARE. ILL
4.7.6 SIMULATION: DOUBLE SLIT EXPERIMENT ........... 113
4.8 CONCLUSIONS ............................. 114
5 STRUCTURE-PRESERVING TIME DISCRETIZATION 117
5.1 LOSSLESS PORT-HAMILTONIAN SYSTEMS ................ 118
5.2 DISCRETE-TIME PH SYSTEMS BASED ON COLLOCATION ........ 119
5.2.1 COLLOCATION METHOD . .. 119
5.2.2 APPROXIMATION OF FLOW AND STATE VARIABLES ....... 119
5.2.3 EFFORT APPROXIMATION AND STRUCTURE EQUATION ...... 121
5.2.4 DISCRETE-TIME SUPPLIED ENERGY. 122
5.2.5 DISCRETE-TIME DIRAC STRUCTURE .............. 122
5.2.6 DISCRETE-TIME PORT-HAMILTONIAN SYSTEM ......... 124
5.2.7 DISCRETE ENERGY BALANCE .................. 125
CONTENTS
XI
5.3 EXAMPLES AND ANALYSIS OF ENERGY ERRORS. 126
5.3.1 GAUSS-LEGENDRE COLLOCATION. 126
5.3.2 LOBATTO IIIA/IIIB PAIRS. 128
5.4 NUMERICAL EXPERIMENTS. 130
5.4.1 ENERGY SUPPLY AND STORAGE IN THE LOSSLESS CASE .... 131
5.4.2 APPROXIMATION OF DISSIPATED ENERGY .. 132
5.5 CONCLUSIONS. 134
6 PRESERVATION OF FLATNESS AND FEEDFORWARD CONTROL 137
6.1 DEFINITIONS .. 139
6.1.1 CONTINUOUS-TIME SYSTEMS. 139
6.1.2 DISCRETE-TIME SYSTEMS .. 140
6.2 ONE-DIMENSIONAL HEAT EQUATION. 141
6.2.1 FEEDFORWARD CONTROL BASED ON THE PDE MODEL. 142
6.2.2 FEEDFORWARD CONTROL BASED ON THE DISCRETIZATION .... 143
6.2.3 NUMERICAL EXPERIMENTS... 144
6.3 ONE-DIMENSIONAL WAVE EQUATION . 146
6.3.1 SOLUTION OF THE PDE MODEL. 147
6.3.2 SEMI-DISCRETIZATION. 148
6.3.3 FULL DISCRETIZATION.. 149
6.4 NONLINEAR HYPERBOLIC SYSTEMS. 153
6.4.1 CONSISTENTLY DISCRETIZED CONSTITUTIVE EQUATIONS .... 154
6.4.2 DISCRETE-TIME STATE REPRESENTATION. 155
6.4.3 FLATNESS-BASED FEEDFORWARD CONTROL. 155
6.4.4 EXAMPLE: ID SHALLOW WATER EQUATIONS. 156
6.5 CONCLUSIONS. 160
A MATHEMATICAL BACKGROUND 161
A.L EXTERIOR DIFFERENTIAL CALCULUS. 161
A.1.1 SMOOTH DIFFERENTIAL FORMS. 161
A. 1.2 STOKES THEOREM . .. 163
A. 1.3 LEBESGUE AND SOBOLEV SPACES OF DIFFERENTIAL FORMS . . . 163
A. 2 GEOMETRIC NUMERICAL INTEGRATION. 164
B COMPUTATIONS 167
B. L CONSISTENCY OF THE FINITE VOLUME APPROXIMATION. 167
B. 1.1 MODEL IN TERMS OF AVERAGE STATES . 167
B.1.2 COMPUTATIONS OF LOCAL ERRORS.. 168
B.2 TRANSFER FUNCTION OF THE ID HEAT EQUATION. 170
B.3 ID SHALLOW WATER EQUATIONS. 170
B.3.1 STEADY STATE SOLUTION .. 171
B.3.2 FLOW REGIME. 172
BIBLIOGRAPHY
174
|
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| indexdate | 2024-07-10T08:42:24Z |
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| spelling | Kotyczka, Paul 1979- Verfasser (DE-588)143631098 aut Numerical methods for distributed parameter port-Hamiltonian systems structure-preserving approaches for simulation and control Paul Kotyczka München TUM.University Press [2019] xi, 187 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier THESES Auf dem Umschlag: Maschinenbau. - Im Vorwort: "This monograph is a slightly edited version of the submitted habilitation". Paperback / softback Conservation Laws Discrete Exterior Calculus Discrete-time Systems Distributed Parameter Systems Feedforward Control Flatness-based Control Geometric Integration Mixed Finite Elements Numerical Methods Partial Differentail Equations Port-Hamiltonian Systems Structure-Preserving Discretization 2682: Taschenbuch / Technik/Maschinenbau, Fertigungstechnik (DE-588)4113937-9 Hochschulschrift gnd-content Universitätsbibliothek (Technische Universität München) (DE-588)2024930-5 pbl Erscheint auch als Online-Ausgabe 10.14459/2019md1510230 https://doi.org/10.14459/2019md1510230 Verlag kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031726718&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kotyczka, Paul 1979- Numerical methods for distributed parameter port-Hamiltonian systems structure-preserving approaches for simulation and control |
| subject_GND | (DE-588)4113937-9 |
| title | Numerical methods for distributed parameter port-Hamiltonian systems structure-preserving approaches for simulation and control |
| title_auth | Numerical methods for distributed parameter port-Hamiltonian systems structure-preserving approaches for simulation and control |
| title_exact_search | Numerical methods for distributed parameter port-Hamiltonian systems structure-preserving approaches for simulation and control |
| title_full | Numerical methods for distributed parameter port-Hamiltonian systems structure-preserving approaches for simulation and control Paul Kotyczka |
| title_fullStr | Numerical methods for distributed parameter port-Hamiltonian systems structure-preserving approaches for simulation and control Paul Kotyczka |
| title_full_unstemmed | Numerical methods for distributed parameter port-Hamiltonian systems structure-preserving approaches for simulation and control Paul Kotyczka |
| title_short | Numerical methods for distributed parameter port-Hamiltonian systems |
| title_sort | numerical methods for distributed parameter port hamiltonian systems structure preserving approaches for simulation and control |
| title_sub | structure-preserving approaches for simulation and control |
| topic_facet | Hochschulschrift |
| url | https://doi.org/10.14459/2019md1510230 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031726718&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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