Modeling, design, and simulation of systems with uncertainties:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg [u.a.]
Springer
2011
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| Schriftenreihe: | Mathematical engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XX, 354 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783642159558 |
Internformat
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
PART I THEORETIC BACKGROUND AND SOFTWARE IMPLEMENTATION 1 IMPLEMENTING A
RIGOROUS ODE SOLVER THROUGH LITERATE PROGRAMMING 3
NEDIALKO S. NEDIALKOV 1.1 INTRODUCTION 3
1.2 LITERATE PROGRAMMING AND VNODE-LP 5
1.3 OVERVIEW OF VNODE-LP 6
1.3.1 THE IVP VNODE-LP SOLVES 6
1.3.2 METHODS AND PACKAGES 7
1.4 EXAMPLES FROM VNODE-LP 8
1.4.1 COMPUTING H SUCH THAT [0,/I]ACB 9
1.4.2 TRANSLATING EXPRESSIONS 10
1.4.3 INTEGRATING THE LORENZ SYSTEM 11
1.5 RELEVANT WORK 14
1.6 SUMMARY OF EXPERIENCE 16
REFERENCES 17
2 A NEW METHOD FOR INNER ESTIMATION OF SOLUTION SETS TO INTERVAL LINEAR
SYSTEMS 21
SERGEY P. SHARY 2.1 INTRODUCTION 21
2.2 REFINEMENT OF PROBLEM STATEMENT 23
2.3 IDEA OF OUR APPROACH 25
2.4 CHOOSING CENTER OF INNER ESTIMATE 25
2.5 FORMULA FOR SIZE OF INNER ESTIMATE 28
2.6 COMPUTING SIZE OF INNER ESTIMATE 33
2.7 NUMERICAL EXAMPLES 37
2.8 CONCLUSIONS 41
REFERENCES 41
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1005646643
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
3 STRUCTURAL ANALYSIS FOR THE DESIGN OF RELIABLE CONTROLLERS AND STATE
ESTIMATORS FOR CONTINUOUS-TIME DYNAMICAL SYSTEMS WITH UNCERTAINTIES 43
ANDREAS RAUH (^ AND HARALD ASCHEMANN 3.1 INTRODUCTION 44
3.2 DAE FORMULATION OF DYNAMIC SYSTEMS FOR FEEDFORWARD CONTROL AND STATE
ESTIMATION 45
3.2.1 MODELING OF CONTINUOUS-TIME CONTROL OBJECTS 46 3.2.2 DAE
FORMULATION OF TRAJECTORY PLANNING AND TRACKING CONTROL FOR SYSTEMS WITH
CONSISTENT INITIAL CONDITIONS . 46 3.2.3 DAE FORMULATION OF STATE
ESTIMATION TASKS 48 3.2.4 RELATIONS TO SENSITIVITY-BASED PREDICTIVE
CONTROL 49 3.3 VERIFIED SIMULATION OF IVPS IN V A L E N C I A - I VP 52
3.3.1 INITIAL VALUE PROBLEMS FOR SYSTEMS OF ODES 52
3.3.2 INITIAL VALUE PROBLEMS FOR SYSTEMS OF DAES 53
3.4 CONTROL OF A DISTRIBUTED HEATING SYSTEM 55
3.4.1 BASIC EXPERIMENTAL SETUP 55
3.4.2 STRUCTURAL ANALYSIS FOR SPECIFICATION OF FLAT OUTPUTS . . . 57
3.4.3 STRUCTURAL ANALYSIS FOR SPECIFICATION OF NON-FLAT OUTPUTS 58 3.4.4
STRUCTURAL ANALYSIS FOR STATE AND DISTURBANCE ESTIMATION 61 3.5 DYNAMIC
EXTENSIONS FOR FEEDFORWARD CONTROL DESIGN 62
3.5.1 EXAMPLE - MODELINGOFAN AUTONOMOUS ROBOT 62 3.5.2 FEEDFORWARD
CONTROL DESIGN 63
3.6 CONCLUSIONS AND OUTLOOK ON FUTURE RESEARCH 65
REFERENCES 67
4 ANALYZING REACHABILITY OF LINEAR DYNAMIC SYSTEMS WITH PARAMETRIC
UNCERTAINTIES 69
MATTHIAS ALTHOFF 0 S ), BRUCE H. KROGH, AND OLAF STURSBERG 4.1
INTRODUCTION 69
4.2 PROBLEM FORMULATION 71
4.3 OVERAPPROXIMATING THE REACHABLE SET 73
4.3.1 OVERAPPROXIMATING THE STATE TRANSITION MATRIX 73 4.3.2 REACHABLE
SETS OF TIME INTERVALS 75
4.3.3 REACHABLE SET OF THE COMPLETE SYSTEM 75
4.4 OVERAPPROXIMATING THE STATE TRANSITION MATRIX 77
4.4.1 MATRIX ZONOTOPES 78
4.4.2 INTERVAL MATRICES 79
4.4.3 NORM BOUNDS 81
4.4.4 DISCUSSION 81
4.4.5 NUMERICAL EVALUATION OF THE SET OF STATE TRANSITION MATRICES 81
4.5 COMPUTATION OF REACHABLE SETS 86
4.5.1 FIVE-DIMENSIONAL EXAMPLE 86
4.5.2 TRANSMISSION LINE 86
IMAGE 3
CONTENTS XI
4.6 CONCLUSIONS 89
REFERENCES 92
5 ROBUSTNESS COMPARISON OF TRACKING CONTROLLERS USING VERIFIED
INTEGRATION 95
MARCO KLETTING AND FELIX ANTRITTER I 13 ) 5.1 INTRODUCTION 95
5.2 FLATNESS BASED CONTROLLER DESIGN 97
5.2.1 DIFFERENTIAL FLATNESS AND FEEDFORWARD CONTROLLER DESIGN. 97 5.2.2
FLATNESS BASED TRACKING CONTROLLER DESIGN 98 5.2.3 OUTPUT FEEDBACK 100
5.3 MAGNETIC LEVITATION SYSTEM 103
5.4 VERIFIED INTEGRATION BASED ON TAYLOR MODELS 106
5.5 ROBUSTNESS ANALYSIS OF THE TRACKING CONTROLLERS 108
5.6 SIMULATION RESULTS 110
5.7 CONCLUSIONS 113
REFERENCES 114
6 PROBABILISTIC SET-MEMBERSHIP STATE ESTIMATOR 117
LUC JAUL IN 6.1 INTRODUCTION 117
6.2 ROBUST STATE ESTIMATOR 119
6.3 PROBABILISTIC ANALYSIS 120
6.4 APPLICATION TO LOCALIZATION 122
6.5 CONCLUSION 125
REFERENCES 126
7 VERIFIED GLOBAL OPTIMIZATION FOR ESTIMATING THE PARAMETERS OF
NONLINEAR MODELS 129
MICHEL KIEFFER C 3 ), MIHALY CSABA MARKET, HERMANN SCHICHL, AND ERIC
WALTER 7.1 INTRODUCTION 130
7.2 BASICS OF GUARANTEED OPTIMIZATION 131
7.2.1 PROBLEM FORMULATION 131
7.2.2 WHY IS GLOBAL OPTIMIZATION FOR PARAMETER ESTIMATION DIFFICULT? 132
7.2.3 INTERVAL BRANCH-AND-BOUND METHODS 132
7.3 IMPROVING THE EFFICIENCY OF GUARANTEED TECHNIQUES 135 7.3.1 THE PAID
CONSTRAINT PROPAGATOR 135
7.3.2 EXCLUSION AND INCLUSION BOXES 136
7.3.3 METHODS REQUIRING AN EXPLICIT EXPRESSION FOR THE COST FUNCTION 138
7.3.4 WITHOUT EXPLICIT EXPRESSION FOR THE COST FUNCTION 139 7.4 EXAMPLE
141
7.4.1 USING AN EXPLICIT EXPRESSION FOR THE MODEL OUTPUT 143
IMAGE 4
XII CONTENTS
7.4.2 WITHOUT USING AN EXPLICIT EXPRESSION FOR THE MODEL OUTPUT 147
7.5 CONCLUSIONS AND PERSPECTIVES 148
REFERENCES 149
8 OPTIMAL CONTROL OF INDUCTION HEATING: THEORY AND APPLICATION . . .
153 DARYA FILATOVA (^ AND MAREK GRZYWACZEWSKI 8.1 INTRODUCTION 153
8.2 PRECISION INDUCTION HEATING PROBLEM 155
8.3 THE LOCAL MAXIMUM PRINCIPLE 156
8.3.1 PRELIMINARIES 157
8.3.2 THE EULER EQUATION ANALYSIS 157
8.4 THE BANG-BANG CONTROL CASE 164
8.5 AN ILLUSTRATIVE EXAMPLE 167
8.6 CONCLUSIONS 168
APPENDIX 172
REFERENCES 172
9 COHERENT UPPER AND LOWER CONDITIONAL PREVISIONS DEFINED BY HAUSDORFF
OUTER AND INNER MEASURES 175
SERENA DORIA 9.1 INTRODUCTION 175
9.2 SEPARATELY COHERENT UPPER AND LOWER CONDITIONAL PREVISIONS . . .
177 9.3 THE RADON-NIKODYM DERIVATIVE MAY FAIL TO BE COHERENT 179 9.4
COHERENT UPPER CONDITIONAL PREVISIONS DEFINED BY HAUSDORFF OUTER
MEASURES 180
9.4.1 HAUSDORFF OUTER MEASURES 181
9.4.2 THE CHOQUET INTEGRAL 183
9.4.3 A NEW MODEL OF COHERENT UPPER CONDITIONAL PREVISIONS 184 9.4.4
EXACTNESS AND N-MONOTONICITY 186
9.5 UNIQUENESS OF THE REPRESENTING SET FUNCTION FOR A COHERENT UPPER
CONDITIONAL PREVISION 187
9.6 COHERENCE WITH RESPECT TO THE UNCONDITIONAL PREVISION 192 9.7
CONCLUSIONS 193
REFERENCES 1 93
PART II APPLICATIONS: UNCERTAINTIES IN ENGINEERING
10 TWO APPROACHES FOR GUARANTEED STATE ESTIMATION OF NONLINEAR
CONTINUOUS-TIME MODELS 1 99
MARCO KLETTING, MICHEL KIEFFER P), AND ERIC WALTER 10.1 INTRODUCTION
199
10.2 IDEALIZED STATE ESTIMATION 201
10.3 PREDICTION STEP 202
10.3.1 USING MIILLER'S THEOREM 202
10.3.2 VERIFIED INTEGRATION BASED ON TAYLOR MODELS 204
IMAGE 5
CONTENTS XIUE
10.4 CORRECTION STEP 207
10.4.1 USING SET INVERSION VIA INTERVAL ANALYSIS 207 10.4.2 USING
CONTRACTORS 208
10.4.3 USING TAYLOR MODELS 210
10.5 SIMULATION RESULTS 212
10.5.1 RESULTS WITH PREDICTION BASED ON MIILLER'S THEOREM 213 10.5.2
PREDICTION AND CORRECTION INVOLVING TAYLOR MODELS 216 10.6 CONCLUSIONS
AND PERSPECTIVES 218
REFERENCES 218
11 QUANTIFYING SPACECRAFT FAILURE IN AN UNCERTAIN ENVIRONMENT: THE CASE
OF JUPITER EUROPA ORBITER 221
MEHRDAD MOSHIR 11.1 INTRODUCTION 221
11.2 MODEL DESCRIPTION 225
11.3 CHARACTERIZATION OF FLIGHT SYSTEM BY ALEATORY UNCERTAINTIES 228
11.3.1 METHODOLOGY DESCRIPTION FOR A NOTIONAL BOARD 229 11.3.2
METHODOLOGY FOR REDUNDANCY AND COMPONENT CORRELATIONS 231
11.3.3 RADIATION SHIELDING AND HARDNESS CAPABILITY 233 11.3.4 SUBSYSTEM
TID CAPABILITY 235
11.3.5 FLIGHT SYSTEM AND PAYLOAD TID CAPABILITY 237 11.4
CHARACTERIZATION OF THE RADIATION ENVIRONMENT AND EPISTEMLC
UNCERTAINTIES 239
11.4.1 USAGE OF LOGNORMAL DISTRIBUTION FOR RADIATION ENVIRONMENT 240
11.4.2 METHODOLOGY FOR GENERATING CORRELATED IONIZING DOSE TIME SERIES
241
11.5 ESTIMATION OF THE SYSTEM LIFETIME 242
11.6 LIFETIME PROBABILITIES AND EFFECTS OF TEMPORAL CORRELATIONS FOR A
FEW SCENARIOS 245
11.7 CONCLUSIONS 246
REFERENCES 248
12 ROBUST STATE AND PARAMETER ESTIMATION FOR NONLINEAR CONTINUOUS-TIME
SYSTEMS IN A SET-MEMBERSHIP CONTEXT 249 DENIS EFIMOV, TAREK RAISSI ^),
AND ALI ZOLGHADRI 12.1 INTRODUCTION 249
12.2 PROBLEM STATEMENT 251
12.3 PRELIMINARIES 252
12.3.1 MONOTONE SYSTEMS 252
12.3.2 PERSISTENCY OF EXCITATION 253
12.4 INTERVAL PARAMETERS ESTIMATION 254
12.4.1 IDEAL CASE 254
12.4.2 ADAPTIVE SET OBSERVER EQUATIONS 255
12.4.3 COMPETITIVE CASE 256
IMAGE 6
XIV CONTENTS
12.4.4 COOPERATIVE CASE 262
12.5 SET STATE OBSERVER 267
12.6 CONCLUSION 271
REFERENCES 272
13 NONLINEAR ADAPTIVE CONTROL OF A BIOPROCESS MODEL WITH UNKNOWN
KINETICS 275
NELI S. DIMITROVA C 3 ) AND MIKHAIL I. KRASTANOV 13.1 INTRODUCTION 275
13.2 MODEL DESCRIPTION AND PREVIOUS RESULTS 277
13.3 ADAPTIVE ASYMPTOTIC STABILIZATION 278
13.4 EXTREMUM SEEKING 284
13.5 NUMERICAL SIMULATION 285
13.6 CONCLUSION 288
REFERENCES 290
14 VERIFIED ANALYSIS OF A MODEL FOR STANCE STABILIZATION 293 EKATERINA
AUER (^), HAIDER ALBASSAM, ANDRES KECSKEMETHY AND WOLFRAM LUTHER 14.1
INTRODUCTION 294
14.2 BACKGROUND 295
14.2.1 VERIFIED METHODS AND LIBRARIES 295
14.2.2 PIECEWISE CONTINUOUS FUNCTIONS 296
14.2.3 MOBILE AND SMARTMOBILE 297
14.3 A MODEL FOR HUMAN STANCE STABILIZATION 299
14.3.1 TWO-CYLINDER FOOT CONTACT MODEL 300
14.3.2 SIMPLIFIED EXPERIMENTAL SETTINGS 302
14.4 CHARACTERIZING UNCERTAINTIES FOR THE PROBLEM OF STANCE
STABILIZATION 303
14.4.1 IMPLEMENTATION ISSUES 303
14.4.2 INFLUENCE OF UNCERTAIN PARAMETERS ON EQUATIONS OF MOTION 305
14.5 CONCLUSIONS AND OUTLOOK 306
REFERENCES 307
15 ADAPTIVE CONTROL STRATEGIES IN HEAT TRANSFER PROBLEMS WITH PARAMETER
UNCERTAINTIES BASED ON A PROJECTIVE APPROACH 309 VASILY V. SAURIN ( H ),
GEORGY V. KOSTIN, ANDREAS RAUH, AND HARALD ASCHEMANN
15.1 INTRODUCTION 310
15.1.1 VARIATIONAL FORMULATIONS AND PROJECTIVE APPROACHES 310 15.1.2
EARLY VS. LATE LUMPING 311
15.1.3 ADVANCED CONTROL STRATEGIES 312
15.2 MATHEMATICAL STATEMENT OF THE HEAT TRANSFER PROBLEM 313 15.3 A
PROJECTIVE APPROACH BASED ON THE METHOD OF INTEGRODIFFERENTIAL RELATIONS
314
IMAGE 7
CONTENTS XV
15.3.1 INTEGRODIFFERENTIAL FORMULATION OF THE HEAT TRANSFER PROBLEM 314
15.3.2 PROJECTIVE FORMULATION 315
15.4 FINITE ELEMENT DISCRETIZATION 316
15.5 OPTIMAL FEEDFORWARD AND ADAPTIVE CONTROL WITH ONLINE PARAMETER
IDENTIFICATION 318
15.5.1 STATEMENT OF THE CONTROL PROBLEM 318
15.5.2 OPTIMAL FEEDFORWARD CONTROL STRATEGY 318
15.5.3 ADAPTIVE CONTROL ALGORITHM 320
15.6 TEST SETUP AND ACTUAL CONTROL STRUCTURE 322
15.7 NUMERICAL SIMULATION 326
15.8 CONCLUSIONS AND OUTLOOK 330
REFERENCES 330
16 STATE AND DISTURBANCE ESTIMATION FOR ROBUST CONTROL OF FAST FLEXIBLE
RACK FEEDERS 333
HARALD ASCHEMANN (^), DOMINIK SCHINDELE, AND JOERAN RITZKE 16.1
INTRODUCTION 333
16.2 CONTROL-ORIENTED MODELING OF THE MECHATRONIC SYSTEM 335 16.3
DECENTRALIZED CONTROL DESIGN 339
16.4 STATE AND DISTURBANCE OBSERVER DESIGN 343
16.5 PARAMETER IDENTIFICATION 345
16.6 EXPERIMENTAL VALIDATION ON THE TEST RIG 346
16.7 CONCLUSIONS 349
REFERENCES 350
NOTATION 353 |
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| id | DE-604.BV042077574 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T01:47:56Z |
| institution | BVB |
| isbn | 9783642159558 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027518702 |
| oclc_num | 752131981 |
| open_access_boolean | |
| owner | DE-706 |
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| physical | XX, 354 S. Ill., graph. Darst. 24 cm |
| publishDate | 2011 |
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| publisher | Springer |
| record_format | marc |
| series2 | Mathematical engineering |
| spelling | Modeling, design, and simulation of systems with uncertainties Andreas Rauh ... eds. Berlin ; Heidelberg [u.a.] Springer 2011 XX, 354 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Mathematical engineering Literaturangaben Engineering mathematics Uncertainty (Information theory) Systementwurf (DE-588)4261480-6 gnd rswk-swf Unsicherheit (DE-588)4186957-6 gnd rswk-swf Technisches System (DE-588)4126276-1 gnd rswk-swf Technisches System (DE-588)4126276-1 s Unsicherheit (DE-588)4186957-6 s Systementwurf (DE-588)4261480-6 s DE-604 Rauh, Andreas edt Erscheint auch als Online-Ausgabe Modeling, Design, and Simulation of Systems with Uncertainties X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3523444&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027518702&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Modeling, design, and simulation of systems with uncertainties Engineering mathematics Uncertainty (Information theory) Systementwurf (DE-588)4261480-6 gnd Unsicherheit (DE-588)4186957-6 gnd Technisches System (DE-588)4126276-1 gnd |
| subject_GND | (DE-588)4261480-6 (DE-588)4186957-6 (DE-588)4126276-1 |
| title | Modeling, design, and simulation of systems with uncertainties |
| title_auth | Modeling, design, and simulation of systems with uncertainties |
| title_exact_search | Modeling, design, and simulation of systems with uncertainties |
| title_full | Modeling, design, and simulation of systems with uncertainties Andreas Rauh ... eds. |
| title_fullStr | Modeling, design, and simulation of systems with uncertainties Andreas Rauh ... eds. |
| title_full_unstemmed | Modeling, design, and simulation of systems with uncertainties Andreas Rauh ... eds. |
| title_short | Modeling, design, and simulation of systems with uncertainties |
| title_sort | modeling design and simulation of systems with uncertainties |
| topic | Engineering mathematics Uncertainty (Information theory) Systementwurf (DE-588)4261480-6 gnd Unsicherheit (DE-588)4186957-6 gnd Technisches System (DE-588)4126276-1 gnd |
| topic_facet | Engineering mathematics Uncertainty (Information theory) Systementwurf Unsicherheit Technisches System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3523444&prov=M&dok%5Fvar=1&dok%5Fext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027518702&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rauhandreas modelingdesignandsimulationofsystemswithuncertainties |