Applied interval analysis: with examples in parameter and state estimation, robust control and robotics
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
London [u.a.]
Springer
2001
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke, CD-ROM und Begleith. u.d.T.: Forte developer 6 CD-ROM-Beil. u.d.T.: Forte developer 6 |
| Physical Description: | XVI, 379 S. Ill., graph. Darst. 1 CD-ROM (12 cm); 1 Begleith. (19 S.) |
| ISBN: | 1852332190 9781447110675 9781447102496 |
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Record in the Search Index
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| adam_text | IMAGE 1
LUC JAULIN, MICHEL KIEFFER, OLIVIER DIDRIT
AND ERIC WALTER
APPLIED
INTERVAL ANALYSIS WITH EXAMPLES IN PARAMETER AND STATE ESTIMATION,
ROBUST CONTROL AND ROBOTICS WITH 125 FIGURES
IMAGE 2
CONTENTS
PREFACE V
NOTATION XIII
PART I. INTRODUCTION
1. INTRODUCTION 3
1.1 WHAT ARE THE KEY CONCEPTS? 4
1.2 HOW DID THE STORY START? 4
1.3 WHAT ABOUT COMPLEXITY? 5
1.4 HOW IS THE BOOK ORGANIZED? 6
PART II. TOOLS
2. INTERVAL ANALYSIS 11
2.1 INTRODUCTION 11
2.2 OPERATIONS ON SETS 11
2.2.1 PURELY SET-THEORETIC OPERATIONS 11
2.2.2 EXTENDED OPERATIONS 12
2.2.3 PROPERTIES OF SET OPERATORS 13
2.2.4 WRAPPERS 15
2.3 INTERVAL ANALYSIS 17
2.3.1 INTERVALS 18
2.3.2 INTERVAL COMPUTATION 19
2.3.3 CLOSED INTERVALS 20
2.3.4 INTERVAL VECTORS 23
2.3.5 INTERVAL MATRICES 25
2.4 INCLUSION FUNCTIONS 27
2.4.1 DEFINITIONS 27
2.4.2 NATURAL INCLUSION FUNCTIONS 29
2.4.3 CENTRED INCLUSION FUNCTIONS 33
2.4.4 MIXED CENTRED INCLUSION FUNCTIONS 34
IMAGE 3
VIII CONTENTS
2.4.5 TAYLOR INCLUSION FUNCTIONS 35
2.4.6 COMPARISON 35
2.5 INCLUSION TESTS 38
2.5.1 INTERVAL BOOLEANS 38
2.5.2 TESTS 40
2.5.3 INCLUSION TESTS FOR SETS 42
2.6 CONCLUSIONS 42
3. SUBPAVINGS 45
3.1 INTRODUCTION 45
3.2 SET TOPOLOGY 46
3.2.1 DISTANCES BETWEEN COMPACT SETS 46
3.2.2 ENCLOSURE OF COMPACT SETS BETWEEN SUBPAVINGS 48
3.3 REGULAER SUBPAVINGS 49
3.3.1 PAVINGS AND SUBPAVINGS 50
3.3.2 REPRESENTING A REGULAER SUBPAVING AS A BINARY TREE 51
3.3.3 BASIC OPERATIONS ON REGULAER SUBPAVINGS 52
3.4 IMPLEMENTATION OF SET COMPUTATION 54
3.4.1 SET INVERSION 55
3.4.2 IMAGE EVALUATION 59
3.5 CONCLUSIONS 63
4. CONTRACTORS 65
4.1 INTRODUCTION 65
4.2 BASIC CONTRACTORS 67
4.2.1 FINITE SUBSOLVERS 67
4.2.2 INTERVALIZATION OF FINITE SUBSOLVERS 69
4.2.3 FIXED-POINT METHODS 72
4.2.4 FORWARD-BACKWARD PROPAGATION 77
4.2.5 LINEAR PROGRAMMING APPROACH 81
4.3 EXTERNAL APPROXIMATION 82
4.3.1 PRINCIPLE 83
4.3.2 PRECONDITIONING 84
4.3.3 NEWTON CONTRACTOR 86
4.3.4 PARALLEL LINEARIZATION 87
4.3.5 USING FORMAL TRANSFORMATIONS 88
4.4 COLLABORATION BETWEEN CONTRACTORS 90
4.4.1 PRINCIPLE 90
4.4.2 CONTRACTORS AND INCLUSION FUNCTIONS 95
4.5 CONTRACTORS FOR SETS 97
4.5.1 DEFMITIONS 97
4.5.2 SETS DEFINED BY EQUALITY AND INEQUALITY CONSTRAINTS 99
4.5.3 IMPROVING CONTRACTORS USING LOCAL SEARCH 99
4.6 CONCLUSIONS 100
IMAGE 4
CONTENTS IX
5. SOLVERS 103
5.1 INTRODUCTION 103
5.2 SOLVING SQUARE SYSTEMS OF NON-LINEAR EQUATIONS 104
5.3 CHARACTERIZING SETS DEFINED BY INEQUALITIES 106
5.4 INTERVAL HUELL OF A SET DEFINED BY INEQUALITIES 111
5.4.1 FIRST APPROACH 112
5.4.2 SECOND APPROACH 113
5.5 GLOBAL OPTIMIZATION 117
5.5.1 THE MOORE-SKELBOE ALGORITHM 120
5.5.2 HANSEN S ALGORITHM 121
5.5.3 USING INTERVAL CONSTRAINT PROPAGATION 125
5.6 MINIMAX OPTIMIZATION 126
5.6.1 UNCONSTRAINED CASE 127
5.6.2 CONSTRAINED CASE 131
5.6.3 DEALING WITH QUANTIFIERS 133
5.7 COST CONTOURS 135
5.8 CONCLUSIONS 136
PART III. APPLICATIONS
6. ESTIMATION 141
6.1 INTRODUCTION 141
6.2 PARAMETER ESTIMATION VIA OPTIMIZATION 144
6.2.1 LEAST-SQUARE PARAMETER ESTIMATION IN COMPARTMENTAL MODELLING 145
6.2.2 MINIMAX PARAMETER ESTIMATION 148
6.3 PARAMETER BOUNDING 155
6.3.1 INTRODUCTION 155
6.3.2 THE VALUES OF THE INDEPENDENT VARIABLES ARE KNOWN 158
6.3.3 ROBUSTIFICATION AGAINST OUTLIERS 160
6.3.4 THE VALUES OF THE INDEPENDENT VARIABLES ARE UNCERTAIN .. 164 6.3.5
COMPUTATION OF THE INTERVAL HUELL OF THE POSTERIOR FEASIBLE SET 167
6.4 STATE BOUNDING 168
6.4.1 INTRODUCTION 168
6.4.2 BOUNDING THE INITIAL STATE 171
6.4.3 BOUNDING ALL VARIABLES 171
6.4.4 BOUNDING BY CONSTRAINT PROPAGATION 174
6.5 CONCLUSIONS 184
7. ROBUST CONTROL 187
7.1 INTRODUCTION 187
7.2 STABILITY OF DETERMINISTIC LINEAR SYSTEMS 188
7.2.1 CHARACTERISTIC POLYNOMIAL 189
IMAGE 5
X CONTENTS
7.2.2 ROUTH CRITERION 189
7.2.3 STABILITY DEGREE 190
7.3 BASIC TESTS FOR ROBUST STABILITY 193
7.3.1 INTERVAL POLYNOMIALS 195
7.3.2 POLYTOPE POLYNOMIALS 196
7.3.3 IMAGE-SET POLYNOMIALS 196
7.3.4 CONCLUSION 198
7.4 ROBUST STABILITY ANALYSIS 198
7.4.1 STABILITY DOMAINS 198
7.4.2 STABILITY DEGREE 201
7.4.3 VALUE-SET APPROACH 205
7.4.4 ROBUST STABILITY MARGINS 211
7.4.5 STABILITY RADIUS 216
7.5 CONTROLLER DESIGN 220
7.6 CONCLUSIONS 223
8. ROBOTICS 225
8.1 INTRODUCTION 225
8.2 FORWARD KINEMATICS PROBLEM FOR STEWART-GOUGH PLATFORMS . . 226 8.2.1
STEWART-GOUGH PLATFORMS 226
8.2.2 FROM THE FRAME OF THE MOBILE PLATE TO THAT OF THE BASE . 227 8.2.3
EQUATIONS TO BE SOLVED 229
8.2.4 SOLUTION 230
8.3 PATH PLANNING 234
8.3.1 GRAPH DISCRETIZATION OF CONFIGURATION SPACE 237
8.3.2 ALGORITHMS FOR FINDING A FEASIBLE PATH 239
8.3.3 TEST CASE 241
8.4 LOCALIZATION AND TRACKING OF A MOBILE ROBOT 248
8.4.1 FORMULATION OF THE STATIC LOCALIZATION PROBLEM 249
8.4.2 MODEL OF THE MEASUREMENT PROCESS 253
8.4.3 SET INVERSION 257
8.4.4 DEALING WITH OUTLIERS 259
8.4.5 STATIC LOCALIZATION EXAMPLE 260
8.4.6 TRACKING 263
8.4.7 EXAMPLE 264
8.5 CONCLUSIONS 267
PART IV. IMPLEMENTATION
9. AUTOMATIC DIFFERENTIATION 271
9.1 INTRODUCTION 271
9.2 FORWARD AND BACKWARD DIFFERENTIATIONS 271
9.2.1 FORWARD DIFFERENTIATION 272
9.2.2 BACKWARD DIFFERENTIATION 273
IMAGE 6
CONTENTS XI
9.3 DIFFERENTIATION OF ALGORITHMS 275
9.3.1 FIRST ASSUMPTION 275
9.3.2 SECOND ASSUMPTION 278
9.3.3 THIRD ASSUMPTION 279
9.4 EXAMPLES 281
9.4.1 EXAMPLE 1 281
9.4.2 EXAMPLE 2 284
9.5 CONCLUSIONS 285
10. GUARANTEED COMPUTATION WITH FLOATING-POINT NUMBERS . . 287 10.1
INTRODUCTION 287
10.2 FLOATING-POINT NUMBERS AND IEEE 754 287
10.2.1 REPRESENTATION 288
10.2.2 ROUNDING 289
10.2.3 SPECIAL QUANTITIES 291
10.3 INTERVALS AND IEEE 754 292
10.3.1 MACHINE INTERVALS 293
10.3.2 CLOSED INTERVAL ARITHMETIC 294
10.3.3 HANDLING ELEMENTARY FUNCTIONS 295
10.3.4 IMPROVEMENTS 297
10.4 INTERVAL RESOURCES 297
10.5 CONCLUSIONS 299
11. DO IT YOURSELF 301
11.1 INTRODUCTION 301
11.2 NOTIONS OF C ++ 301
11.2.1 PROGRAM STRUCTURE 302
11.2.2 STANDARD TYPES 303
11.2.3 POINTERS 304
11.2.4 PASSING PARAMETERS TO A FUNCTION 304
11.3 INTERVAL CLASS 305
11.3.1 CONSTRUCTORS AND DESTRUCTOR 307
11.3.2 OTHER MEMBER FUNCTIONS 308
11.3.3 MATHEMATICAL FUNCTIONS 313
11.4 INTERVALS WITH PROFIL/BIAS 315
11.4.1 BIAS 315
11.4.2 PROFIL 316
11.4.3 GETTING STARTED 317
11.5 EXERCISES ON INTERVALS 318
11.6 INTERVAL VECTORS 319
11.6.1 INTERVAL_VECT0R CLASS 320
11.6.2 CONSTRUCTORS, ASSIGNMENT AND FUNCTION CALL OPERATORS . . . 321
11.6.3 FRIEND FUNCTIONS 323
11.6.4 UTILITIES 325
11.7 VECTORS WITH PROFIL/BIAS 326
IMAGE 7
XII CONTENTS
11.8 EXERCISES ON INTERVAL VECTORS 327
11.9 INTERVAL MATRICES 331
11.10 MATRICES WITH PROFIL/BIAS 332
11.11 EXERCISES ON INTERVAL MATRICES 333
11.12 REGULAER SUBPAVINGS WITH PROFIL/BIAS 336
11.12.1 NODE CLASS 336
11.12.2 SET INVERSION WITH SUBPAVINGS 339
11.12.3 IMAGE EVALUATION WITH SUBPAVINGS 342
11.12.4 SYSTEM SIMULATION AND STATE ESTIMATION WITH SUBPAVINGS 347 11.13
ERROR HANDLING 349
11.13.1 USING E X IT 349
11.13.2 EXCEPTION HANDLING 350
11.13.3 MATHEMATICAL ERRORS 351
REFERENCES 353
INDEX 373
|
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| indexdate | 2024-07-09T18:50:14Z |
| institution | BVB |
| isbn | 1852332190 9781447110675 9781447102496 |
| language | English |
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| physical | XVI, 379 S. Ill., graph. Darst. 1 CD-ROM (12 cm); 1 Begleith. (19 S.) |
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| spelling | Applied interval analysis with examples in parameter and state estimation, robust control and robotics Luc Jaulin ... Forte developer 6 London [u.a.] Springer 2001 XVI, 379 S. Ill., graph. Darst. 1 CD-ROM (12 cm); 1 Begleith. (19 S.) txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke, CD-ROM und Begleith. u.d.T.: Forte developer 6 CD-ROM-Beil. u.d.T.: Forte developer 6 Interval analysis (Mathematics) Intervallanalyse (DE-588)4162150-5 gnd rswk-swf Intervallmathematik (DE-588)4130580-2 gnd rswk-swf Intervallanalyse (DE-588)4162150-5 s DE-604 Intervallmathematik (DE-588)4130580-2 s Jaulin, Luc Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009352860&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Applied interval analysis with examples in parameter and state estimation, robust control and robotics Interval analysis (Mathematics) Intervallanalyse (DE-588)4162150-5 gnd Intervallmathematik (DE-588)4130580-2 gnd |
| subject_GND | (DE-588)4162150-5 (DE-588)4130580-2 |
| title | Applied interval analysis with examples in parameter and state estimation, robust control and robotics |
| title_alt | Forte developer 6 |
| title_auth | Applied interval analysis with examples in parameter and state estimation, robust control and robotics |
| title_exact_search | Applied interval analysis with examples in parameter and state estimation, robust control and robotics |
| title_full | Applied interval analysis with examples in parameter and state estimation, robust control and robotics Luc Jaulin ... |
| title_fullStr | Applied interval analysis with examples in parameter and state estimation, robust control and robotics Luc Jaulin ... |
| title_full_unstemmed | Applied interval analysis with examples in parameter and state estimation, robust control and robotics Luc Jaulin ... |
| title_short | Applied interval analysis |
| title_sort | applied interval analysis with examples in parameter and state estimation robust control and robotics |
| title_sub | with examples in parameter and state estimation, robust control and robotics |
| topic | Interval analysis (Mathematics) Intervallanalyse (DE-588)4162150-5 gnd Intervallmathematik (DE-588)4130580-2 gnd |
| topic_facet | Interval analysis (Mathematics) Intervallanalyse Intervallmathematik |
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