Stochastic optimization methods: applications in engineering and operations research
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2015
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIV, 368 S. graph. Darst. |
| ISBN: | 9783662462133 |
Internformat
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| 245 | 1 | 0 | |a Stochastic optimization methods |b applications in engineering and operations research |c Kurt Marti |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2015 | |
| 300 | |a XXIV, 368 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804152835607101440 |
|---|---|
| adam_text | CONTENTS
1 STOCHASTIC OPTIMIZATION METHODS 1
1.1 INTRODUCTION 1
1.2 DETERMINISTIC SUBSTITUTE PROBLEMS: BASIC FORMULATION 3
1.2.1 MINIMUM OR BOUNDED EXPECTED COSTS 4
1.2.2 MINIMUM OR BOUNDED MAXIMUM COSTS (WORST CASE) 6
1.3 OPTIMAL DECISION/DESIGN PROBLEMS WITH RANDOM PARAMETERS 7
1.4 DETERMINISTIC SUBSTITUTE PROBLEMS IN OPTIMAL DECISION/DESIGN 12
1.4.1 EXPECTED COST OR LOSS FUNCTIONS 13
1.5 BASIC PROPERTIES OF DETERMINISTIC SUBSTITUTE PROBLEMS 16
1.6 APPROXIMATIONS OF DETERMINISTIC SUBSTITUTE PROBLEMS
IN OPTIMAL DESIGN/DECISION 18
1.6.1 APPROXIMATION OF THE LOSS FUNCTION 18
1.6.2 APPROXIMATION OF STATE (PERFORMANCE) FUNCTIONS 21
1.6.3 TAYLOR EXPANSION METHODS 24
1.7 APPROXIMATION OF PROBABILITIES: PROBABILITY INEQUALITIES 28
1.7.1 BONFERRONI-TYPE INEQUALITIES 28
1.7.2 TSCHEBYSCHEFF-TYPE INEQUALITIES 30
2 OPTIMAL CONTROL UNDER STOCHASTIC UNCERTAINTY 37
2.1 STOCHASTIC CONTROL SYSTEMS 37
2.1.1 RANDOM DIFFERENTIAL AND INTEGRAL EQUATIONS 39
2.1.2 OBJECTIVE FUNCTION 45
2.2 CONTROL LAWS 49
2.3 CONVEX APPROXIMATION BY INNER LINEARIZATION 52
2.4 COMPUTATION OF DIRECTIONAL DERIVATIVES 57
2.5 CANONICAL (HAMILTONIAN) SYSTEM OF DIFFERENTIAL
EQUATIONS/TWO-POINT BOUNDARY VALUE PROBLEM 67
2.6 STATIONARY CONTROLS 69
2.7 CANONICAL (HAMILTONIAN) SYSTEM OF DIFFERENTIAL 71
XXI
HTTP://D-NB.INFO/1064179126
XXII CONTENTS
2.8 COMPUTATION OF EXPECTATIONS BY MEANS OF TAYLOR EXPANSIONS 73
2.8.1 COMPLETE TAYLOR EXPANSION 74
2.8.2 INNER OR PARTIAL TAYLOR EXPANSION 75
3 STOCHASTIC OPTIMAL OPEN-LOOP FEEDBACK CONTROL 79
3.1 DYNAMIC STRUCTURAL SYSTEMS UNDER STOCHASTIC UNCERTAINTY 79
3.1.1 STOCHASTIC OPTIMAL STRUCTURAL CONTROL: ACTIVE CONTROL 79
3.1.2 STOCHASTIC OPTIMAL DESIGN OF REGULATORS 81
3.1.3 ROBUST (OPTIMAL) OPEN-LOOP FEEDBACK CONTROL 82
3.1.4 STOCHASTIC OPTIMAL OPEN-LOOP FEEDBACK CONTROL 82
3.2 EXPECTED TOTAL COST FUNCTION 84
3.3 OPEN-LOOP CONTROL PROBLEM ON THE REMAINING TIME
INTERVAL [?/,,?/] 85
3.4 THE STOCHASTIC HAMILTONIAN OF (3.7A-D) 85
3.4.1 EXPECTED HAMILTONIAN (WITH RESPECT TO THE TIME
INTERVAL [TF,
,TJ] AND INFORMATION %
H
) 86
3.4.2 //-MINIMAL CONTROL ON [TH,
TF] 86
3.5 CANONICAL (HAMILTONIAN) SYSTEM 87
3.6 MINIMUM ENERGY CONTROL 88
3.6.1 ENDPOINT CONTROL 89
3.6.2 ENDPOINT CONTROL WITH DIFFERENT COST FUNCTIONS 93
3.6.3 WEIGHTED QUADRATIC TERMINAL COSTS 95
3.7 NONZERO COSTS FOR DISPLACEMENTS 98
3.7.1 QUADRATIC CONTROL AND TERMINAL COSTS 100
3.8 STOCHASTIC WEIGHT MATRIX Q = Q(T,
CO) 103
3.9 UNIFORMLY BOUNDED SETS OF CONTROLS D, ,TO T
TF 107
3.10 APPROXIMATE SOLUTION OF THE TWO-POINT BOUNDARY
VALUE PROBLEM (BVP) 112
3.11 EXAMPLE 115
4 ADAPTIVE OPTIMAL STOCHASTIC TRAJECTORY PLANNING
AND CONTROL (AOSTPC) 119
4.1 INTRODUCTION 119
4.2 OPTIMAL TRAJECTORY PLANNING FOR ROBOTS 121
4.3 PROBLEM TRANSFORMATION 124
4.3.1 TRANSFORMATION OF THE DYNAMIC EQUATION 126
4.3.2 TRANSFORMATION OF THE CONTROL CONSTRAINTS 127
4.3.3 TRANSFORMATION OF THE STATE CONSTRAINTS 128
4.3.4 TRANSFORMATION OF THE OBJECTIVE FUNCTION 129
4.4 OSTP: OPTIMAL STOCHASTIC TRAJECTORY PLANNING 129
4.4.1 COMPUTATIONAL ASPECTS 137
4.4.2 OPTIMAL REFERENCE TRAJECTORY, OPTIMAL
FEEDFORWARD CONTROL 141
CONTENTS XXIII
4.5 AOSTP: ADAPTIVE OPTIMAL STOCHASTIC TRAJECTORY PLANNING 142
4.5.1 (OSTP)-TRANSFORMATION 146
4.5.2 THE REFERENCE VARIATIONAL PROBLEM 148
4.5.3 NUMERICAL SOLUTIONS OF (OSTP) IN REAL-TIME 150
4.6 ONLINE CONTROL CORRECTIONS: PD-CONTROLLER 157
4.6.1 BASIC PROPERTIES OF THE EMBEDDING Q(T, E) 158
4.6.2 THE 1ST ORDER DIFFERENTIAL DQ 161
4.6.3 THE 2ND ORDER DIFFERENTIAL D
2
Q 168
4.6.4 THIRD AND HIGHER ORDER DIFFERENTIALS 172
4.7 ONLINE CONTROL CORRECTIONS: PID CONTROLLERS 173
4.7.1 BASIC PROPERTIES OF THE EMBEDDING Q(T, E) 176
4.7.2 TAYLOR EXPANSION WITH RESPECT TO 177
4.7.3 THE 1 ST ORDER DIFFERENTIAL DQ 178
5 OPTIMAL DESIGN OF REGULATORS 195
5.1 TRACKING ERROR 197
5.1.1 OPTIMAL PD-REGULATOR 198
5.2 PARAMETRIC REGULATOR MODELS 200
5.2.1 LINEAR REGULATOR 200
5.2.2 EXPLICIT REPRESENTATION OF POLYNOMIAL REGULATORS 201
5.2.3 REMARKS TO THE LINEAR REGULATOR 202
5.3 COMPUTATION OF THE EXPECTED TOTAL COSTS OF THE OPTIMAL
REGULATOR DESIGN 203
5.3.1 COMPUTATION OF CONDITIONAL EXPECTATIONS
BY TAYLOR EXPANSION 204
5.3.2 QUADRATIC COST FUNCTIONS 206
5.4 APPROXIMATION OF THE STOCHASTIC REGULATOR OPTIMIZATION
PROBLEM 207
5.4.1 APPROXIMATION OF THE EXPECTED COSTS:
EXPANSIONS OF 1ST ORDER 209
5.5 COMPUTATION OF THE DERIVATIVES OF THE TRACKING ERROR 216
5.5.1 DERIVATIVES WITH RESPECT TO DYNAMIC PARAMETERS
AT STAGE J 217
5.5.2 DERIVATIVES WITH RESPECT TO THE INITIAL VALUES
AT STAGE J 221
5.5.3 SOLUTION OF THE PERTURBATION EQUATION 224
5.6 COMPUTATION OF THE OBJECTIVE FUNCTION 230
5.7 OPTIMAL PID-REGULATOR 233
5.7.1 QUADRATIC COST FUNCTIONS 235
5.7.2 THE APPROXIMATE REGULATOR OPTIMIZATION PROBLEM 250
6 EXPECTED TOTAL COST MINIMUM DESIGN OF PLANE FRAMES 253
6.1 INTRODUCTION 253
6.2 STOCHASTIC LINEAR PROGRAMMING TECHNIQUES 254
6.2.1 LIMIT (COLLAPSE) LOAD ANALYSIS OF STRUCTURES
AS A LINEAR PROGRAMMING PROBLEM 254
6.2.2 PLANE FRAMES 257
XXIV CONTENTS
6.2.3 YIELD CONDITION IN CASE OF M-N-INTERACTION 263
6.2.4 APPROXIMATION OF THE YIELD CONDITION BY USING
REFERENCE CAPACITIES 270
6.2.5 ASYMMETRIC YIELD STRESSES 273
6.2.6 VIOLATION OF THE YIELD CONDITION 279
6.2.7 COST FUNCTION 280
7 STOCHASTIC STRUCTURAL OPTIMIZATION WITH QUADRATIC LOSS FUNCTIONS...
289
7.1 INTRODUCTION 289
7.2 STATE AND COST FUNCTIONS 292
7.2.1 COST FUNCTIONS 296
7.3 MINIMUM EXPECTED QUADRATIC COSTS 299
7.4 DETERMINISTIC SUBSTITUTE PROBLEMS 304
7.4.1 WEIGHT (VOLUME)-MINIMIZATION SUBJECT
TO EXPECTED COST CONSTRAINTS 304
7.4.2 MINIMUM EXPECTED TOTAL COSTS 306
7.5 STOCHASTIC NONLINEAR PROGRAMMING 308
7.5.1 SYMMETRIC, NON UNIFORM YIELD STRESSES 311
7.5.2 NON SYMMETRIC YIELD STRESSES 312
7.6 RELIABILITY ANALYSIS 315
7.7 NUMERICAL EXAMPLE: 12-BAR TRUSS 318
7.7.1 NUMERICAL RESULTS: MEC 320
7.7.2 NUMERICAL RESULTS: ECBO 322
8 MAXIMUM ENTROPY TECHNIQUES 323
8.1 UNCERTAINTY FUNCTIONS BASED ON DECISION PROBLEMS 323
8.1.1 OPTIMAL DECISIONS BASED ON THE TWO-STAGE
HYPOTHESIS FINDING (ESTIMATION) AND DECISION
MAKING PROCEDURE 323
8.1.2 STABILITY/INSTABILITY PROPERTIES 328
8.2 THE GENERALIZED INACCURACY FUNCTION H{X, /3) 331
8.2.1 SPECIAL LOSS SETS V 334
8.2.2 REPRESENTATION OF H
E
(X, /I) AND H(X,
FI)
BY MEANS OF LAGRANGE DUALITY 342
8.3 GENERALIZED DIVERGENCE AND GENERALIZED MINIMUM
DISCRIMINATION INFORMATION 346
8.3.1 GENERALIZED DIVERGENCE 346
8.3.2 /-, ./-PROJECTIONS 352
8.3.3 MINIMUM DISCRIMINATION INFORMATION 353
REFERENCES 357
INDEX
365
|
| any_adam_object | 1 |
| author | Marti, Kurt 1943- |
| author_GND | (DE-588)115845690 |
| author_facet | Marti, Kurt 1943- |
| author_role | aut |
| author_sort | Marti, Kurt 1943- |
| author_variant | k m km |
| building | Verbundindex |
| bvnumber | BV042274523 |
| classification_rvk | QH 424 |
| ctrlnum | (OCoLC)899154319 (DE-599)BVBBV042274523 |
| dewey-full | 330 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330 |
| dewey-search | 330 |
| dewey-sort | 3330 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-10T01:17:02Z |
| institution | BVB |
| isbn | 9783662462133 |
| language | English |
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| physical | XXIV, 368 S. graph. Darst. |
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| spelling | Marti, Kurt 1943- Verfasser (DE-588)115845690 aut Stochastic optimization methods applications in engineering and operations research Kurt Marti 3. ed. Berlin [u.a.] Springer 2015 XXIV, 368 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-662-46214-0 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027712025&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marti, Kurt 1943- Stochastic optimization methods applications in engineering and operations research Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4057625-5 |
| title | Stochastic optimization methods applications in engineering and operations research |
| title_auth | Stochastic optimization methods applications in engineering and operations research |
| title_exact_search | Stochastic optimization methods applications in engineering and operations research |
| title_full | Stochastic optimization methods applications in engineering and operations research Kurt Marti |
| title_fullStr | Stochastic optimization methods applications in engineering and operations research Kurt Marti |
| title_full_unstemmed | Stochastic optimization methods applications in engineering and operations research Kurt Marti |
| title_short | Stochastic optimization methods |
| title_sort | stochastic optimization methods applications in engineering and operations research |
| title_sub | applications in engineering and operations research |
| topic | Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Stochastische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027712025&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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