Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Aachen
Shaker
2013
|
| Series: | Berichte aus der Verfahrenstechnik
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 193 S. graph. Darst. |
| ISBN: | 9783844016352 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
CONTENTS
1. I N T R O D U C T I O N 1
2. T H E O R Y O F C O N T I N U O U S SENSITIVITY ANALYSIS 3
2.1. INTRODUCTION 3
2.2. CONTINUOUS FORWARD SENSITIVITY EQUATIONS 6
2.3. CONTINUOUS ADJOINT EQUATIONS 8
2.3.1. ADJOINT EQUATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS 8
2.3.2. ADJOINTS FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS 13
2.3.3. COMPOSITE ADJOINTS 15
2.3.4. COMPOSITE ADJOINTS A N D STIELTJES INTEGRATION 19
2.3.5. ADJOINTS OF HIGHER ORDER 19
2.4. SENSITIVITY ANALYSIS FOR NON-SMOOTH SYSTEMS 21
2.4.1. FORWARD SENSITIVITY ANALYSIS 2 3
2.4.2. HIGHER-ORDER FORWARD SENSITIVITY ANALYSIS 25
2.4.3. ADJOINT SENSITIVITY ANALYSIS 27
2.4.4. HIGHER ORDER NON-SMOOTH ADJOINTS 3 3
2.4.5. ILLUSTRATIVE CASE STUDY 33
2.5. SUMMARY A N D DISCUSSION 36
3. O P T I M A L C O N T R O L 3 9
3.1. INTRODUCTION 39
3.2. OPTIMAL CONTROL WITH ORDINARY DIFFERENTIAL EQUATIONS 42
3.2.1. PROBLEM FORMULATION 4 3
3.2.2. RESTRICTIONS T O T H E PROBLEM FORMULATION 44
3.3. NECESSARY CONDITIONS OF OPTIMALITY FOR OPTIMAL CONTROL WITH O D E
CONSTRAINTS 45
3.3.1. PRELIMINARIES 45
3.3.2. GLOBAL ASSUMPTIONS 46
VII
HTTP://D-NB.INFO/1029387060
IMAGE 2
CONTENTS
3.3.3. T H E MINIMUM PRINCIPLE 47
3.4. OPTIMAL CONTROL WITH DIFFERENTIAL-ALGEBRAIC EQUATIONS 51
3.4.1. VOLATILE A N D NON-VOLATILE ALGEBRAIC VARIABLES 51
3.4.2. RESTRICTIONS T O T H E PROBLEM FORMULATION 53
3.4.3. CANONICAL DAE-CONSTRAINED OPTIMAL CONTROL PROBLEM 53
3.5. NECESSARY CONDITIONS OF OPTIMALITY FOR OPTIMAL CONTROL WITH D A E
CONSTRAINTS 54
3.5.1. REFORMULATION AS A N ODE-CONSTRAINED PROBLEM 55
3.5.2. HAMILTONIAN A N D ALTERNATIVE HAMILTONIAN 56
3.5.3. N C O FOR DAE-CONSTRAINED OPTIMAL CONTROL PROBLEMS 58
3.5.4. INTERPRETATION OF ADJOINTS 60
3.6. DIRECT SINGLE SHOOTING 61
3.6.1. PARAMETRIZATION OF T H E CONTROL VECTOR 61
3.6.2. HANDLING OF T H E P A T H CONSTRAINTS 62
3.6.3. T H E NONLINEAR PROGRAMMING PROBLEM 63
3.6.4. T H E KARUSH-KUHN-TUCKER CONDITIONS 64
3.7. COMPOSITE ADJOINTS 64
3.7.1. CHARACTERIZATION OF COMPOSITE ADJOINTS 65
3.7.2. GRADIENT COMPUTATION OF T H E LAGRANGIAN 67
3.7.3. INTERPRETATION OF COMPOSITE ADJOINTS 68
3.8. CONVERGENCE RELATIONS 69
3.8.1. MULTIPLIERS ASSOCIATED WITH T H E CONTROL BOUNDS 69
3.8.2. GENERAL CONVERGENCE RELATIONS 70
3.9. VERIFICATION OF ADAPTIVE DIRECT SINGLE SHOOTING 76
3.9.1. CHECK OF WEAK-STAR CONVERGENCE BY TEST FUNCTIONS 76
3.9.2. APPROXIMATION OF SWITCHING FUNCTIONS 77
3.9.3. A NOVEL STOPPING CRITERION FOR ADAPTIVE REFINEMENT 78
3.9.4. A N IMPROVED ADAPTIVE SHOOTING ALGORITHM 79
3.9.5. SCALABILITY 79
3.10. ILLUSTRATIVE CASE S T U D Y 80
3.10.1. BACKGROUND OF T H E OPTIMAL CONTROL PROBLEM 80
3.10.2. T H E TRUE SOLUTION 81
3.10.3. SEQUENCE OF DIRECT SINGLE SHOOTING SOLUTIONS 8 3
3.10.4. MULTIPLIER FUNCTION OF T H E P A T H CONSTRAINT 86
3.11. SUMMARY A N D DISCUSSION 88
4. NUMERICAL M E T H O D S FOR SENSITIVITY ANALYSIS 9 1
4.1. INTRODUCTION 91
VIII
IMAGE 3
CONTENTS
4.2. A SHORT EXCURSION T O ALGORITHMIC DIFFERENTIATION 92
4.2.1. TERMINOLOGY 93
4.2.2. FORWARD A N D REVERSE MODE BY M A T R I X MULTIPLICATION 94
4.2.3. COMPONENT-WISE FORWARD A N D REVERSE MODE 98
4.2.4. INTERPRETATION OF ADJOINTS AS LAGRANGE MULTIPLIERS 102
4.2.5. LAGRANGIAN APPROACH FOR T H E DERIVATION OF DISCRETE ADJOINTS . .
102
4.3. FORWARD SENSITIVITY ANALYSIS BY ONE-STEP EXTRAPOLATION 103
4.3.1. S T A T E INTEGRATION 103
4.3.2. DISCRETIZATION APPLIED T O SENSITIVITY EQUATIONS 104
4.3.3. MODIFICATIONS T O INCREASE T H E COMPUTATIONAL EFFICIENCY 105
4.4. ADJOINT SENSITIVITY ANALYSIS BY ONE-STEP EXTRAPOLATION 106
4.4.1. DISCRETE ADJOINTS FOR T H E LINEARLY-IMPLICIT EULER M E T H O D .
. . . 106
4.4.2. MODIFICATIONS T O DISCRETE ADJOINTS 108
4.4.3. MODIFIED DISCRETE ADJOINTS - T H E GENERAL CASE 110
4.4.4. REMARKS ON EXTRAPOLATION, COMPOSITE ADJOINTS A N D HIGHER
ORDER DERIVATIVES I L L
4.4.5. CONSISTENCY OF DISCRETE A N D CONTINUOUS ADJOINTS 112
4.4.6. COMPARISON OF CONTINUOUS A N D DISCRETE ADJOINTS BY EXAMPLE . 113
4.4.7. DISCRETE ADJOINTS W I T H FINAL NEWTON CORRECTION STEP 116
4.4.8. RECONCILIATION OF DISCRETE A N D CONTINUOUS ALGEBRAIC ADJOINTS .
118
4.4.9. CHOOSING FINAL CONDITIONS FOR DISCRETE ADJOINTS 119
4.4.10. DISCRETE ADJOINTS FOR NON-SMOOTH SYSTEMS 121
4.5. NIXE - A SOLVER FOR MODIFIED DISCRETE ADJOINTS 123
4.5.1. IMPLEMENTATION DETAILS 123
4.5.2. PERFORMANCE 126
4.5.3. N I X E VERSUS IDAS 127
4.5.4. COMPARISON W I T H BLACK BOX ALGORITHMIC DIFFERENTIATION 130
4.6. SUMMARY A N D DISCUSSION 132
5. A C - S A M M M 1 3 5
5.1. INTRODUCTION 135
5.2. SKETCH OF T H E AC-SAMMM INFRASTRUCTURE 136
5.2.1. DIFFERENT LAYERS OF A N AC-SAMMM APPLICATION 137
5.2.2. WORKFLOW 138
5.3. DETAILS OF AC-SAMMM 138
5.3.1. T H E E Q U A T I O N SET O B J E C T 139
5.3.2. T H E M E T A E S O 141
5.3.3. N I X E DRIVER FOR SENSITIVITY ANALYSIS 142
IX
IMAGE 4
CONTENTS
*5.4. DETERMINATION OF VOLATILE VARIABLES 143
5.4.1. A N ALGORITHM T O DETERMINE VOLATILE VARIABLES 143
5.4.2. VOLATILE VARIABLES IN T H E P O L Y TEST PROBLEM 145
5.5. S U M M A R Y A N D DISCUSSION 146
6. S U M M A R Y A N D O U T L O O K 147
6.1. S U M M A R Y A N D CONTRIBUTIONS OF THIS WORK 147
6.2. OUTLOOK T O FUTURE RESEARCH DIRECTIONS 149
A. M A T H E M A T I C A L PRELIMINARIES 1 5 1
A . L . MEASURE A N D INTEGRATION THEORY 151
A.1.1. T H E R I E M A N N INTEGRAL 151
A.1.2. T H E LEBESGUE INTEGRAL 153
A. 1.3. MEASURABLE FUNCTIONS 154
A.1.4. EXTENSIONS OF T H E LEBESGUE INTEGRAL 157
A.1.5. T H E LEBESGUE-STIELTJES INTEGRAL 157
A. 1.6. T H E RIEMANN-STIELTJES INTEGRAL 158
A.1.7. PROPERTIES OF STIELTJES INTEGRALS 159
A.2. SPACE OF ESSENTIALLY BOUNDED FUNCTIONS 160
A.3. SOBOLEV SPACE OF ABSOLUTELY CONTINUOUS FUNCTIONS 162
A.4. FUNCTIONS OF BOUNDED VARIATION 163
A.5. NECESSARY CONDITIONS OF OPTIMALITY FOR NONLINEAR PROGRAMS 164
A.6. NECESSARY CONDITIONS OF OPTIMALITY FOR NONLINEAR PROGRAMS IN BANACH
SPACES 166
A.6.1. BASICS FROM FUNCTIONAL ANALYSIS 166
A.6.2. OPTIMIZATION IN BANACH SPACES 172
B. ADJOINTS - M O D E L P A R A M E T E R S A S INITIAL VALUES 1 7 5
C. T E S T P R O B L E M S 1 7 7
C . L . R E A K - CHEMICAL REACTION KINETICS 177
C.2. TANK - HEAT STORAGE T A N K 178
C.3. P O L Y - LARGE-SCALE INDUSTRIAL POLYMERIZATION PROCESS 179
X
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV040928794 |
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| indexdate | 2024-07-10T00:35:34Z |
| institution | BVB |
| isbn | 9783844016352 |
| language | English |
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| publishDate | 2013 |
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| spelling | Hannemann-Tamás, Ralf 1975- Verfasser (DE-588)1030592772 aut Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations Ralf Hannemann-Tamás Aachen Shaker 2013 XX, 193 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Verfahrenstechnik Zugl.: Aachen, Techn. Hochsch., Diss., 2012 Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Sensitivitätsanalyse (DE-588)4129730-1 gnd rswk-swf Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s Optimale Kontrolle (DE-588)4121428-6 s Sensitivitätsanalyse (DE-588)4129730-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025907780&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hannemann-Tamás, Ralf 1975- Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations Optimale Kontrolle (DE-588)4121428-6 gnd Sensitivitätsanalyse (DE-588)4129730-1 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4129730-1 (DE-588)4229517-8 (DE-588)4113937-9 |
| title | Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations |
| title_auth | Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations |
| title_exact_search | Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations |
| title_full | Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations Ralf Hannemann-Tamás |
| title_fullStr | Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations Ralf Hannemann-Tamás |
| title_full_unstemmed | Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations Ralf Hannemann-Tamás |
| title_short | Adjoint Sensitivity Analysis for Optimal Control of Non-Smooth Differential-Algebraic Equations |
| title_sort | adjoint sensitivity analysis for optimal control of non smooth differential algebraic equations |
| topic | Optimale Kontrolle (DE-588)4121428-6 gnd Sensitivitätsanalyse (DE-588)4129730-1 gnd Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd |
| topic_facet | Optimale Kontrolle Sensitivitätsanalyse Differential-algebraisches Gleichungssystem Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025907780&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hannemanntamasralf adjointsensitivityanalysisforoptimalcontrolofnonsmoothdifferentialalgebraicequations |