Inverse problems for ordinary differential equations: dynamical solutions
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Basel
Gordon and Breach
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 625 S. graph. Darst. |
| ISBN: | 2881249442 |
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MARC
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| 100 | 1 | |a Osipov, Jurij Sergeevič |d 1936- |e Verfasser |0 (DE-588)139804943 |4 aut | |
| 245 | 1 | 0 | |a Inverse problems for ordinary differential equations |b dynamical solutions |c Yu. S. Osipov ; A. V. Kryazhimskii |
| 264 | 1 | |a Basel |b Gordon and Breach |c 1995 | |
| 300 | |a XX, 625 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
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| 700 | 1 | |a Kryazhimskii, A. V. |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007317238 | ||
Record in the Search Index
| _version_ | 1804125428487553024 |
|---|---|
| adam_text | Contents
Preface xv
Basic Notations xix
Chapter 1. Motion Approximation 1
1. Example 1
1.1. Problem description 1
1.2. Motion equations 2
1.3. A way to designing a solution algorithm 4
1.4. Solution algorithm 6
1.5. Algorithm as a control process 11
2. Problem Formulations 13
2.1. Dynamical system with disturbance (informal dis¬
cussion) 13
2.2. Disturbances and motions 14
2.3. Preliminary problem formulation 15
2.4. Positional algorithms (informal description) 16
2.5. Positional algorithms (definitions) 18
2.6. Dynamical algorithms 19
2.7. Stable and uniformly stable families of algorithms.
Problems of dynamical motion approximation 20
2.8. c Optimal and asymptotically optimal families 22
vi CONTENTS
3. Stability Conditions 23
3.1. Condition necessary for a stable family to exist 23
3.2. Necessary existence condition for stable family of
dynamical algorithms 24
3.3. Comparing of conditions 26
4. Uniform Stability Conditions 35
4.1. Existence criterion for uniformly stable family of
algorithms 35
4.2. Necessary existence conditions for uniformly stable
family of dynamical algorithms 39
4.3. Conditions comparison 43
4.4. Existence criterion for uniformly stable families of
dynamical and positional algorithms 48
4.5. Systems with closed sets of motions 54
Comments 56
Chapter 2. Nondegenerate Systems 57
5. Stable Motion Approximation 57
5.1. Assumptions. Representation of the t/ reconstruc
tion operator 57
5.2. A way to solving the problem (informal discussion) 60
5.3. Approximation of unobserved motions by 5 moti
ons 61
5.4. Difference approximation (informal discussion) 64
5.5. Stable families: (^ projected difference approxima¬
tion and difference approximation 64
5.6. Extremal shift 71
5.7. Coordinate shift 77
5.8. Stable families: (^ regularized and regularized ex¬
tremal shift 82
5.9. Stable family: locally regularized extremal shift 93
6. Uniformly Stable Motion Approximation 100
6.1. System affine in disturbance 100
6.2. Existence of a uniformly stable family 104
CONTENTS vii
6.3. Uniform approximation of unobserved motions by
5 motions 107
6.4. ^ Projected difference approximation and diffe¬
rence approximation families 110
6.5. Extremal shift and coordinate shift families 114
6.6. Local extremal shift and local coordinate shift fa¬
milies 117
6.7. Families with modified models 118
7. Upper Accuracy Bounds 120
7.1. Assumptions. Notations 120
7.2. Deviation of 6 motion from the unobserved one:
upper bound 121
7.3. ^ Projected difference approximation and diffe¬
rence approximation families 139
7.4. Extremal shift and coordinate shift families 146
7.5. Local coordinate shift and extremal shift families 152
7.6. Numerical examples 158
8. c Optimality conditions 167
8.1. Plan of analysis 167
8.2. Lower bounds for unimprovable accuracy 168
8.3. c Optimality 176
9. Calculation of Optimality Coefficients.
Asymptotical Optimality 178
9.1. Assumptions 178
9.2. Implicit accuracy bounds for three c optimal fami¬
lies 183
9.3. Increment of unobserved motion: differential 191
9.4. Upper differential of flooCO at zero 204
9.5. Differential of fi(/i) and Qoo(/i) at zero 213
9.6. Calculation of optimality coefficients. Asymptoti¬
cal optimality 229
Comments 234
viii CONTENTS
Chapter 3. Degenerate and Combined
Systems 235
10. y Degenerate System 235
10.1. Assumptions. Notations 235
10.2. Euler family. An upper accuracy bound 236
10.3. Calculation of optimality coefficient. Asymptoti¬
cal optimality 240
11. z Degenerate System 261
11.1. Assumptions 261
11.2. Algebraic inversion family. An upper accuracy
bound 262
11.3. c Optimality conditions 265
11.4. Particular case: dynamical approximation of Lip
schitz derivative 271
12. Combined System 281
12.1. Informal discussion 281
12.2. Assumptions. Representation of the y reconst
ruction operator 285
12.3. Additional assumptions. 5 Motions 291
12.4. Approximation of unobserved motions by ^ mo¬
tions 295
12.5. Stable families 302
12.6. System affine in disturbance. A uniformly stable
family 306
Comments 311
Chapter 4. Strong Motion Approximation 313
13. Problem Formulations 313
13.1. Strong motion approximation problems 313
13.2. Solvability conditions 315
CONTENTS ix
14. Stable and Uniformly Stable Strong
Approximation 318
14.1. Nondegenerate system: stable strong approxima¬
tion 318
14.2. Nondegenerate system: uniformly stable strong
approximation 319
14.3. y Degenerate system 328
14.4. 2 Degenerate system 329
14.5. Combined system: remarks 334
15. Optimal Accuracy Orders 334
15.1. Nondegenerate system: assumptions 335
15.2. Difference approximation family: an upper accu¬
racy bound 336
15.3. Difference approximation family: a lower accura¬
cy bound and optimal accuracy order 339
15.4. Regularized extremal shift family: an upper accu¬
racy bound 349
15.5. Regularized extremal shift family: a lower accu¬
racy bound and optimal accuracy order 357
15.6. Optimal accuracy order in the class of all admis¬
sible algorithms 369
15.7. y Degenerate system 376
15.8. z Degenerate system 379
Comments 382
Chapter 5. Disturbance Approximation 383
16. Problem Formulations. Nonsolvability Examples 383
16.1. Stable families of algorithms 383
16.2. Positional algorithms. Problem formulations 388
16.3. Case of complete information 390
16.4. Weakly ^ stable and ^ stable families: a non
existence example 391
16.5. Compactly stable family: a nonexistence example 395
x CONTENTS
17. Stable Approximation 400
17.1. Relaxed disturbances 400
17.2. Difference approximation and regularized extre¬
mal shift 403
17.3. Inner extremal shift 407
17.4. Nondegenerate system 411
17.5. y Degenerate system 414
17.6. z Degenerate system 415
18. ^ Stable and Weakly ^ Stable Approximation 416
18.1. Regularized differences 416
18.2. Inner shift: discrepancy regularization 426
18.3. Inner shift: smoothing regularization 430
18.4. Nondegenerate system 435
18.5. y Degenerate system 438
18.6. z Degenerate system 441
18.7. Numerical examples 445
19. Uniformly Stable Approximation 450
19.1. Uniformly stable families of algorithms. Problem
formulations 450
19.2. Solvability conditions 452
19.3. Uniformly stable family: case of complete infor¬
mation 463
19.4. Uniformly stable families: nondegenerate system 468
19.5. Uniformly stable families: y degenerate system 469
19.6. Uniformly stable families: z degenerate system 470
19.7. Uniformly ^ stable families: case of complete
information 470
19.8. Uniformly ^ stable families: nondegenerate sys¬
tem 477
19.9. Uniformly ^ stable families: y degenerate system 478
19.10. Uniformly ^ stable families: z degenerate system 478
Comments 479
CONTENTS xi
Chapter 6. Dynamical Set Approximation 481
20. Disturbance Set Approximation 481
20.1. Problem formulation 482
20.2. Affine system: equivalent problem formulation,
link to weak ^ stability 484
20.3. Case of complete information 490
20.4. Particular case of complete information: finite
dimensional solution 496
20.5. j/ Degenerate system 498
20.6. z Degenerate system 499
20.7. Problem nonsolvability for nonaffine system 500
20.8. Uniform Hausdorff stability: general remarks 501
20.9. Uniform Hausdorff stability: affine system 502
21. Motion Set Approximation 506
21.1. Assumptions. Hausdorff stable families 507
21.2. Upper stability. Positional algorithms 514
21.3. Solution 518
21.4. Remarks on uniform HausdorfF stability 528
21.5. Generalized problem 529
22. Process Set Approximation 531
22.1. Assumptions. Stability types 531
22.2. Positional algorithms 536
22.3. Hausdorff semi stable and HausdorfF stable fa¬
milies 539
22.4. Mosco stable family 543
22.5. Generally Mosco stable family 548
Comments 550
Chapter 7. Dynamical Approximation and
Feedback Control 553
23. Tracking Controlled Motions 553
23.1. Informal discussion 554
23.2. Controls, disturbances and motions 554
xii CONTENTS
23.3. z Control algorithms 556
23.4. Control problems. Unimprovability of z control
algorithms 558
23.5. Stable families of x control algorithms 561
23.6. Generalized z control algorithms. Tracking fa¬
milies 563
23.7. a; Control algorithms. Tracking problem 566
23.8. Solution pattern 569
23.9. Nondegenerate affine system 572
23.10. i/ Degenerate system 577
23.11. 2 Degenerate system 578
23.12. Numerical example 578
24. Tracking Counter Controlled Motions 581
24.1. Asumptions. Counter strategies 581
24.2. Stable families of counter strategies 582
24.3. Case of complete information: counter control
algorithms, problem formulation, solution pat¬
tern 586
24.4. Case of complete information: solutions 591
24.5. Case of incomplete information: problem formu¬
lation, solution pattern 597
24.6. Nondegenerate affine system 599
24.7. t/ Degenerate system 601
24.8. z Degenerate system 602
24.9. Numerical example 604
Comments 607
Bibliography 609
Subject Index 621
|
| any_adam_object | 1 |
| author | Osipov, Jurij Sergeevič 1936- Kryazhimskii, A. V. |
| author_GND | (DE-588)139804943 |
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| physical | XX, 625 S. graph. Darst. |
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| spelling | Osipov, Jurij Sergeevič 1936- Verfasser (DE-588)139804943 aut Inverse problems for ordinary differential equations dynamical solutions Yu. S. Osipov ; A. V. Kryazhimskii Basel Gordon and Breach 1995 XX, 625 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential equations Numerical solutions Inverse problems (Differential equations) Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Kryazhimskii, A. V. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007317238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Osipov, Jurij Sergeevič 1936- Kryazhimskii, A. V. Inverse problems for ordinary differential equations dynamical solutions Differential equations Numerical solutions Inverse problems (Differential equations) Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 |
| title | Inverse problems for ordinary differential equations dynamical solutions |
| title_auth | Inverse problems for ordinary differential equations dynamical solutions |
| title_exact_search | Inverse problems for ordinary differential equations dynamical solutions |
| title_full | Inverse problems for ordinary differential equations dynamical solutions Yu. S. Osipov ; A. V. Kryazhimskii |
| title_fullStr | Inverse problems for ordinary differential equations dynamical solutions Yu. S. Osipov ; A. V. Kryazhimskii |
| title_full_unstemmed | Inverse problems for ordinary differential equations dynamical solutions Yu. S. Osipov ; A. V. Kryazhimskii |
| title_short | Inverse problems for ordinary differential equations |
| title_sort | inverse problems for ordinary differential equations dynamical solutions |
| title_sub | dynamical solutions |
| topic | Differential equations Numerical solutions Inverse problems (Differential equations) Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differential equations Numerical solutions Inverse problems (Differential equations) Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007317238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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