Selected works: 4 The mathematical theory of optimal processes
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Gordon and Breach Science Publishers
1986
|
| Schriftenreihe: | Classics of Soviet Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 360 Seiten Illustration |
| ISBN: | 2881240771 |
Internformat
MARC
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| 100 | 1 | |a Pontrjagin, Lev S. |d 1908-1988 |e Verfasser |0 (DE-588)118741489 |4 aut | |
| 240 | 1 | 0 | |a Einheitssacht.: Matematiceskaja teorija optimal 'nych processov |
| 245 | 1 | 0 | |a Selected works |n 4 |p The mathematical theory of optimal processes |c L. S. Pontryagin. Edited by R. V. Gamkrelidze |
| 264 | 1 | |a New York, NY [u.a.] |b Gordon and Breach Science Publishers |c 1986 | |
| 300 | |a XXIII, 360 Seiten |b Illustration | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Classics of Soviet Mathematics | |
| 650 | 4 | |a Dynamische Optimierung - Aufsatzsammlung | |
| 650 | 4 | |a Mathematik - Aufsatzsammlung | |
| 650 | 4 | |a Pontrjagin, Lev S. - Bibliographie | |
| 650 | 4 | |a Topologie - Aufsatzsammlung | |
| 700 | 1 | |a Gamkrelidze, R. V. |d 1927- |e Sonstige |0 (DE-588)174092245 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1817062294768582656 |
|---|---|
| adam_text |
Contents
Editor's Preface xi
Preface to the English Translation xxiii
Introduction 1
Chapter I. The Maximum Principle 9
1. Admissible Controls 9
2. Statement of the Fundamental Problem 11
3. The Maximum Principle 17
4. Discussion of the Maximum Principle 21
5. Examples. The Synthesis Problem 22
6. The Problem with Variable Endpoints and the Trans
versality Conditions 45
7. The Maximum Principle for Non Autonomous Systems . 58
8. Fixed Time Problems 66
9. The Relation of the Maximum Principle to the Method of
Dynamic Programming 69
Chapter II. The Proof of the Maximum Principle 75
10. Admissible Controls 75
11. The Formulation of the Maximum Principle for an Arbi¬
trary Class of Admissible Controls 79
12. The System of Variational Equations and its Adjoint
System 83
13. Variations of Controls and Trajectories 86
14. Fundamental Lemmas 92
15. The Proof of the Maximum Principle 99
16. The Derivation of the Transversality Conditions 108
Chapter III. Linear Time Optimal Processes 115
17. Theorems on the Number of Switchings 115
18. Uniqueness Theorems 123
vii
viii CONTENTS
19. Existence Theorems 127
20. The Synthesis of the Optimal Control 135
21. Examples 140
22. A Simulation of Linear Time Optimal Processes by Means
of Relay Circuits 172
23. Linear Equations with Variable Coefficients 181
Chapter IV. Miscellaneous Problems 189
24. The Case Where the Functional is Given by an Improper
Integral 189
25. Optimal Processes with Parameters 191
26. An Application of the Theory of Optimal Processes to
Problems in the Approximation of Functions 197
27. Optimal Processes with a Delay 213
28. A Pursuit Problem 226
Chapter V. The Maximum Principle and the Calculus of Variations 239
29. The Fundamental Problem of the Calculus of Variations 240
30. The Problem of Lagrange 248
Chapter VI. Optimal Processes with Restricted Phase Coordinates 257
31. Statement of the Problem 258
32. Optimal Trajectories Which Lie on the Boundary of the
Region 264
33. The Proof of Theorem 22 (Fundamental Constructions). 270
34. The Proof of Theorem 22 (Conclusion) 291
35. Some Generalizations 298
36. The Jump Condition 300
37. Statement of the Fundamental Result. Examples 311
Chapter VII. A Statistical Optimal Control Problem 317
38. The Concept of a Markov Process. The Kolmogorov
Differential Equation 318
CONTENTS ix
39. The Precise Statement of the Statistical Problem 322
40. The Reduction of the Evaluation of the Functional / to
the Solution of a Boundary Value Problem for the
Kolmogorov Equation 324
41. The Evaluation of the Functional J in the Case Where the
Kolmogorov Equation has Constant Coefficients . 327
42. The Evaluation of the Functional J in the General Case 348
References 354
Index 357 |
| adam_txt |
Contents
Editor's Preface xi
Preface to the English Translation xxiii
Introduction 1
Chapter I. The Maximum Principle 9
1. Admissible Controls 9
2. Statement of the Fundamental Problem 11
3. The Maximum Principle 17
4. Discussion of the Maximum Principle 21
5. Examples. The Synthesis Problem 22
6. The Problem with Variable Endpoints and the Trans
versality Conditions 45
7. The Maximum Principle for Non Autonomous Systems . 58
8. Fixed Time Problems 66
9. The Relation of the Maximum Principle to the Method of
Dynamic Programming 69
Chapter II. The Proof of the Maximum Principle 75
10. Admissible Controls 75
11. The Formulation of the Maximum Principle for an Arbi¬
trary Class of Admissible Controls 79
12. The System of Variational Equations and its Adjoint
System 83
13. Variations of Controls and Trajectories 86
14. Fundamental Lemmas 92
15. The Proof of the Maximum Principle 99
16. The Derivation of the Transversality Conditions 108
Chapter III. Linear Time Optimal Processes 115
17. Theorems on the Number of Switchings 115
18. Uniqueness Theorems 123
vii
viii CONTENTS
19. Existence Theorems 127
20. The Synthesis of the Optimal Control 135
21. Examples 140
22. A Simulation of Linear Time Optimal Processes by Means
of Relay Circuits 172
23. Linear Equations with Variable Coefficients 181
Chapter IV. Miscellaneous Problems 189
24. The Case Where the Functional is Given by an Improper
Integral 189
25. Optimal Processes with Parameters 191
26. An Application of the Theory of Optimal Processes to
Problems in the Approximation of Functions 197
27. Optimal Processes with a Delay 213
28. A Pursuit Problem 226
Chapter V. The Maximum Principle and the Calculus of Variations 239
29. The Fundamental Problem of the Calculus of Variations 240
30. The Problem of Lagrange 248
Chapter VI. Optimal Processes with Restricted Phase Coordinates 257
31. Statement of the Problem 258
32. Optimal Trajectories Which Lie on the Boundary of the
Region 264
33. The Proof of Theorem 22 (Fundamental Constructions). 270
34. The Proof of Theorem 22 (Conclusion) 291
35. Some Generalizations 298
36. The Jump Condition 300
37. Statement of the Fundamental Result. Examples 311
Chapter VII. A Statistical Optimal Control Problem 317
38. The Concept of a Markov Process. The Kolmogorov
Differential Equation 318
CONTENTS ix
39. The Precise Statement of the Statistical Problem 322
40. The Reduction of the Evaluation of the Functional / to
the Solution of a Boundary Value Problem for the
Kolmogorov Equation 324
41. The Evaluation of the Functional J in the Case Where the
Kolmogorov Equation has Constant Coefficients . 327
42. The Evaluation of the Functional J in the General Case 348
References 354
Index 357 |
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| author | Pontrjagin, Lev S. 1908-1988 |
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| author_sort | Pontrjagin, Lev S. 1908-1988 |
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| dewey-ones | 510 - Mathematics 519 - Probabilities and applied mathematics |
| dewey-raw | 510 519 |
| dewey-search | 510 519 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV022022112 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:12:20Z |
| indexdate | 2024-11-29T13:07:21Z |
| institution | BVB |
| isbn | 2881240771 |
| language | English |
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| owner_facet | DE-706 DE-188 |
| physical | XXIII, 360 Seiten Illustration |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Gordon and Breach Science Publishers |
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| series2 | Classics of Soviet Mathematics |
| spelling | Pontrjagin, Lev S. 1908-1988 Verfasser (DE-588)118741489 aut Einheitssacht.: Matematiceskaja teorija optimal 'nych processov Selected works 4 The mathematical theory of optimal processes L. S. Pontryagin. Edited by R. V. Gamkrelidze New York, NY [u.a.] Gordon and Breach Science Publishers 1986 XXIII, 360 Seiten Illustration txt rdacontent n rdamedia nc rdacarrier Classics of Soviet Mathematics Dynamische Optimierung - Aufsatzsammlung Mathematik - Aufsatzsammlung Pontrjagin, Lev S. - Bibliographie Topologie - Aufsatzsammlung Gamkrelidze, R. V. 1927- Sonstige (DE-588)174092245 oth (DE-604)BV021846411 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015236752&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pontrjagin, Lev S. 1908-1988 Selected works Dynamische Optimierung - Aufsatzsammlung Mathematik - Aufsatzsammlung Pontrjagin, Lev S. - Bibliographie Topologie - Aufsatzsammlung |
| title | Selected works |
| title_alt | Einheitssacht.: Matematiceskaja teorija optimal 'nych processov |
| title_auth | Selected works |
| title_exact_search | Selected works |
| title_exact_search_txtP | Selected works |
| title_full | Selected works 4 The mathematical theory of optimal processes L. S. Pontryagin. Edited by R. V. Gamkrelidze |
| title_fullStr | Selected works 4 The mathematical theory of optimal processes L. S. Pontryagin. Edited by R. V. Gamkrelidze |
| title_full_unstemmed | Selected works 4 The mathematical theory of optimal processes L. S. Pontryagin. Edited by R. V. Gamkrelidze |
| title_short | Selected works |
| title_sort | selected works the mathematical theory of optimal processes |
| topic | Dynamische Optimierung - Aufsatzsammlung Mathematik - Aufsatzsammlung Pontrjagin, Lev S. - Bibliographie Topologie - Aufsatzsammlung |
| topic_facet | Dynamische Optimierung - Aufsatzsammlung Mathematik - Aufsatzsammlung Pontrjagin, Lev S. - Bibliographie Topologie - Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015236752&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021846411 |
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