Variational methods in optimum control theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
1968
|
| Schriftenreihe: | Mathematics in science and engineering
45 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 216 S. graph. Darst. |
Internformat
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| 240 | 1 | 0 | |a Variacionnye metody teorii optimal'nogo upravlenija |
| 245 | 1 | 0 | |a Variational methods in optimum control theory |c Iu. P. Petrov |
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1968 | |
| 300 | |a IX, 216 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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Contents
From the Preface to the Russian Edition vii
I. Fundamental Concepts of the Calculus of Variations . 1
1. Functionals 1
2. Admissible Lines. Function Classes 3
3. Nearness of Functions 5
4. Classification of Extremums 6
5. Euler Equation 7
6. Discussion of the Euler Equation 13
7. The Legendre Condition 16
II. Generalizations of the Simplest Problem of Calculus of
Variations 20
8. Problems with Variable Endpoints. General Formula for the Variations 20
9. Transversality Conditions 22
10. Extremals with Breaks. Weierstrass Erdmann Conditions . 24
11. Functionals Dependent on Several Unknown Functions . 27
12. Functionals Dependent on Higher Order Derivatives . 29
13. Conditional Extremum 34
14. Isoperimetric Problem 37
15. General Lagrange Problem. Maier and Bolza Problems. . 41
16. Variational Problems in Parametric Form 43
17. Canonical Form of the Euler Equations 45
18. Extremum of a Functional Dependent on a Function of Several
Variables 46
III. Applying the Euler Equation to the Solution of Engineering
Problems 50
19. Direct Current Electric Motor 50
vii
viii contents
20. Estimate of the Change in a Functional When the Actual Function
Deviates from the Extremal 57
21. Reciprocity Principle; Its Boundedness 61
22. Selection of the Optimum Gear Ratio. Extremals with a Parameter . 65
23. Electric Load Driver with Time Dependent Resistance Moment.
Boundary Conditions at Infinity 72
24. More General Problems of Optimum Control. Electric Drive with a
Resistance Moment Dependent on the Velocity, and a Magnetic Flux
Dependent on the Armature Current 75
IV. Field Theory. Sufficient Conditions for an Extremum. 83
25. Field of Extremals 83
26. Jacobi and Legendre Conditions 85
27. Strong Extremum. Weierstrass Condition 90
28. Summary of Necessary and Sufficient Conditions for an Extremum . 96
29. Degenerate Functional 99
30. The Work of V. F. Krotov 103
V. Extremum Problem with Constraints 115
31. Problems with Constraints in Classical Calculus of Variations . . 115
32. Linear Optimum Control Problems 126
33. The Maximum Principle 133
34. Synthesis of an Optimum Control 138
35. Dynamic Programming 141
36. Nonstandard Functional 144
37. Appropriate Methods of Solution 147
VI. Examples of the Application of Variational Methods . . . 151
38. Optimum Control of DC Electric Motors with Velocity and Armature
Current Constraints 151
39. Control Assuring Minimum Rated Generator Power (Example with
a Nonstandard Functional) 157
40. Control of a Compound with Independent Excitation in the Armature
and Excitation Loops 159
41. Control with a Voltage Constraint 162
42. Determination of the Maximum Allowable Dynamic Effect. . . 166
43. Control of the Excitation of a Synchronous Machine Assuring the
Highest Degree of Stability 170
CONTENTS iX
44. Optimum Control of Locomotive Motion 175
45. Amplitude and Frequency Control of Asynchronous Electric Motors 182
Appendix I: Historical Survey 194
Appendix II: Glossary 201
References 204
Author Index 213
Subject Index 215 |
| any_adam_object | 1 |
| author | Petrov, Jurij P. |
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| id | DE-604.BV004160983 |
| illustrated | Illustrated |
| indexdate | 2024-11-14T15:01:27Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002594797 |
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| physical | IX, 216 S. graph. Darst. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | Acad. Press |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spelling | Petrov, Jurij P. Verfasser (DE-588)135650674 aut Variacionnye metody teorii optimal'nogo upravlenija Variational methods in optimum control theory Iu. P. Petrov New York [u.a.] Acad. Press 1968 IX, 216 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 45 Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Optimierung (DE-588)4043664-0 s Mathematics in science and engineering 45 (DE-604)BV000001196 45 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002594797&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petrov, Jurij P. Variational methods in optimum control theory Mathematics in science and engineering Kontrolltheorie (DE-588)4032317-1 gnd Optimierung (DE-588)4043664-0 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4043664-0 (DE-588)4062355-5 |
| title | Variational methods in optimum control theory |
| title_alt | Variacionnye metody teorii optimal'nogo upravlenija |
| title_auth | Variational methods in optimum control theory |
| title_exact_search | Variational methods in optimum control theory |
| title_full | Variational methods in optimum control theory Iu. P. Petrov |
| title_fullStr | Variational methods in optimum control theory Iu. P. Petrov |
| title_full_unstemmed | Variational methods in optimum control theory Iu. P. Petrov |
| title_short | Variational methods in optimum control theory |
| title_sort | variational methods in optimum control theory |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd Optimierung (DE-588)4043664-0 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Kontrolltheorie Optimierung Variationsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002594797&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001196 |
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