A primer on the calculus of variations and optimal control theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2009
|
| Series: | Student mathematical library
50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 252 S. Ill., graph. Darst. |
| ISBN: | 9780821847725 |
Staff View
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| 100 | 1 | |a Mesterton-Gibbons, Mike |d 1954- |e Verfasser |0 (DE-588)140077049 |4 aut | |
| 245 | 1 | 0 | |a A primer on the calculus of variations and optimal control theory |c Mike Mesterton-Gibbons |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2009 | |
| 300 | |a XIII, 252 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a Student mathematical library |v 50 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Calculus of variations | |
| 650 | 4 | |a Control theory | |
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Record in the Search Index
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| adam_text | Titel: A primer on the calculus of variations and optimal control theory
Autor: Mesterton-Gibbons, Mike
Jahr: 2009
Contents
Foreword ix
Acknowledgments xiii
Lecture 1. The Brachistochrone 1
Lecture 2. The Fundamental Problem. Extremais 7
Appendix 2: The Fundamental Lemma 15
Lecture 3. The Insufficiency of Extremality 19
Appendix 3: The Principle of Least Action 26
Lecture 4. Important First Integrals 29
Lecture 5. The du Bois-Reymond Equation 35
Appendix 5: Another Fundamental Lemma 40
Lecture 6. The Corner Conditions 41
Lecture 7. Legendre s Necessary Condition 51
Appendix 7: Yet Another Lemma 55
Lecture 8. Jacobi s Necessary Condition 57
Appendix 8: On Solving Jacobi s Equation 65
vii
viii Contents
Lecture 9. Weak Versus Strong Variations 67
Lecture 10. Weierstrass s Necessary Condition 73
Lecture 11. The Transversality Conditions 81
Lecture 12. Hilbert s Invariant Integral 91
Lecture 13. The Fundamental Sufficient Condition 101
Appendix 13: The Equations of an Envelope 108
Lecture 14. Jacobi s Condition Revisited 111
Lecture 15. Isoperimetrical Problems 119
Appendix 15: Constrained Optimization 124
Lecture 16. Optimal Control Problems 127
Lecture 17. Necessary Conditions for Optimality 135
Appendix 17: The Calculus of Variations Revisited 146
Lecture 18. Time-Optimal Control 149
Lecture 19. A Singular Control Problem 159
Lecture 20. A Biological Control Problem 163
Lecture 21. Optimal Control to a General Target 167
Appendix 21: The Invariance of the Hamiltonian 180
Lecture 22. Navigational Control Problems 183
Lecture 23. State Variable Restrictions 195
Lecture 24. Optimal Harvesting 203
Afterword 219
Solutions or Hints for Selected Exercises 221
Bibliography 245
Index 249
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T21:57:56Z |
| institution | BVB |
| isbn | 9780821847725 |
| language | English |
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| physical | XIII, 252 S. Ill., graph. Darst. |
| publishDate | 2009 |
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| spelling | Mesterton-Gibbons, Mike 1954- Verfasser (DE-588)140077049 aut A primer on the calculus of variations and optimal control theory Mike Mesterton-Gibbons Providence, RI American Math. Soc. 2009 XIII, 252 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Student mathematical library 50 Includes bibliographical references and index Calculus of variations Control theory Mathematical optimization Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Variationsrechnung (DE-588)4062355-5 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Student mathematical library 50 (DE-604)BV013184751 50 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018338769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mesterton-Gibbons, Mike 1954- A primer on the calculus of variations and optimal control theory Student mathematical library Calculus of variations Control theory Mathematical optimization Variationsrechnung (DE-588)4062355-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4032317-1 (DE-588)4123623-3 |
| title | A primer on the calculus of variations and optimal control theory |
| title_auth | A primer on the calculus of variations and optimal control theory |
| title_exact_search | A primer on the calculus of variations and optimal control theory |
| title_full | A primer on the calculus of variations and optimal control theory Mike Mesterton-Gibbons |
| title_fullStr | A primer on the calculus of variations and optimal control theory Mike Mesterton-Gibbons |
| title_full_unstemmed | A primer on the calculus of variations and optimal control theory Mike Mesterton-Gibbons |
| title_short | A primer on the calculus of variations and optimal control theory |
| title_sort | a primer on the calculus of variations and optimal control theory |
| topic | Calculus of variations Control theory Mathematical optimization Variationsrechnung (DE-588)4062355-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Calculus of variations Control theory Mathematical optimization Variationsrechnung Kontrolltheorie Lehrbuch |
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