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The Calculus of Variations and Optimal Control : An Introduction - George Leitmann
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The Calculus of Variations and Optimal Control : An Introduction - Livres de poche

2013

ISBN: 1489903356

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Leitmann, George:
The Calculus of Variations and Optimal Control An Introduction - Livres de poche

2013, ISBN: 1489903356

Softcover reprint of the original 1st ed. 1981 Kartoniert / Broschiert Maschinenbau, optimalcalculus; differentialequation; extrema; Optimization, mit Schutzumschlag 11, [PU:Springer US]

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The Calculus of Variations and Optimal Control: An Introduction George Leitmann Author

When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

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EAN (ISBN-13): 9781489903358
ISBN (ISBN-10): 1489903356
Version reliée
Livre de poche
Date de parution: 2013
Editeur: Springer US Core >1

Livre dans la base de données depuis 2014-03-11T15:22:06+01:00 (Paris)
Page de détail modifiée en dernier sur 2024-03-16T18:18:30+01:00 (Paris)
ISBN/EAN: 9781489903358

ISBN - Autres types d'écriture:
1-4899-0335-6, 978-1-4899-0335-8
Autres types d'écriture et termes associés:
Auteur du livre: leitman, leitmann, bolza
Titre du livre: calc, mathematical methods optimal control, introduction optimal control, introduction the calculus variations


Données de l'éditeur

Auteur: George Leitmann
Titre: Mathematical Concepts and Methods in Science and Engineering; The Calculus of Variations and Optimal Control - An Introduction
Editeur: Springer; Springer US
312 Pages
Date de parution: 2013-05-23
New York; NY; US
Imprimé / Fabriqué en
Langue: Anglais
106,99 € (DE)
109,99 € (AT)
118,00 CHF (CH)
POD
XVI, 312 p.

BC; Hardcover, Softcover / Mathematik/Sonstiges; Optimierung; Verstehen; Calculus of Variations; Optimal control; calculus; control; differential equation; extrema; optimization; Calculus of Variations and Optimization; Mechanical Engineering; Maschinenbau; BB; EA

I. Calculus of Variations.- 1. Introduction.- 2. Problem Statement and Necessary Conditions for an Extremum.- 3. Integration of the Euler—Lagrange Equation.- 4. An Inverse Problem.- 5. The Weierstrass Necessary Condition.- 6. Jacobi’s Necessary Condition.- 7. Corner Conditions.- 8. Concluding Remarks.- II. Optimal Control.- 9. Introduction.- 10. Problem Statement and Optimality.- 11. Regular Optimal Trajectories.- 12. Examples of Extremal Control.- 13. Some Generalizations.- 14. Special Systems.- 15. Sufficient Conditions.- 16. Feedback Control.- 17. Optimization with Vector-Valued Cost.- References.

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