Lectures on the Calculus of Variations and Optimal Control Theory - Hardcover
This is not a print-on-demand or facsimile copy but a hardcover book published by Chelsea Publishing Company, New York as a Second (corr.) Edition 1980. The Second Edition is identical to the First Edition, except for the correction of errata. It is Library of Congress Catalog Card Number 79-57387 and ISBN 0-8284-0304-X. It has an Index and 337 numbered pages. This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and ``automatic'' existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.
"synopsis" may belong to another edition of this title.
Review:
... A beautiful book ... that is bound to stimulate many mathematicians and students of mathematics. MAA Monthly
"About this title" may belong to another edition of this title.
- PublisherChelsea Pub Co
- Publication date1980
- ISBN 10 082840304X
- ISBN 13 9780828403047
- BindingHardcover
- Edition number2
- Number of pages337
(No Available Copies)
Search Books: Create a WantIf you know the book but cannot find it on AbeBooks, we can automatically search for it on your behalf as new inventory is added. If it is added to AbeBooks by one of our member booksellers, we will notify you!
Create a Want