Primer on the Calculus of Variations and Optimal Control Theory

ISBN-10: 0821847724

ISBN-13: 9780821847725

Edition: 2009

Authors: Mike Mesterton-Gibbons

List price: $48.00
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Description:

The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.
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Book details

List price: $48.00
Copyright year: 2009
Publisher: American Mathematical Society
Publication date: 7/17/2009
Binding: Paperback
Pages: 252
Size: 5.50" wide x 8.75" long x 0.50" tall
Weight: 0.748
Language: English

Mike Mesterton-Gibbons, PhD, is Professor of Mathematics at Florida State University.

The Brachistochrone
The fundamental problem
Extremals The insufficiency of extremality
Important first integrals
The du Bois-Reymond equation
The corner conditions
Legendre's necessary condition
Jacobi's necessary condition
Weak versus strong variations
Weierstrass's necessary condition
The transversality conditions
Hilbert's invariant integral
The fundamental sufficient condition
Jacobi's condition revisited
Isoperimetrical problems
Optimal control problems
Necessary conditions for optimality
Time-optional control
A singular control problem
A biological control problem
Optimal control to a general target
Navigational control problems
State variable restrictions
Optimal harvesting
Afterword Solutions or hints for selected exercises
Bibliography
Index
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