Primer on the Calculus of Variations and Optimal Control Theory

Name: Primer on the Calculus of Variations and Optimal Control Theory
Price: 36.09 USD
Availability: InStock
ISBN: 9780821847725

ISBN-10: 0821847724

ISBN-13: 9780821847725

Edition: 2009

Authors: Mike Mesterton-Gibbons

List price: $51.00

30 day, 100% satisfaction guarantee!

Marketplace

1 new & used from $36.09

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

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,…

Book details

List price: $51.00
Copyright year: 2009
Publisher: American Mathematical Society
Publication date: 8/30/2009
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