BN.com Gift Guide

Optimal Control and the Calculus of Variations / Edition 1

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $48.24
Usually ships in 1-2 business days
(Save 43%)
Other sellers (Paperback)
  • All (10) from $48.24   
  • New (5) from $84.37   
  • Used (5) from $48.24   

More About This Textbook

Overview

This book provides the core material for undergraduate courses on optimal control, the modern development that has grown out of the calculus of variations and classical optimization theory.
Read More Show Less

Product Details

  • ISBN-13: 9780198514893
  • Publisher: Oxford University Press, USA
  • Publication date: 9/28/1995
  • Edition description: Reprint
  • Edition number: 1
  • Pages: 248
  • Product dimensions: 6.13 (w) x 9.19 (h) x 0.61 (d)

Table of Contents

1 Introduction 1
The maxima and minima of functions 1
The calculus of variations 4
Optimal control 9
2 Optimization In R[superscript n] 13
Functions of one variable 13
Critical points, end-points, and points of discontinuity 16
Functions of several variables 18
Minimization with constraints 22
A geometrical interpretation 25
Distinguishing maxima from minima 28
3 The calculus of variations 33
The fixed end-point problem 33
Problems in which the end-points are not fixed 41
Finding minimizing curves 46
Isoperimetric problems 54
Sufficiency conditions 58
Fields of extremals 59
Hilbert's invariant integral 62
Semi-fields and the Jacobi condition 66
4 Optimal control I: Theory 70
Introduction 70
Control of a simple first-order system 70
Systems governed by ordinary differential equations 72
The optimal control problem 74
The Pontryagin maximum principle 80
Optimal control to target curves 100
5 Optimal control II: Applications 103
Introduction 103
Time-optimal control of linear systems 103
Optimal control to target curves 139
Singular controls 149
Fuel-optimal control 151
Problems where the cost depends on x(t[subscript 1]) 159
Linear systems with quadratic cost 163
The steady-state Riccati equation 168
The calculus of variations revisited 170
6 Proof of the maximum principle of Pontryagin 175
Convex sets in R[superscript n] 176
The linearized state equations 182
The behaviour of H on an optimal path 184
Sufficiency conditions for optimal control 206
Appendix: Answers and hints for the exercises 208
Bibliography 231
Index 233
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)