Optimal control and the calculus of variations / Enid R. Pinch.

Format:

Book

Author/Creator:

Pinch, Enid R., author.

Language:

English

Subjects (All):

Calculus of variations.

Control theory.

Physical Description:

1 online resource (234 pages) : illustrations

Edition:

1st ed.

Place of Publication:

New York : Oxford University Press, 2002.

Language Note:

English

Summary:

This introduction to optimal control theory is intended for undergraduate mathematicians and for engineers and scientists with some knowledge of classical analysis. It includes sections on classical optimization and the calculus of variations. All the important theorems are carefully proved. There are many worked examples and exercises for the reader to attempt.

Contents:

Cover

Title Page

Copyright

Preface

Contents

1. Introduction

The maxima and minima of functions

The calculus of variations

Optimal control

2. Optimization in Rn

Functions of one variable

Critical points, end-points, and points of discontinuity

Functions of several variables

Minimization with constraints

A geometrical interpretation

Distinguishing maxima from minima

3. The calculus of variations

The fixed end-point problem

Problems in which the end-points are not fixed

Finding minimizing curves

Isoperimetric problems

Sufficiency conditions

Fields of extremals

Hilbert's invariant integral

Semi-fields and the Jacobi condition

4. Optimal control I: Theory

Introduction

Control of a simple first-order system

Systems governed by ordinary differential equations

The optimal control problem

The Pontryagin maximum principle

Optimal control to target curves

5. Optimal control II: Applications

Time-optimal control of linear systems

Singular controls

Fuel-optimal control

Problems where the cost depends on x(t1)

Linear systems with quadratic cost

The steady-state Riccati equation

The calculus of variations revisited

6. Proof of the maximum principle of Pontryagin

Convex sets in Rn

The linearized state equations

The behaviour of H on an optimal path

Sufficiency conditions for optimal control

Appendix: Answers and hints for the exercises

Bibliography

Index.

Notes:

Previously published in 1995.

Description based on print version record.

ISBN:

1-280-86969-0

9786610869695