Optimal Control Linear Quadratic Methods.PDF

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Optimal Control

PRENTICE HALL INFORMATION

AND SYSTEM SCIENCES SERIES

Thomas Kailath, Editor

AN~ERSO~&MOORE

AN~ERSON&MOORE

AsTRo~ &WITTENNIAR~

GARDNER

Goo~wI~ &SHN

GRAY&DAVISSON

HAYKIN

JAIN

JOHNSON

KAILATH

KUMAR&VARAIYA

KUNG

KUNG,WHITEHOUSE,

&KAILATHEDS,

KWAKERNAA&SIVAN

LANDAU

Optimal Control

Optimal Filtering

Computer-ControlledSystems: Theory and Design, 21e

StatisticalSpectral Analysis: A Nonprobabilistic Theory

Adaptive Filtering, Prediction, and Control

Random Processes:A MathematicalApproach for Engineers

Adaptive Filter Theory

Fundamentalsof Digital Image Processing

Lectures on Adaptive ParameterEstimation

Linear Systems

StochasticSystems

VLSI Array Processors

VLSI and Modern Signal Processing

Signals & Systems

System Identification and Control Design Using

P.I. M. + Software

System Identification

Medical Imaging Systems

Digital Control & Estimation

Stable Adaptive Systems

Adaptive Control: StabiliVJ Convergence,and Robustness

Continuous and Discrete Signals and Systems

Digital Communications by Satellite

Designing Digital Filters

LJUNG

MACOVSKI

MIDDLETO&GOODWIN

NARENDR&A~NASWANiY

SASTR&BOLMON

SOLIMA&SRINATH

SPILKER

WILLIAMS

Optimal Control

LINEAR QUADRATIC

METHODS

BRIAN

D. O. ANDERSON

JOHN

B. MOORE

Department of Systems Engineering

Australian National University, Canberra

3 — — Prentice-Hall International, Inc.

ISBN 0-13 -638651-2

This edition may be sold only in those countries to which

it is consigned by Prentice-Hall International. It is not to

be re-exported and it is not for sale in the U. S. A., Mexico,

or Canada.

—

@ 1989 by Prentice-Hall, Inc.

A Division of Simon & Schuster

Englewood Cliffs, NJ 07632

reproduced, in any form or by any means,

without permission in writing from the publisher.

Printed in the United States of America

10987654321

ISBN O-13 -L313L51j-i2

Prentice-Hall International (UK) Limited, London

Prentice-Hall of Australia Pty. Limited, Sydney

Prentice-Hall Canada Inc., Toronto

Prentice-Hall Hispanoamericana, S. A., Mexico

Prentice-Hall of India Private Limited, New De/hi

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Simon & Schuster Asia Pte. Ltd., .Wrgapore

Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro

Prentice-Hall, Inc., Eng/ewood C/iffs, New Jersey

Contents

Preface ix

Part I. Basic Theory of the Optimal Regulator

Introduction

1.1 Linear Optimal Control 1

1.2 About This Book in Particular 4

1.3 Part and Chapter Outline 5

The Standard Regulator Problem—1

2.1 A Review of the Regulator Problem 7

2.2 The Hamilton-Jacobi Equation 12

2.3 Solution of the Finite-Time Regulator Problem 20

2.4 Discrete Time Systems 28

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