FUZZY LOGIC for Embedded Systems Applications FUZZY LOGIC for Embedded Systems Applications by Ahmad M. Ibrahim, Ph.D. Senior Member, IEEE AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Newnes is an imprint of Elsevier Science. Copyright © 2004, Elsevier Science (USA). All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopy- ing, recording, or otherwise, without the prior written permission of the publisher. Recognizing the importance of preserving what has been written, Elsevier Science prints its books on acid-free paper whenever possible. Library of Congress Cataloging-in-Publication Data ISBN: 0-7506-7699-X British Library Cataloging-in-Publication Data A catalogue record for this book is available from the British Library. The publisher offers special discounts on bulk orders of this book. For information, please contact: Manager of Special Sales Elsevier Science 200 Wheeler Road Burlington, MA 01803 Tel: 781-313-4700 Fax: 781-313-4880 For information on all Newnes publications available, contact our World Wide Web home page at: http://www.newnespress.com 10 9 8 7 6 5 4 3 2 1 Printed in the United States of America Contents Preface ................................................................................................ xi About the Author ............................................................................. xv What’s on the CD-ROM? ................................................................. xvi 1. Embedded Systems: An Overview ............................................... 1 1.1 Definition and Examples ................................................................ 1 1.2 Further Features of Embedded Systems .......................................... 2 1.3 Design Metrics ............................................................................... 4 1.4 Implementation ............................................................................. 6 1.4.1 Processor Technologies....................................................... 6 1.4.2 Integrated Circuit Technologies .......................................... 7 1.4.3 Design Technologies......................................................... 11 1.5 Fuzzy Logic and Embedded Systems ............................................. 12 Concluding Remarks............................................................................. 13 Bibliography ......................................................................................... 14 Web Resources ..................................................................................... 16 2. Fuzzy Sets .................................................................................... 23 2.1 Introduction ................................................................................. 23 2.2 Classical Sets ................................................................................ 23 2.3 Set Operations ............................................................................. 25 2.4 Boolean Logic .............................................................................. 31 2.5 Basic Concepts of Fuzzy Sets ........................................................ 31 2.6 Other Representations of Fuzzy Sets............................................. 32 2.7 Determination of Membership Functions ..................................... 35 2.8 Fuzzy Sets Properties .................................................................... 35 2.9 Operations on Fuzzy Sets ............................................................. 37 v Contents 2.9.1 Logic Operations .............................................................. 37 2.9.2 Algebraic Operations on Fuzzy Sets .................................. 42 3. Fuzzy Relations............................................................................ 53 3.1 Introduction ................................................................................. 53 3.2 Classical Relations ........................................................................ 53 3.3 Classical Reasoning ...................................................................... 58 3.4 Fundamentals of Fuzzy Relations .................................................. 59 3.5 Operations on Binary Fuzzy Relations ........................................... 59 3.6 Types of Fuzzy Relations ............................................................... 62 3.7 Fuzzy Reasoning .......................................................................... 63 Concluding Remarks ............................................................................. 65 Bibliography ......................................................................................... 66 Web Resources ..................................................................................... 67 4. Embedded Fuzzy Applications ................................................... 69 4.1 Introduction ................................................................................. 69 4.2 Conventional Control Systems ..................................................... 69 4.2.1 Description....................................................................... 69 4.2.2 Analysis............................................................................ 71 4.2.3 Design ............................................................................. 72 4.2.4 PID Control ...................................................................... 72 4.3 Fuzzy Logic Controller (FLC) ......................................................... 73 4.3.1 Description....................................................................... 73 4.3.2 Design ............................................................................. 74 4.3.3 Defuzzification ................................................................. 75 4.3.4 Analysis............................................................................ 78 4.4 Simplified Examples of Applications ............................................. 83 4.4.1 Washing machine ............................................................ 83 4.4.2 Vacuum cleaner ............................................................... 89 Concluding Remarks ............................................................................. 89 Bibliography ......................................................................................... 90 Web Resources ..................................................................................... 93 vi Contents 5. Critique of Fuzzy Logic ............................................................... 99 5.1 Introduction ................................................................................. 99 5.2 Objectives of Fuzzy Logic.............................................................. 99 5.3 What’s in a Name?..................................................................... 100 5.4 Fuzziness vs. Probability ............................................................. 101 5.5 Fuzzy Logic vs. Multiple-Valued Logic ......................................... 102 5.6 Philosophical Issues .................................................................... 103 5.7 Engineering Applications Issues ................................................. 105 Concluding Remarks........................................................................... 107 Bibliography ....................................................................................... 108 6. Neural Networks ....................................................................... 111 6.1 Introduction ............................................................................... 111 6.2 Background ............................................................................... 111 6.3 Learning .................................................................................... 112 6.4 The Basic Neuron Model ............................................................ 112 6.5 The Perceptron........................................................................... 116 6.6 The Multilayer Perceptron .......................................................... 118 6.7 Recurrent Network ..................................................................... 122 6.7.1 Hopfield Networks ......................................................... 122 6.7.2 Boltzmann Machine Networks ....................................... 124 6.8 Kohonen Self-Organizing Networks ........................................... 125 6.8.1 Background ................................................................... 125 6.8.2 Description..................................................................... 126 6.8.3 Determining the winning neuron ................................... 127 6.8.4 Learning algorithm ......................................................... 127 6.9 Adaptive Resonance Theory, ART ............................................... 128 6.9.1 Background ................................................................... 128 6.9.2 ART................................................................................ 128 Concluding Remarks........................................................................... 131 Bibliography ....................................................................................... 132 Web Resources ................................................................................... 134 vii Contents 7. Hybrid Systems