Reliable Control and Filtering of Linear Systems with Adaptive Mechanisms

252 Pages·2011·1.7 MB·English

by  Guang-Hong Yang

Reliable Control and
Filtering of Linear
Systems with
Adaptive Mechanisms
AUTOMATION AND CONTROL ENGINEERING
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Series Editors
FRANK L. LEWIS, Ph.D., SHUZHI SAM GE, Ph.D.,
Fellow IEEE, Fellow IFAC Fellow IEEE
Professor Professor
Automation and Robotics Research Institute Interactive Digital Media Institute
The University of Texas at Arlington The National University of Singapore

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Automation and Control Engineering Series

Reliable Control and
Filtering of Linear

Systems with

Adaptive Mechanisms

Guang-Hong Yang
Northeastern University
Shenyang, People’s Republic of China
Dan Ye
Northeastern University
Shenyang, People’s Republic of China

Boca Raton London New York
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Library of Congress Cataloging‑in‑Publication Data
Yang, Guang-Hong.
Reliable control and filtering of linear systems with adaptive mechanisms /
Guang-Hong Yang, Dan Ye.
p. cm. -- (Automation and control engineering)
“A CRC title.”
Includes bibliographical references and index.
ISBN 978-1-4398-3522-7 (hardcover : alk. paper)
1. Linear control systems--Reliability. 2. Adaptive control systems--Reliability. 3.
Fault tolerance (Engineering) I. Ye, Dan, 1979- II. Title. III. Series.
TJ220.Y36 2011
629.8’32--dc22 2010019543
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Contents
Preface ix
Symbol Description xi
1 Introduction 1
2 Preliminaries 5
2.1 Linear Matrix Inequalities . . . . . . . . . . . . . . . . . . . 5
2.2 H∞ Control Problem . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 H∞ Performance Index . . . . . . . . . . . . . . . . . 6
2.2.2 State Feedback H∞ Control . . . . . . . . . . . . . . . 7
2.2.3 Dynamic Output Feedback H∞ Control . . . . . . . . 8
2.3 Some Other Lemmas . . . . . . . . . . . . . . . . . . . . . . 13
3 Adaptive Reliable Control against Actuator Faults 19
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 State Feedback Control . . . . . . . . . . . . . . . . . . . . . 21
3.4 Dynamic Output Feedback Control . . . . . . . . . . . . . . 27
3.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4 Adaptive Reliable Control against Sensor Faults 47
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Adaptive Reliable H∞ Dynamic Output Feedback Controller
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5 Adaptive Reliable Filtering against Sensor Faults 63
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Adaptive Reliable H∞ Filter Design . . . . . . . . . . . . . . 68
5.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
v
vi
6 Adaptive Reliable Control for Time-Delay Systems 79
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Adaptive Reliable Memory-Less Controller Design . . . . . . 80
6.2.1 Problem Statement . . . . . . . . . . . . . . . . . . . . 80
6.2.2 H∞ State Feedback Control . . . . . . . . . . . . . . 81
6.2.3 Guaranteed Cost Dynamic Output Feedback Control . 90
6.2.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3 Adaptive Reliable Memory Controller Design . . . . . . . . . 109
6.3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . 110
6.3.2 H∞ State Feedback Control . . . . . . . . . . . . . . . 110
6.3.3 Guaranteed Cost State Feedback Control . . . . . . . 119
6.3.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7 Adaptive Reliable Control with Actuator Saturation 139
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.2 State Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.2.1 Problem Statement . . . . . . . . . . . . . . . . . . . . 140
7.2.2 A Condition for Set Invariance . . . . . . . . . . . . . 142
7.2.3 Controller Design . . . . . . . . . . . . . . . . . . . . . 147
7.2.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.3 Output Feedback . . . . . . . . . . . . . . . . . . . . . . . . 155
7.3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . 155
7.3.2 A Condition for Set Invariance . . . . . . . . . . . . . 155
7.3.3 Controller Design . . . . . . . . . . . . . . . . . . . . . 163
7.3.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8 ARC with Actuator Saturation and L2-Disturbances 169
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.2 State Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.2.1 Problem Statement . . . . . . . . . . . . . . . . . . . . 170
8.2.2 ARC Controller Design . . . . . . . . . . . . . . . . . 171
8.2.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.3 Output Feedback . . . . . . . . . . . . . . . . . . . . . . . . 183
8.3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . 183
8.3.2 ARC Controller Design . . . . . . . . . . . . . . . . . 183
8.3.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
9 Adaptive Reliable Tracking Control 199
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
9.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 200
9.3 Adaptive Reliable Tracking Controller Design . . . . . . . . 201
9.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
vii
9.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
10 Adaptive Reliable Control for Nonlinear Time-Delay Sys-
tems 217
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
10.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 218
10.3 Adaptive Reliable Controller Design . . . . . . . . . . . . . . 219
10.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
10.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Bibliography 237
Index 251
Preface
More and more advanced technological systems rely on sophisticated control
systems to increase their safety and performances. In the event of system
component faults, the conventional feedback control designs may result in
unsatisfactory performances or even instability, especially for complex safety
critical systems, e.g., aircraft, space craft and nuclear power plant, etc. This
has ignitedenormousresearchactivities inthe searchfornew designmethod-
ologies, for accommodating the component failures and maintaining the ac-
ceptable system stability and performances, so that abrupt degradation and
total system failures can be averted. Fault-tolerant control (FTC) is a rela-
tively new field of research addressing the design of feedback controllers that
ensure safe and efficient operations despite the occurrence of faults. Fault-
tolerant design approaches can be broadly classified into two types: passive
approach and active approach.
Traditional reliable controlis a kind of passive controlapproach,in which
a controller with fixed gain is used throughout normal and fault cases, such
that this type of controller is easily implemented. Moreover, several perfor-
mance indexes suchasH∞,H2, andcostfunctions mainly basedonalgebraic
Riccati equation (ARE) or linear matrix inequality (LMI) methods, can be
usedtodescribetheperformancesoftheclosed-loopsystems.However,asthe
numberofpossiblefailuresandthe degreeofsystemredundancyincrease,the
passivereliablecontrollerswithfixedgainsbecomemoreconservative,andat-
tainable control performance indexes may not necessarily be satisfactory. On
theotherhand,adaptivecontrolisaneffectivemethodtodesignfault-tolerant
controllers, too. They rely on the potential of the adjustments of parameters
to assure reliability of closed-loop systems in the presence of a wide range of
unknownfaults. Hence, the resultantsolvable conditions can be more relaxed
and the corresponding controller gains are variable.
In this book, the aim is to present our recentresearchresults in designing
reliable controllers/filtersfor linear systems. The main feature of this book is
that adaptive mechanisms are successfully introduced into the traditional re-
liable control/filtering and based on the online estimation of eventual faults,
the proposed adaptive reliable controller/filter parameters are updated au-
tomatically to compensate the fault effects on systems. Moreover, the adap-
tive performancesof resultant closed-loopsystems in both normaland actua-
tor/sensor faults cases are optimized, and asymptotic stability is guaranteed.
The designed conditions, which are given in the frameworks of linear matrix
inequalities(LMIs),areproventobelessconservativethanthoseofthetradi-
ix
x
tionalreliable control/filtering.Designs for linear systems with both actuator
failuresandsensorfailuresarecovered,respectively.Wealsoextendthedesign
idea from linear systems to linear time-delay systems via both memory-less
controllers and memory controllers. Moreover, some more recent results for
the corresponding adaptive reliable control against actuator saturation are
included here. This book provides a coherent approach, and contains valu-
able reference materials for researcherswishing to explore the area of reliable
control. Its contents are also suitable for a one-semester graduate course.
The book focuses exclusively on the issues of reliable control/filtering in
the framework of indirect adaptive method, and LMI techniques, starting
from the development and main research methods in fault-tolerant control,
and offering a systematic presentation of the newly proposed methods for
adaptive reliable control/filtering of linear systems against actuator/sensor
faults.Designsandguidelinesprovidedheremaybeusedtodevelopadvanced
fault-tolerant control techniques to improve reliability, maintainability, and
survivability of complex control systems.
This work was partially supported in part by National 973 Program of
China (Grant No. 2009CB320604), the Funds of National Science of China
(GrantNo.60821063,60804024,60974043),ChinaPostdoctoralScienceFoun-
dation (Grant No. 20090451276),and 111 Project (B08015).
We would like to thank Dr. Wei Guan for his great help in preparing
Chapters 7 and 8.
Guang-HongYang andDanYe
NortheasternUniversity,China