Table Of ContentCommunications and Control Engineering
Ruiyun Qi
Gang Tao
Bin Jiang
Fuzzy System
Identification and
Adaptive Control
Communications and Control Engineering
Series Editors
Alberto Isidori, Roma, Italy
Jan H. van Schuppen, Amsterdam, The Netherlands
Eduardo D. Sontag, Boston, USA
Miroslav Krstic, La Jolla, USA
Communications and Control Engineering is a high-level academic monograph
series publishing research in control and systems theory, control engineering and
communications. It has worldwide distribution to engineers, researchers, educators
(severalofthetitlesinthisseriesfinduseasadvancedtextbooksalthoughthatisnot
their primary purpose), and libraries.
Theseriesreflectsthemajortechnologicalandmathematicaladvancesthathave
a great impact in the fields of communication and control. The range of areas to
which control and systems theory is applied is broadening rapidly with particular
growth being noticeable in the fields of finance and biologically-inspired control.
Books in this series generally pull together many related research threads in more
matureareasofthesubjectthanthehighly-specialisedvolumesofLectureNotesin
ControlandInformationSciences.Thisseries’smathematicalandcontrol-theoretic
emphasis is complemented by Advances in Industrial Control which provides a
much more applied, engineering-oriented outlook.
Indexed by SCOPUS and Engineering Index.
Publishing Ethics: Researchers should conduct their research from research
proposaltopublication inlinewithbestpracticesandcodesofconductofrelevant
professional bodies and/or national and international regulatory bodies. For more
details on individual ethics matters please see:
https://www.springer.com/gp/authors-editors/journal-author/journal-author-
helpdesk/publishing-ethics/14214
More information about this series at http://www.springer.com/series/61
Ruiyun Qi Gang Tao Bin Jiang
(cid:129) (cid:129)
fi
Fuzzy System Identi cation
and Adaptive Control
123
RuiyunQi Gang Tao
Collegeof Automation Engineering Schoolof Engineering andAppliedScience
NanjingUniversity ofAeronautics University of Virginia
andAstronautics Charlottesville, VI, USA
Nanjing, Jiangsu,China
BinJiang
Collegeof Automation Engineering
NanjingUniversity ofAeronautics
andAstronautics
Nanjing, Jiangsu,China
ISSN 0178-5354 ISSN 2197-7119 (electronic)
Communications andControl Engineering
ISBN978-3-030-19881-7 ISBN978-3-030-19882-4 (eBook)
https://doi.org/10.1007/978-3-030-19882-4
MATLAB® and Simulink® are registered trademarks of The MathWorks, Inc., 1 Apple Hill Drive,
Natick,MA01760-2098,USA,http://www.mathworks.com.
MathematicsSubjectClassification(2010):93C40,93C42,93B52,70Q05,93C83
©SpringerNatureSwitzerlandAG2019
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom
therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, expressed or implied, with respect to the material contained
hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard
tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
To my family and the memory of Mietek
A. Brdys
Ruiyun Qi
To our families
Gang Tao, Bin Jiang
Preface
Controlofuncertainnonlineardynamicsystemshasbeenachallengingtopicinthe
last few decades. For nonlinear systems with parametric uncertainties, adaptive
nonlinear control combined with backstepping, feedback linearization, sliding
model control techniques has been extensively studied and applied to solve many
practical problems successfully. For nonlinear systems with functional uncertain-
ties, adaptive approximation-based control designs, using neural networks, fuzzy
systems, and traditional adaptive approximators, have attracted much research
interest in the last two decades and evolved to create powerful approaches which
canhelpachievestabilityandtrackingresultsforawideclassofuncertainnonlinear
systems.
In adaptive approximation-based control designs, neural networks, fuzzy sys-
tems,orothertraditional function approximators suchaspolynomials, splines, and
wavelets are employed to approximate unknown nonlinear functions. From a
mathematical perspective, those function approximators can be used in a similar
way when their role is to approximate some static nonlinear functions in dynamic
nonlinear systems. Actually, most adaptive approximation-based control designs
have used neural networks or fuzzy systems in this way: for some classes of
nonlinear systems (strict-feedback, pure feedback, feedback linearizable, etc.),
suitable nonlinear control techniques, such as backstepping and feedback lin-
earization, are applied to develop nonlinear controllers where the unknown non-
linear functions are approximated by neural networks or fuzzy systems. The
parameters or weights of neural networks/fuzzy systems are adaptively adjusted to
compensate the nonlinear effects to achieve desirable control performance.
When not only some nonlinear functions but also the structure of a nonlinear
dynamic system are unknown, dynamic neural networks and dynamic fuzzy sys-
tems provide effective tools to represent the whole unknown dynamic nonlinear
system. Based on some available qualitative (i.e., experience, expert knowledge)
and quantitative (i.e., input–output data) information on the nonlinear system, the
initialstructureandparametersofthedynamicneuralnetworksorfuzzysystemcan
bedeterminedthroughsomeofflineidentificationmethods.Whenthosemodelsare
vii
viii Preface
used in online control, their structures and parameters can be further adjusted
through evolutionary and adaptive algorithms.
Among various dynamic approximation models, the fuzzy dynamic system,
usually called Takagi–Sugeno (T–S) fuzzy system, has been widely studied.
DifferentfromconventionalMamdanifuzzysystems,theruleconsequentsofaT–S
fuzzy system are represented by local linear models rather than fuzzy sets. The
overall T–S fuzzy system is a nonlinear dynamic model by smoothly blending all
thelocallinearmodelsusingfuzzymembershipfunctions.Comparedwithdynamic
neural networks, T–S fuzzy modeling isintuitivelyeasiertounderstand since each
of its local models represents the local behavior of a nonlinear dynamic system in
certain operating region defined by the fuzzy sets in the rule premise. From the
controlsynthesisandanalysis perspective,T–S fuzzysystemsareverysuitablefor
systematic control designs and stability analysis.
From the 1990s to 2000s, extensive studies were carried out on T–S fuzzy
systems,leadingtomanyfundamentaltheoreticalresultsonidentification,stability
analysis, and control synthesis of T–S fuzzy systems. Since there exist uncertain
parameters in real-life nonlinear systems, when T–S fuzzy systems are used to
representreal-lifenonlinearsystems,theyhaveuncertainparametersaswell,which
motivated the adaptive control designs for T–S fuzzy systems. Since T–S fuzzy
systemscanbeviewedasaclassofnonlineardynamicsystems,adaptivecontrolof
T–S fuzzy systems is not only an important branch of T–S fuzzy-model-based
control synthesis and analysis but also provides solutions for adaptive control of a
more general class of uncertain nonlinear systems.
This book aims at providing a systematic and unified framework for identifi-
cation and adaptive control of fuzzy systems, especially T–S fuzzy systems. It is
well-known that adaptive control algorithms for both linear and nonlinear systems
arerelatedcloselytothesystemstructures,whichdeterminesthedesignconditions,
thecontrollerstructure,theestimationerrormodel,theparameteradaptivelaws,etc.
In literature, T–S fuzzy systems appear indifferent forms: state-spaceform, input–
output form, continuous-time form, discrete-time form, single-input–single-output
(SISO)form, multi-input–multi-output (MIMO)form. On theother hand,from the
perspectiveofcontrolobjective,itcanbestatetrackingoroutputtracking;fromthe
perspective of available information for control designs, one can choose state
feedback control or output feedback control. Different system forms, control
objectives, and available information lead to different adaptive control design
methodologies for T–S fuzzy systems, which will be carefully considered and
rigorously addressed within a sound analytical framework in this book.
This book has been written at the first-year graduate level with prerequisite
knowledgeoflinearalgebra,dynamicsystems,andfeedbackcontrol.Thisbookcan
be used as a textbook for graduate students in a course of fuzzy modeling and
control, and also a technical reference for graduate students, scholars, engineers in
thefieldsofmechanicalengineering,electricalengineering,aerospaceengineering,
computer science, applied mathematics, and others who have some basic knowl-
edge of linear feedback control.
Preface ix
Organization. With 10 chapters, this book systematically presents identifica-
tion,adaptivestatetrackingcontrolandoutputtrackingcontrolalgorithmsforT–S
fuzzy systems of different forms and with unknown parameters.
Chapter1introducessomebackgroundknowledge.Thebasicconceptsoffuzzy
sets, fuzzy logic, and fuzzy inference system are presented. Some typical fuzzy
systems including Mamdani fuzzy system and T–S fuzzy system are briefly
introduced. A literature review on fuzzy system identification and T–S fuzzy
model-based adaptive nonlinear control is also given.
Chapter 2 aims at giving readers a clear and concise description on some
importantfeaturesandpropertiesofT–Sfuzzysystems,whichrelatecloselytothe
problemsofT–Sfuzzysystemidentificationandcontroldesigns,includingdifferent
system architectures, approximation capability, stability conditions, stabilization
control, and tracking control.
Chapter3reviewsbasicconceptsanddesignmethodologiesofadaptivecontrol.
Since T–S fuzzy systems are locally linear models and semi-globally nonlinear
models,theiradaptivecontroldesignscanbecarriedoutusingbothadaptivelinear
control and adaptive nonlinear control approaches. The goal of this chapter is to
help readers who are not familiar with adaptive control to understand the basic
ideas, classical design methods, and key issues of adaptive linear control and
adaptive nonlinear control.
Chapter 4 presents the identification methods for T–S fuzzy systems. Both lin-
earization based and data-based methods are provided. In the data-based methods,
both offline identification and online identification approaches are studied, where
fuzzy clustering methods are used to identify the model structure and linear and
nonlinear parameter learning methods are adopted to estimate model parameters.
Chapter 5 deals with adaptive state tracking for continuous-time T–S fuzzy
systemsinstate-spaceforms.Thischapterpresentsanextensivestudyonhowstate
tracking can be achieved for T–S fuzzy systems via various controller structures
andreferencemodelstructures.Actually,thecontroldesignforT–Sfuzzysystems
canbeveryflexibleduetotheirstructurefeatures.Itisrevealedinthischapterthat
by choosing suitable controller structure and reference model, the necessary
plant-model matching conditions for state tracking control can be relaxed. State
trackingcontrol problems for both single-input andmulti-input T–S fuzzy systems
are handled with detailed design and analysis. The issue on how to guarantee the
input matrix with estimated parameters nonsingular in the adaptive controller for
multi-input T–S fuzzy systems is also addressed.
Chapter 6 develops a solution framework for adaptive state feedback output
tracking control of general discrete-time state-space T–S fuzzy systems. A normal
formisderivedforaglobalT–Sfuzzymodel,whichhasanexplicitrelativedegree
structure and a proper causality property. Such a model is an approximation of a
discrete-time nonlinear system with a general relative degree, based on which an
adaptivestatefeedbackcontrolschemecanbedevelopedwithdesiredstabilityand
output tracking performance.
x Preface
Chapter 7 considers adaptive output feedback control for discrete-time SISO
T–Sfuzzysystemsdescribedbyinput–outputmodels.Akeyadvantageofusingan
input–output approach over a state-space approach is that desired system tracking
performance can be characterized and achieved based on much relaxed design
conditions for adaptive control, in the presence of system parameter uncertainties.
TwononlinearpredictionmodelsforT–Sfuzzysystemswithmultipleinput–output
delaysaredevelopedandforeachofthem,adaptivecontrolschemeswithcomplete
stability and convergence analysis are presented.
Chapter 8 extends the results in Chap. 7 to adaptive control of MIMO
discrete-time T–S fuzzy systems with general delay matrices. The results of this
chapter include the derivation of a global prediction fuzzy system model with a
general delay structure, parametrization and parameter estimation, development of
an adaptive control scheme, stability and tracking analysis of such an adaptive
controlsystem,andillustrationofnewfeaturesandconceptsofadaptivecontrolfor
MIMO fuzzy systems.
Chapter 9 considers discrete-time input–output multiple-delay T–S fuzzy sys-
tems with unknown membership function parameters and consequent parameters,
and derived a solution for it. A fuzzy system with such uncertain parameters leads
to a nonlinearly parametrized estimation error model, for which the gradient
algorithm can be applied to derive an adaptive law to adaptively update the esti-
matesofboththemembershipfunctionparametersandruleconsequentparameters.
The properties of the parameter adaptive laws and closed-loop stability have been
studiedwithsomekeydesignconditionsspecifiedandestablishedfortheGaussian
membership functions.
Chapter 10 presents two adaptive actuator fault compensation scheme for non-
linear systems represented by T–S fuzzy systems with redundant actuators.
Acknowledgements This book cannot be completed without the inspiration and
knowledge from many contributors in the fields of fuzzy systems and adaptive
control on whose work our book is based. In particular, we want to mention:
LotfiA.Zadeh,TomohiroTakagi,MichioSugeno,Li-XinWang,GangFeng,Hao
Ying, Graham Goodwin, Ioan Landau, Petros A. Ioannou, Marios M. Polycarpou,
Jay A. Farrell, Jing Sun, Miroslav Krstić, Hua O. Wang, Kazuo Tanaka, Ronald
Yager, B. Babuska, Shaocheng Tong, Han-Xiong Li, Kevin M. Passino, and
Plamen P. Angelov.
This first author would like to thank Narasimhan Sundarajan, who introduced
hertothefieldoffuzzysystemsbackin2002,andMietekA.Brdyswhosupervised
her Ph.D. work in adaptive fuzzy control from 2003 to 2007.
We would like to thank our former Ph.D. students Chang Tan, Xuelian Yao,
Liyan Wen, Yanjun Zhang, Zhifeng Gao, Qikun Shen and master students Yuhai
Huang, Limeng Zhu, Xiapeng Zhou, and Lin Jiang for their collaboration in the
development and implementation of various fuzzy identification and adaptive
control techniques, and Yicheng Chen, Le Wang, Yue Liang, Zhiyu Peng, and
Xinlei Dong for their assistance in carrying out some of the simulation studies
contained in this book and proofreading the manuscript.
