System Identification and Adaptive Control: Theory and Applications of the Neurofuzzy and Fuzzy Cognitive Network Models

316 Pages·2014·8.1 MB·English

by  Yiannis Boutalis

Advances in Industrial Control
Yiannis Boutalis
Dimitrios Theodoridis
Theodore Kottas
Manolis A. Christodoulou
System
Identification and
Adaptive Control
Theory and Applications of the
Neurofuzzy and Fuzzy Cognitive
Network Models
Advances in Industrial Control
Series editors
Michael J. Grimble, Glasgow, UK
Michael A. Johnson, Kidlington, UK
For furthervolumes:
http://www.springer.com/series/1412
Yiannis Boutalis Dimitrios Theodoridis
•
Theodore Kottas Manolis A. Christodoulou
•
System Identification
and Adaptive Control
Theory and Applications of the Neurofuzzy
and Fuzzy Cognitive Network Models
123
YiannisBoutalis Manolis A.Christodoulou
Dimitrios Theodoridis Kifisia
Theodore Kottas Greece
Department of Electrical
andComputer Engineering
Democritus University ofThrace
Xanthi
Greece
ISSN 1430-9491 ISSN 2193-1577 (electronic)
ISBN 978-3-319-06363-8 ISBN 978-3-319-06364-5 (eBook)
DOI 10.1007/978-3-319-06364-5
Springer ChamHeidelberg New YorkDordrecht London
LibraryofCongressControlNumber:2014936844
(cid:2)SpringerInternationalPublishingSwitzerland2014
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Series Editors’ Foreword
TheseriesAdvancesinIndustrialControlaimstoreportandencouragetechnology
transfer in control engineering. The rapid development of control technology has
animpactonallareasofcontroldiscipline.Newtheory,newcontrollers,actuators,
sensors, new industrial processes, computer methods, new applications, new phi-
losophies…, and new challenges. Much of this development work resides in
industrial reports, feasibility study papers, and the reports of advanced collabo-
rative projects. The series offers an opportunity for researchers to present an
extendedexpositionofsuchnewworkinallaspectsofindustrialcontrolforwider
and rapid dissemination.
Theso-called ‘‘intelligent control’’movement ismotivatedbytheideathatthe
typesofsystemsthatcanberepresentedandanalyzedbytraditionalmathematical
approaches are limited in scope. Two particular system characteristics that engi-
neers wish to accommodate, namely unknown (nonlinear) systems and ‘‘soft’’
information (expert knowledge, linguistic knowledge) led to the introduction of
neural networks and fuzzy logic into the control engineer’s toolkit.
Theseadditionstothetoolsandtechniquesavailabletothecontrolengineercan
be followed in the publication lists of the Advances in Industrial Control mono-
graph series and its sister series Advanced Textbooks in Control and Signal Pro-
cessing. For neural network approaches, we can cite:
• Neuro-control and Its Applications by Sigeru Omatu, Marzuki Khalid and
Rubiyah Yusof (ISBN 978-3-540-19965-6, 1995);
• NeuralNetwork EngineeringinDynamic ControlSystemsedited byKennethJ.
Hunt, George R. Irwin and Kevin Warwick (ISBN 978-3-540-19973-1, 1995);
• Adaptive Control with Recurrent High-order Neural Networks by George A.
Rovithakis and Manolis A. Christodoulou (ISBN 978-1-85233-623-3, 2000);
• Nonlinear Identification andControl:A NeuralNetworkApproach byGuoping
Liu (ISBN 978-1-85233-342-3, 2001);
and the widely used textbook:
• Neural Networks for Modelling and Control of Dynamic Systems by Magnus
Norgaard,OleRavn,NielsK.PoulsenandLarsK.Hansen(ISBN978-1-85233-
227-3, 2000).
v
vi SeriesEditors’Foreword
For the fuzzy-logic approaches, there are fewer entries, but we can cite:
• ExpertAidedControlSystemDesignbyColinTebbutt(ISBN978-3-540-19894-
9, 1994);
• Fuzzy Logic, Identification and Predictive Control by Jairo Espinosa, Joos
Vandewalle and Vincent Wertz (ISBN 978-1-85233-828-2, 2005); and
• Advanced Fuzzy Logic Technologies in Industrial Applications edited by Ying
Bai, Hanqi Zhuang and Dali Wang (ISBN 978-1-84628-468-6, 2006).
In an attempt to gain even more flexibility for system representation, it is not
surprising to find researchers combining neural networks with fuzzy-logic
approaches to create a neuro-fuzzy modeling approach. Such a synthesis is
developed, analyzed, and applied in the first part of this Advances in Industrial
Control monograph, System Identification and Adaptive Control: Theory and
Applications of the Neurofuzzy and Fuzzy Cognitive Network Models by Yiannis
Boutalis,DimitriosTheodoridis,TheodoreKottas,andManolisChristodoulou.As
can be seen from the above list of monographs, Manolis Christodoulou has pre-
viously written on Recurrent High-order Neural Networks with George A. Rov-
ithakis. However, this newer monograph involves different authors and presents
exciting and innovative developments for system identification and adaptive
control using neuro-fuzzy models. Part II of the monograph travels in a different
direction and reports how cognitive maps and fuzzy-logic concepts can be com-
bined as fuzzy cognitive network models. Such models can be used in various
ways to solve process control problems or control decision-making tasks. One
strength of the monograph is the description of a number of simulation studies
using benchmark nonlinear systems and case-study systems. The case studies
include one laboratory motor experiment and some industrial power system
problems. The examples are developed and presented to show the different fea-
tures and characteristics of the neuro-fuzzy and fuzzy cognitive network identi-
fication and control methods.
In conclusion, the monograph reports and demonstrates new extensions and
syntheses ofthe concepts ofneuralnetworks,fuzzy logic, and cognitivemaps for
the control ofawide rangeofplants andindustrialprocesses.Controlresearchers
and industrial engineers will find new concepts in this monograph and will
undoubtedly appreciate the introductory explanatory sections and the many sim-
ulated examples as a route to comprehending these new developments in the
‘‘intelligent control’’ paradigm.
Glasgow, Scotland, UK M. J. Grimble
M. A. Johnson
Preface
Contemporary man-made engineering systems or systems associated with
socioeconomical or biological processes can be particularly complex, character-
izedbypossiblyunknownnonlinearities,operatinginuncertainenvironments.The
complexity of these systems hinders the design of suitable control techniques,
because the dynamical mathematical model required by ‘‘conventional’’ control
approaches is unknown most of the times. Even in the case that the mathematical
description is possible, there exist difficulties in the adaptation of the feedback
controllerswhenthesystemistimevaryingwithanunknowntothedesignerway.
These drawbacks have led the recent research effort to ‘‘intelligent’’ techniques,
seekingthedevelopmentofnewapproximationmodelsandcontroltechniquesthat
havetheabilitytolearnandadapttovaryingenvironmentalconditionsorinternal
dynamical behavior of the system.
Artificial neural networks and adaptive fuzzy systems constitute a reliable
choice for modeling unknown systems, since they can be considered as universal
approximators.Inthissense,theycanapproximateanysmoothnonlinearfunction
to any prescribed accuracy in a convex compact region, provided that sufficient
hidden neurons and training data or fuzzy rules are available. Recently, the
combinationofartificialneuralnetworksandadaptivefuzzysystemshasledtothe
creation of new approaches, fuzzy-neural, or neuro-fuzzy approaches that capture
the advantages of both fuzzy logic and neural networks and intend to approach
systems in a more successful way. Another modeling approach, that stems from
fuzzy cognitive maps, is the creation of a cognitive graph capturing the causal
relationshipsbetweenthecrucial variablesofthesystemassociatedwith thenode
values of the graph. Numerous applications and recent theoretical developments
haveshownthat,underpropertraining,thismodeliscapableofapproximatingthe
behavior of complex nonlinear systems in the engineering field and beyond.
This book is based on recent developments of the theory of Neuro-Fuzzy and
the Fuzzy Cognitive Network (FCN) models and their potential applications.
Its primary purpose is to present a set of alternative approaches, which would
allow the design of:
vii
viii Preface
• potent neuro-fuzzy system approximators and controllers able to guarantee
stability, convergence, and robustness for dynamical systems with unknown
nonlinearities
• appropriate cognitive graph modeling with guaranteed operational convergence
and parameter identification algorithms.
The book is the outcome of the recent research efforts of its authors. Its is
dividedintotwoparts,eachonebeingassociatedwitheachofthesemodels.PartI
is devoted to the Neuro-Fuzzy approach. It is based on the development ofa new
adaptive recurrent neuro-fuzzy approximation scheme, which is used for system
identification and the construction of a number of controllers with guaranteed
stability and robustness. The central idea in the development of the new approx-
imationschemeisanalternativedescriptionofaclassicaldynamicalfuzzysystem,
which allows its approximation by high-order neural networks (HONNs), a point
thatconstitutesaninnovativeelementofthepresentedscheme.Thecapabilitiesof
the developed approximators and controllers are tested on a number of simulated
benchmark problems and a real DC motor system.
Part II of the book is devoted to the FCN model. Fuzzy Cognitive Networks
stem from fuzzy cognitive maps (FCM), initially introduced by Bart Kosko in
1986. An FCN is actually an operational extension of FCM which assumes, first,
that it always reaches equilibrium points during its operation and second, it is in
continuous interaction with the system it describes and may be used to control it.
This way, the FCN is capable of capturing steady-state operational conditions of
the system it describes and associates them with input values and appropriate
weight sets. Inthe sequence, itstores the acquired knowledgeinfuzzy rule-based
databases, which can be used in determining subsequent control actions. Part II
presents basic theoretical results related to the existence and uniqueness of equi-
librium points in FCN, the adaptive weight estimation based on system operation
data, the fuzzy rule storage mechanism, and the use of the entire framework to
control unknown plants. The operation of the FCN framework is simulated and
tested on a number of selected applications, ranging from a well-known bench-
mark problem to real-life potential projects, like hydroelectric power plant coor-
dination and a novel scheme for optimal operation of a small-scale smart electric
grid of renewable power plants based on real meteorological data. Through these
examples, various aspects of the application of the FCN framework of operation
are revealed.
Xanthi, Greece, March 2014 Yiannis Boutalis
Dimitrios Theodoridis
Theodore Kottas
Manolis A. Christodoulou
Contents
Part I The Recurrent Neurofuzzy Model
1 Introduction and Scope of Part I. . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Recurrent High-Order Neural Networks. . . . . . . . . . . . . . . . . 5
1.3 Functional Representation of Adaptive Fuzzy Systems . . . . . . 8
1.3.1 COA Defuzzification and Indicator Functions . . . . . . 9
1.4 Outline of Adaptive Dynamic Identification and Control
Based on the Neurofuzzy Mode. . . . . . . . . . . . . . . . . . . . . . 10
1.5 Goals and Outline of Part I . . . . . . . . . . . . . . . . . . . . . . . . . 15
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Identification of Dynamical Systems Using Recurrent
Neurofuzzy Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1 The Recurrent Neurofuzzy Model. . . . . . . . . . . . . . . . . . . . . 25
2.2 Approximation Capabilities of the Neurofuzzy Model. . . . . . . 30
2.3 Learning Algorithms for Parameter Identification. . . . . . . . . . 33
2.3.1 Simple Gradient Descent. . . . . . . . . . . . . . . . . . . . . 34
2.3.2 Pure Least Squares. . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4 Robust Learning Algorithms . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.5.1 Parameter Identification in a Known
Model Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.5.2 Two Link Robot Arm. . . . . . . . . . . . . . . . . . . . . . . 47
2.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Indirect Adaptive Control Based on the Recurrent
Neurofuzzy Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1 Neurofuzzy Identification of Affine in the Control Systems. . . 57
3.1.1 Neurofuzzy Modeling. . . . . . . . . . . . . . . . . . . . . . . 58
3.1.2 Adaptive Parameter Identification. . . . . . . . . . . . . . . 61
ix
x Contents
3.2 The Indirect Control Scheme. . . . . . . . . . . . . . . . . . . . . . . . 63
3.2.1 Parametric Uncertainties . . . . . . . . . . . . . . . . . . . . . 64
3.2.2 The Method of Parameter Hopping. . . . . . . . . . . . . . 66
3.2.3 Parametric Plus Dynamic Uncertainties. . . . . . . . . . . 71
3.3 Simulation Results on the Speed Regulation
of a DC Motor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4 Direct Adaptive Neurofuzzy Control of SISO Systems. . . . . . . . . 87
4.1 Direct Adaptive Regulation . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.1.1 Neurofuzzy Modeling. . . . . . . . . . . . . . . . . . . . . . . 88
4.1.2 Adaptive Regulation with Modeling Error Effects . . . 90
4.2 Adaptive Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2.1 Complete Matching Case. . . . . . . . . . . . . . . . . . . . . 105
4.2.2 Inclusion of a Non-zero Approximation Error . . . . . . 109
4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.1 Inverted Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.2 Van der Pol Oscillator. . . . . . . . . . . . . . . . . . . . . . . 113
4.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5 Direct Adaptive Neurofuzzy Control of MIMO Systems. . . . . . . . 119
5.1 Regulation of MIMO Systems Assuming Only
Parametric Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.2 Robustness Analysis Assuming the Presence
of Modeling Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2.1 Modeling Errors Depending on System States . . . . . . 125
5.2.2 Modeling Errors Depending on System States
and a Not-Necessarily-Known Constant Value. . . . . . 129
5.3 The Model Order Problem. . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.2 Adaptive Regulation. . . . . . . . . . . . . . . . . . . . . . . . 133
5.4 State Trajectory Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.4.1 The Complete Model Matching Case . . . . . . . . . . . . 144
5.4.2 Inclusion of a Non-zero Approximation Error . . . . . . 146
5.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.5.1 Exact Model Order. . . . . . . . . . . . . . . . . . . . . . . . . 149
5.5.2 Reduced Model Order. . . . . . . . . . . . . . . . . . . . . . . 150
5.5.3 Trajectory Tracking . . . . . . . . . . . . . . . . . . . . . . . . 154
5.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158