Soft computing methods for control and instrucmention

List of AbbreviationsACE Adaptive Critic Element Adaline Adaptive Linear Element ADC Analog to Digital Converter AI Artificial Intelligence ANFIS Adaptive Neural Fuzzy Inference System o

SOFT COMPUTING METHODS FOR CONTROL AND INSTRUMENTATION

Thesis for the degree of Doctor of Science in Technology

Xiao-Zhi Gao

SOFT COMPUTING METHODS FOR CONTROL

AND INSTRUMENTATION

Xiao-Zhi Gao

Dissertation for the degree of Doctor of Science in Technology to be presented withdue permission for public examination and debate in Auditorium S4 at HelsinkiUniversity of Technology (Espoo, Finland) on the 21st of June, 1999, at 12 o’clocknoon

Helsinki University of Technology

Department of Electrical and Communications Engineering

Helsinki University of Technology

Institute of Intelligent Power Electronics

The development of soft computing methods has attracted considerable research interest over thepast decade They are applied to important fields such as control, signal processing, and systemmodeling Although soft computing methods have shown great potential in these areas, they sharesome common shortcomings that hinder them from being used more widely For example, neuralnetworks, a component of soft computing, often suffer from a slow learning rate This drawbackrenders neural networks less than suitable for time critical applications Therefore, the objective ofthis thesis is to explore and investigate the soft computing theory so that new and enhanced meth-ods can be put forward The applications of soft computing in control and instrumentation are alsostudied to solve demanding real-world problems

In this work, the existing soft computing techniques have been enhanced, and applied to controland instrumentation areas First, new soft computing methods are proposed A Modified ElmanNeural Network (MENN) is introduced to provide fast convergence speed Based on Muller’smethod, we propose a new reinforcement learning method, which can converge faster than theoriginal algorithm As a fusion of fuzzy logic and neural networks, a new fuzzy filter using the self-organizing map to fine tune the membership functions is studied The new soft computing schemespresented in this thesis improve the performance of those earlier methods

Second, we study the MENN-based identification and control problems A dynamical systemidentification scheme as well as a trajectory tracking configuration using the MENNs are discussed,respectively Our MENN-based identification structure belongs to the ‘black box’ identificationcatalogue It has the advantageous feature of not knowing the exact order of the system The in-verted pendulum is utilized here as a testbed for the MENN-based trajectory control scheme It isshown that neural networks are very efficient in dealing with nonlinear system identification andcontrol In addition, they need little prior information of the plant to be identified or controlled.However, the existence of local minima, under-fitting, and over-fitting may reduce the identifica-tion and control accuracy

Third, the applications of soft computing methods in velocity and acceleration acquisition inmotion control systems are discussed The aforementioned fuzzy filter is applied to filter out thevelocity noise in the feedback loop without introducing any harmful delay This could lead to abetter servo control performance Moreover, we construct a neural network-based acceleration ac-quisition scheme to obtain clean and delayless acceleration signals Our method has the advantage

of implicit adaptation It can be used for any slowly altering velocity signal, which overcomes thedrawback of polynomial predictor-based approaches.

Finally, the power prediction and regulation in mobile communications systems are studied withthese soft computing methods An optimal neural predictor is selected by applying the PredictiveMinimum Description Length (PMDL) principle A Temporal Difference (TD)-based multi-stepahead prediction scheme is also considered for the fading signals Simulations demonstrate that theneural predictors offer better results than conventional filters Their weakness is the accompanyinghigh computational complexity We introduce an MENN-based power controller at the base station,which takes advantage of the inverse radio channel model On the other hand, the efficiency of thepower controller employed is clearly limited by the single-bit command transmission mode Mean-while, an Embedded Fuzzy Unit (EFU) is proposed to provide versatile alternatives The EFU caneffectively tackle the bottle-neck of incremental command transmission mode, and thus achievebetter power regulation Additionally, a comparison between the conventional and soft computing-based power control methods is made This research gives us useful guidance in determining appro-priate power regulation configurations in terms of effectiveness and complexity

In conclusion, the theory and applications of soft computing methods are studied in this thesis.Nevertheless, our research is not aiming at implementation of the proposed schemes Therefore, thevalidation is verified only by numerical simulations All the simulations are based on simplified ap-plication models without consideration to practical details

It was a great pleasure for me to work on this thesis I hope, too, readers will find it useful and fortable to read

com-First and foremost, I am truly indebted to my advisor, Professor Seppo J Ovaska, who guided

me throughout the whole of my research work Professor Ovaska has proposed countless tions during this thesis writing procedure as well as through my course study I have learnt quite alot from his comments, which are always inspiring and fruitful I also thank him for providing mewith the invaluable opportunity enabling me to come to Finland and study for my D.Sc (Tech.) de-gree at the Helsinki University of Technology Here, I can only extend my best wishes to him in hisfuture career Thank you very much indeed, Seppo

sugges-And, I want to thank all the personnel at the laboratory of Electric Drives and Power ics Professor Jorma Kyyr is especially thanked for his warm-hearted help Secretary Leena

Electron-V is nen deserves my gratitude for helping me cope with practical matters including all the culties that a student may encounter in a foreign country Laboratory manager Ismo Vainiom ki andlaboratory technician Ilkka Hanhivaara are thanked for their efficient efforts in creating such a freshand pleasant research environment I really enjoy working in this laboratory

diffi-I am very grateful to my colleagues, Jarno Tanskanen, Sami V liviita, Vlad Grigore, and AdrianDumitrescu, with whom I had so many helpful discussions Special thanks go to Jarno Tanskanenand Sami V liviita for their cooperative work in our joint publications

I am also very much obliged to the secretary of the Graduate School of Electronics, munications, and Automation (GETA), Marja Lepp harju, for her kind assistance in my graduatestudy at GETA

Telecom-Joe O’Reilly is thanked for checking the language used in this thesis All the errors possiblyremaining in the text have been introduced by me alone at the final stages of revision

Last but not the least, I want to say a heart-felt ‘thank you’ to my parents and brother They play

an important role in my life, study and work, both morally and financially

The author wishes to express his deep thanks to the Center for International Mobility (CIMO)and GETA for their financial support

Otaniemi, May 1999

Xiao-Zhi Gao

Table of Contents

1 Introduction……… 1

1.1 Definition of Soft Computing……… 2

1.2 Intelligent Control……… 6

1.3 Aim of This Dissertation……… 8

2 Introduction to Soft Computing Methods……….12

2.1 Neural Networks……… 12

2.1.1 Back-Propagation Neural Network……… 13

2.1.2 Elman Neural Network……… 16

2.1.3 Self-organizing Map……… 19

2.2 Fuzzy Logic……… 22

2.2.1 Basic Theory of Fuzzy Logic Systems……… 22

2.2.2 Fuzzy Logic-based Control……… 26

2.2.3 Fuzzy Neural Network……… 30

2.3 Reinforcement Learning……… 33

2.3.1 Single-step-ahead Predictor-based Critic-Actor Algorithm……… 35

2.3.2 Temporal Difference Method-based Prediction……… 38

3 Related Research……… 42

3.1 Predictive Filtering Methods and Their Applications……… 42

3.1.1 Predictive Filtering Methods……… 42

3.1.2 Power Prediction in Mobile Communications Systems……… 46

3.1.3 Acceleration Acquisition in Motor Control Systems……… 49

3.2 Neural Network-based Dynamical System Identification……… 53

3.2.1 Neural Network-based Forward Model Identification……… 54

3.2.2 Neural Network-based Inverse Model Identification……… 57

3.3 Neural Network-based Control Applications………60

3.3.1 Neural Network-based Control Schemes……… 60

3.3.2 Power Regulation in Mobile Communications Systems……… 66

3.3.3 Inverted Pendulum Control……… 71

4 Summary of Publications……… 78

4.1 Neural Network-based System Identification Techniques……… 78

4.1.1 Publication [P1]……… 78

4.2 Neural Network-based Control Methods……… 83

4.2.1 Publication [P2]……….83

4.3 Soft Computing Methods in Instrumentation……….87

4.3.1 Publication [P3]……….87

4.3.2 Publication [P4].……… 90

4.3.3 Publication [P5] ……… 93

4.3.4 Conclusions of Publications [P3]—[P5]………96

4.4 Power Prediction in Mobile Communications Systems……… 96

4.4.1 Publication [P6]……….96

4.4.2 Publication [P7]……… 101

4.4.3 Conclusions of Publications [P6]—[P7]……….103

4.5 Power Control in Mobile Communications Systems……… 103

4.5.1 Publication [P8]……… 103

4.5.2 Publication [P9]……… 107

4.5.3 Publication [P10]……… 111

4.5.4 Conclusions of Publications [P8]—[P10]……… 115

4.6 Contribution of the Author……… 116

5 Conclusions and Discussion……….119

5.1 Main Results……….119

5.2 Scientific Importance of the Author’s Work……… 120

5.3 Topics for Future Research……….….… 122

6 References………124 Appendix A: Publications [P1]—[P10]

Appendix B: Errata

List of Publications

This thesis consists of an introduction and the following ten publications which are referred to by[P1], [P2], …, [P10] in the text:

[P1] X Z Gao, X M Gao, and S J Ovaska, “A modified Elman neural network model with

application to dynamical systems identification,” in Proceedings of the 1996 IEEE

International Conference on Systems, Man, and Cybernetics, Beijing, P R China, October

1996, pp 1376-1381

[P2] X Z Gao, X M Gao, and S J Ovaska, “Trajectory control based on a modified Elman

neural network,” in Proceedings of the 1997 IEEE International Conference on Systems,

Man, and Cybernetics, Orlando, FL, October 1997, pp 2505-2510.

[P3] X M Gao, X Z Gao, and S J Ovaska, “Power command enhancement in mobile

communication systems using an embedded fuzzy unit,” in Proceedings of the 1997 IEEE

International Conference on Systems, Man, and Cybernetics, Orlando, FL, October 1997,

pp 4364-4369

the acquisition of acceleration from noisy velocity signal,” in Proceedings of the 1998 IEEE

Instrumentation and Measurement Technology Conference, St Paul, MN, May 1998, pp.

935-940

[P5] X Z Gao and S J Ovaska, “A new fuzzy filter with application in motion control

systems,” in Proceedings of the 1999 IEEE International Conference on Systems, Man, and

Cybernetics, Tokyo, Japan, October 1999, IN PRESS.

[P6] X Z Gao, “A temporal difference method-based prediction scheme applied to fading power

signals,” in Proceedings of the 1998 IEEE International Joint Conference on Neural

Networks, Anchorage, AK, May 1998, pp 1954-1959.

[P7] X M Gao, X Z Gao, J M A Tanskanen, and S J Ovaska, “Power prediction in mobile

communication systems using an optimal neural-network structure,” IEEE Transactions on

Neural Networks, vol 8, no 6, pp 1446-1455, November 1997.

[P8] X M Gao, X Z Gao, J M A Tanskanen, and S J Ovaska, “Power control for mobile

DS/CDMA systems using a modified Elman neural network controller,” in Proceedings of

the 47th IEEE Vehicular Technology Conference, Phoenix, AZ, May 1997, pp 750-754.

[P9] X Z Gao, X M Gao, and S J Ovaska, “Fast reinforcement learning algorithm for power

control in cellular communication systems,” in Proceedings of the 1997 IEEE International

Conference on Systems, Man, and Cybernetics, Orlando, FL, October 1997, pp 3883-3888.

[P10] X Z Gao and S J Ovaska, “Comparison of conventional and soft computing-based control

methods in a power regulation application,” in Proceedings of the 1998 IEEE International

Conference on Systems, Man, and Cybernetics, San Diego, CA, October 1998, pp

2075-2082

List of Abbreviations

ACE Adaptive Critic Element

Adaline Adaptive Linear Element

ADC Analog to Digital Converter

AI Artificial Intelligence

ANFIS Adaptive Neural Fuzzy Inference System or

Adaptive Network-based Fuzzy Inference SystemASE Associative Search Element

CMAC Cerebellar Model Articulation Controller

DCL Differential Competitive Learning

DS/CDMA Direct Sequence Code Division Multiple AccessDSP Digital Signal Processing

FIR Finite Impulse Response

IIR Infinite Impulse Response

IMC Internal Model Control

LSN Linear Smoothed Newton

MIMO Multiple-Input and Multiple-Output

MDL Minimum Description Length

MENN Modified Elman Neural Network

MLP Multilayer Perceptron

MRAC Model Reference Adaptive Control

RLSN Recursive Linear Smoothed Newton

SNR Signal to Noise Ratio

SOM Self-Organizing Map

d Vector of desired output of the neural network

d i Desired output of the neural network or

Euclidean distance in the self-organizing map

e Feedback error in control systems or

Identification error

∆e Feedback error change

E Cost function of the neural network

˙e First order derivative of the feedback error

˙˙

e Second order derivative of the feedback error

f( )⋅ Function relationship between reinforcement signal and control actions

Force applied to the cart

g Gravity acceleration

h( )⋅ Function of fuzzy rule base

H L N( )z Transfer function of the Newton predictor for polynomial degree L and the number

of prediction steps N

I MENN Input set of the MENN

j Index variable

J Trajectory control performance index of the Elman neural network-based controller

or

Instant power regulation index

J* Cumulative trajectory control index of the Elman neural network-based controller or

Cumulative control criterion for power regulation

Iteration step index in neural network training or

Scaling constant in reinforcement learning

K Length of the Newton predictor

l Number of nodes in the hidden layer in neural network or

Index variable for predictor

l p Half length of the pole in the inverted pendulum

L Polynomial degree assumed for the input signal

m Number of nodes in the input layer in neural network or

Length of a sequence or Index variable for predictor or

Order of the plant output

m c Mass of the cart in the inverted pendulum

m p Mass of the pole in the inverted pendulum

Number of support values

n Number of nodes in the output layer in neural network or

Order of the input of the plant

n f Number of fuzzy inputs

n r

Number of fuzzy rules

N Number of prediction steps ahead or

Order of the neuro predictive filter

NG White noise gain of the Newton predictor

n Noise in the input signal of the predictor

N c Neighborhood in the self-organizing map

net q Input of node q in the hidden layer

Output of node i in layer l in the ANFIS

O Context Output set of the context nodes in the MENN

O MENN

Output set of the MENN

o c_ i Output of context node i in the Elman neural network

P Consequent parameters in the ANFIS or

Transmitting signal power

P Ref Desired power level for the received power at the base station

Number of membership functions for each input in the ANFIS

q q Number of quantization levels

R General variable form of the reinforcement learning signal

Ref Reference signal for closed loop control systems

R i Fuzzy reasoning rule i

S Oscillator coefficients

t Discrete sampling point

T Length of training sequence or

General variable form of control action in reinforcement learning

u nn

Identification output of the neural network-based inverse model

u∗ Optimal output for the action network to learn in reinforcement learning

˜

u Actual control applied to the plant in reinforcement learning or

Output of the fuzzy power command enhancement unit

u Approximation of u∗ by secant method

∆u Output of the stochastic unit

∆u FLC

Incremental output of the fuzzy power controller

v qj Weight connecting node j in the input layer with node q in the hidden layer in the BP

w General presentation of weights in neural networks

W Both the weights v qj and w iq

wi Weights in the self-organizing map

w new General presentation of updated weights in neural networks

w old

General presentation of previous weights in neural networks

w iq Weight connecting node q in the hidden layer with node i in the output layer in the

BP neural network

∆wiq Update change of w iq

w1i j, Weight connecting node i in the input layer to node j in the hidden layer in the

Elman neural network

w2i j, Weight connecting node i in the hidden layer to node j in the output layer in the

Elman neural network

w3i j, Weight connecting context node i to node j in the hidden layer in the Elman neural

network

w4i j, Weight connecting context node i to node j in the output layer in the Elman neural

network

W1 Weight set of w1i j,

Sequence samples

˙x Velocity of the cart in the inverted pendulum

˙˙

x Acceleration of the cart in the inverted pendulum

x Input pattern for the neural network

Input of node i at iteration k in the Elman neural network

x i f Linguistic input variables

y Clean primary signal or

General variable or

Trajectory output of the plant

y Output of the predictor

ˆy Identification output of the Elman neural network or

Noisy input signal of the predictor

y f Linguistic output of the fuzzy rule base

y m Output of the reference model in MRAC

y n Prediction output of the neural network model in IMC

y nn Neural network identification output

y p Output response of the plant

y d Reference trajectory

y i Output of node i in the output layer in the neural network

y( )j k Output of node j in the output layer in the Elman neural network at iteration k

Y i

k

( )

Desired output for node i in the Elman neural network at iteration k

z Final outcome of a sequence signal

z q Output of node q in the hidden layer

z−1 Unit delay

z o j Amount of output at quantization level j

z s j Support value at which the membership function reaches the maximum value

z COA* Crisp output of the COA defuzzification method

z MOM* Crisp output of the MOM defuzzification method

θ Angle of the pole in the inverted pendulum

˙

θ Angular velocity of the pole in the inverted pendulum

˙˙

θ Angular acceleration of the pole in the inverted pendulum

λ Scaling constant in reinforcement learning or

Forgetting factor in TD learning

δ oi General back-propagation error term for node i in the output layer

δhi General back-propagation error term for node i in the hidden layer

η Learning rate of the neural network

φ Gaussian density function or

Inverse function of ϕ

ϕ Function relationship realized by the neuro predictor or

General function of a system

ϕ−1 Inverse function of ϕ

ˆ

ϕ Approximated mapping of the system realized by the neural network

ˆ

ϕ−1 Approximated inverse mapping of the system realized by the neural network

ϑ Mapping realized by the fuzzy command enhancement unit

σ Variance of the output of the stochastic unit

µA Fuzzy membership function A

µc Coefficient of friction of cart on track

µC Fuzzy membership function C

µF Fuzzy membership function F

µp Coefficient of friction of pole on cart

1 Introduction

Soft computing, as pointed out by Dr Zadeh, is not a single methodology [Zad94] Instead, it is afusion of several methodologies, i.e., neural networks, fuzzy logic, and genetic algorithms Different

from conventional (hard) computing, soft computing takes advantage of intuition, which implies that

the human mind-based intuitive and subjective thinking is realized in soft computing The tion of applying the human intuition is that a large number of real-world problems cannot be solved

motiva-by hard computing methods due to the fact that either they are too complex to handle or they not be described or catalogued by analytical and exact models However, in some cases, human ex-perts are marvellously successful in dealing with these problems, e.g., face recognition in a noisybackground Dr Zadeh emphasises that precise measurement and control approaches are not always

can-effective in coping with such difficult problems, but perception can often help [Zad98] Therefore,

the goal of soft computing is to exploit the imprecision and uncertainty in human decision makingprocedure, and achieve simple, reliable, and low-cost solutions

Currently, the techniques in control and instrumentation fields are facing difficulties in meetingthe growing needs of modern industry For example, numerous nonlinear and time-variant plantscannot be efficiently stabilized or regulated using classical control methods Additionally, as for theacceleration acquisition in motion control systems, the existing signal processing techniques fail to

provide clean and delayless acceleration estimates because of the inherent noise in the measured

ve-locity For instance, conventional Finite Impulse Response (FIR) and Infinite Impulse Response(IIR) filters always introduce some delay in the filtered output It is advantageous to apply softcomputing methods in these cases, since soft computing offers us a totally new perspective by pro-viding a set of techniques to solve practical problems in which ambiguity and uncertainty prevail[Jan97]

Fuzzy logic, a branch of soft computing, has been an active partner in the process control for atleast the last two decades [Dri93] Besides control engineering, fuzzy logic in instrumentation isdrawing great research interest [Rus96] Neural networks are also investigated in control and instru-mentation such as on-line tuning of controller parameters [Kaw98], friction compensation in servomotion control systems [Gao99], and Analog to Digital Converter (ADC) resolution enhancement[Gao97a] The application of soft computing, in fact, covers a variety of application areas Besidescontrol and instrumentation, other important aspects include speech recognition [Kom92], signalprocessing [Cic93], telecommunications [Yuh94], power electronics systems [Dot98, pp 143-185],and system diagnosis [Cho92] Recent advances of soft computing methods and their applications

in engineering design and manufacturing can be found in [Roy98] With the rapid development ofhardware platforms, e.g., Digital Signal Processing (DSP) and neural networks chips, it is becomingmore feasible to apply soft computing methods into practice.

1.1 Definition of Soft Computing

Soft computing is a collection of methods to construct computationally intelligent systems By telligent systems’, we here mean those systems that are capable of imitating the human reasoning

‘in-process as well as handling quantitative and qualitative knowledge It is well known that the

intelli-gent systems, which can provide human like expertise such as domain knowledge, uncertain ing, and adaptation to a noisy and time-varying environment, are important in tackling practicalcomputing problems Specifically, in the modern control system design and analysis, there is apromising trend going on to employ some heuristic methods that can benefit from human experts,because the currently existing complex plants cannot be accurately described by rigorous mathe-

reason-matical models, and are, therefore, difficult to control using conventional model-based methods.

Meanwhile, in practice, experienced operators are often able to obtain fairly satisfactory controlquality Soft computing is an appropriate candidate for creating these knowledge-based intelligentsystems It has attracted the growing interest of researchers from various scientific and engineeringcommunities during recent years [Lin96]

Basically, soft computing is considered as an emerging approach to computing which parallelsthe remarkable ability of the human mind to reason and learn in a circumstance of uncertainty andimprecision The pioneer of fuzzy logic, Dr Zadeh, has pointed out that ‘the guiding principle ofsoft computing is to exploit the tolerance for imprecision, uncertainty, and partial truth to achievetractability, robustness, low solution cost, better rapport with reality’ [Zad92] In contrast withhard computing methods, which only deal with precision, certainty, and rigor, soft computing is ef-fective in acquiring imprecise or sub-optimal but economical and competitive solutions In short,because of its unique feature in coping with real-world problems, e.g., intelligent control, decisionmaking support, nonlinear programming and optimization, soft computing has drawn increasing re-search attention from people of different backgrounds [Jan97]

In general, soft computing methods consist of three essential paradigms: neural networks[Hay98], fuzzy logic [Wan97], and genetic algorithms (evolutionary programming) [Gol89] Never-theless, soft computing is an open instead of conservative concept That is, it is evolving those rele-vant techniques together with the important advances in other new computing methods such as arti-

ficial immune systems [Das98] To condense the following presentation, we concentrate only on theabove three principal methods In the triumvirate of soft computing, neural networks are concernedwith adaptive learning, nonlinear function approximation, and universal generalization; fuzzy logicwith imprecision and approximate reasoning; and genetic algorithms with uncertainty and propaga-tion of belief Table 1.1 lists these three methodologies together with their advantages.

Table 1.1 Soft computing constituents

Neural Networks Learning and Approximation

Fuzzy Logic Approximate Reasoning

Genetic Algorithms Systematic Random Search

However, in soft computing, they are complementary rather than competitive More precisely, it

is advantageous to employ neural networks, fuzzy logic, and genetic algorithms in combination stead of exclusively A typical example to support this argument is the popular fuzzy neural net-work model, which takes advantage of the capabilities of both fuzzy logic and neural networks[Buc94] The fuzzy neural network is constructed to merge fuzzy inference mechanism and neuralnetworks into an integrated system so that their individual weaknesses are overcome Normally, theneuro-fuzzy technique can have the same topology with the feedforward neural network, i.e., nodesand layers On the other hand, the node functions inside are replaced with fuzzy membership func-tions such as Gaussian functions And, the commonly used back-propagation learning algorithm isapplied to adjust the parameters of these fuzzy membership functions In this way, the fuzzy neu-ral network retains the approximate inference characteristics and imprecise information processingcapability of fuzzy logic, meanwhile it also has the strength of adaptation and generalization by in-troducing the learning algorithm from neural networks It has found many application prospects,e.g., in image processing [Gho93] and speech recognition [Qi93] A growing number of consumerproducts, for example, washing machines and air conditioners, are released with the embeddedneuro-fuzzy technique The same principal idea applies to other kinds of hybrid schemes amongneural networks, fuzzy logic, and genetic algorithms, which are in fact already available [Tak97].Refer to Figure 1.1 for other alternatives

in-Fuzzy Logic

Genetic Algorithm Neural Network

Genetic-Neuro

Figure 1.1 Framework of soft computing

We only present two representative examples, genetic-neuro and genetic-fuzzy techniques here

In general, a genetic algorithm is a derivative-free and stochastic optimization method [Man96] Itsorientation comes from ideas borrowed from natural selection as well as the evolutionary process

As a general purpose solution to demanding problems, it has the distinguishing feature of parallelsearch and global optimization In addition, genetic algorithm needs less prior information about theproblems to be solved than the conventional optimization schemes, such as the steepest descentmethod, which often require the derivative of the objective functions [Jan97, pp 129-168] Thus, it

is attractive to employ a genetic algorithm to optimize the parameters and structures of neural works and fuzzy logic systems instead of using the back-propagation learning algorithm alone Forinstance, to optimize the weights of the neural network for a specified problem, we can first encodeeach weight of the neural network into a binary bit string Next, we concatenate these sub-strings

net-into a complete string, which is usually called a chromosome A fixed number of the chromosome candidates forms one generation The value of the cost function to be optimized of every chromo-

some is then calculated and assigned to the chromosome as its ‘fitness’ The cost function is alwaysproblem dependent Based on individual fitness value, genetic algorithm uses the operators such as

reproduction, crossover and mutation to get the next generation that may contain chromosomes

providing better fitnesses This evolutionary process evolves from generation to generation until apreset cost function criterion has been reached Due to the unique advantages of genetic algorithms,i.e., derivative free, stochastic, and global search [Tan96a], this kind of genetic-neuro technique is

suitable for some special situations, where no derivative or other auxiliary knowledge of the costfunction is available for the neural network back-propagation learning algorithm Additionally, since

the genetic algorithms are all based on probabilistic rather than deterministic search, the

genetic-neuro technique overcomes the severe shortcoming of applying pure back-propagation learning rithm to train the neural networks The steepest descent-based method is easily trapped into thelocal minima in the nonlinear search space of weights

algo-For the genetic-fuzzy scheme, the genetic algorithms are applied to get optimal fuzzy inferenceparameters [Far98] We point out that not only the parameters of the fuzzy inference structure,such as the antecedent and consequent coefficients, can be optimized by the genetic algorithms, butalso the tailoring of the fuzzy reasoning rules, e.g., adding new rules and deleting invalid ones, is ap-propriate for the utilization of the genetic algorithms In a word, genetic algorithms play an impor-tant role in the parameter and structure learning in both the genetic-neuro and genetic-fuzzy tech-niques However, it is to be emphasized that the combination of soft computing methods is notonly limited on the algorithm level as discussed previously There are also potential fusion alterna-tives on the system level For example, in a hierarchical system, a fuzzy logic controller and a neuralnetwork predictor can act independently and co-operatively with different tasks attributed by thetop level process supervisor We will demonstrate the effectiveness of such a hybrid scheme by theillustrative example of power regulation in a mobile communications system in the following chap-ters

Among the attempts to mimic the human brain intelligence, soft computing is not the first trial

In fact, soft computing has some similarities with the conventional expert systems in Artificial telligence (AI) [Rus95] Their common goal is to explore and realize machine intelligence Basically,expert systems target to imitate intelligence in the form of language expressions or symbolic rules

In-On the other hand, there are no symbolic manipulations in soft computing This feature makes itfree from the handicap inherent in the expert systems-oriented classical symbolicism, which can re-

sult in the ‘dimension curse’ Instead, the knowledge acquisition procedure in soft computing is

based on learning from practical data samples as well as operator experience Neural networks areoften trained by the application data from measurement or provided by the supervisor The antece-dent and consequent of the mostly used IF-THEN rules in the fuzzy inference are interpreted bythe linguistic variables arising from the knowledge of the operation experts Random but globalsearch using genetic algorithms is preferred in obtaining the optimal solution Therefore, soft com-puting can also be viewed as a kind of data driven intelligent technique

1.2 Intelligent Control

Over the past four decades, we have observed numerous successful applications and tions of conventional control, ranging from autonomous robotics to chemical process and air trafficcontrol The classic control approaches are based on analytical methods derived from thephysical models, such as Laplace transformation and linear state space Bode diagrams, Nyquist andLyapunov stability criteria, and root-locus methods are still widely utilized in practical control en-gineering However, control of a wider class of modern complex systems, e.g., time-varying, nonlin-ear, multi-variable, and multi-loop industrial systems, is difficult with these conventional tech-niques An interesting example is the famous control benchmark truck backer-upper problem Toback a trailer truck when applying the classical control scheme, we must first write out the full-defined mathematical model of the truck including the dynamical kinematics between the displace-ment of the truck with the angels of the truck and the trailer The finalized model is instinctuallynonlinear Once this step is finished, we have to solve the equations with some numerical methods,because normally there are no straightforward analytical methods for nonlinear systems Neverthe-less, even using the numerical methods, the acquisition of the approximated solutions is still unprac-tically time consuming The underlying reason is due to the existing high dimensional input variablesand strong nonlinearity of the model On the other hand, for the skilled truck drivers, this work isreasonably easy They just look at the distance between the truck and the dock, as well as the angle

implementa-of the truck and trailer, and based on this vague information together with a few reasoning rules,they make their judgements to turn the truck a little bit in the right direction, and repeat the aboveprocess until the truck is backed into the dock Thus, it is clear that intelligent, for example, softcomputing-based, methods are advantageous for such kind of problems Nguyen has applied a two-layer feedforward network to control the above simulated truck [Ngu90] Kong proposes a fuzzysystem approach based on the Differential Competitive Learning (DCL) to get an even improvedresult [Kon92] In conclusion, the demand for higher performance criteria and economical solutionsnecessities the invention of intelligent control systems

There is no formal or single definition of an intelligent control system Generally, an intelligentsystem should satisfy the famous Turing test, which can be concisely expressed as follows: if a manand a machine (or a program) perform the same task, then if one cannot distinguish between the ma-chine and the human by examining only the nature of their performances, the machine is said to beintelligent, otherwise not [Tur50] However, intelligent control systems can be broadly described asthe use of artificial intelligence-related methods to design and implement automatic control systems

Dr Fu first introduced the term ‘intelligent control’, and initiated studies in this area as early as the1950s [Fu71] At the initial stage of the development of intelligent control, there were tight ties be-tween artificial intelligence and automatic control The advances in computer science, especially op-erations research, also contributed to intelligent control during the years that followed The conse-quence is the study of cybernetics, robotics, and learning machines such as Michie’s broom balancer

‘BOXES’ [Mic68] Figure 1.2 gives an illustrative diagram of the relationship between the intelligentcontrol and these four aforementioned fields

communications Automatic Control

Artificial Intelligence

Intelligent Control

management planning coordination

object oriented design distributed processing

feedback dynamics

learning memory heuristics

Figure 1.2 Techniques employed in intelligent control [Bro94, pp 5]

Today, several AI methods have been well established Expert systems are applied in many plication areas including dynamic decision making and medical diagnosis [Rus95] Soft computing isthe most prominent AI technique in the control field Modern control system design and implemen-tation face three main difficulties [Nar91]: first, the heavy computational complexity, which thenew control methods require The second is the presence of nonlinear systems with a large number

ap-of degrees ap-of freedom [Slo91] The third is the uncertainty that includes varying parameters (in boththe systems to be controlled and controllers themselves) and environment Fuzzy logic and neuralnetworks are already utilized in various control systems, for example, washing machines, ship navi-gation, subway train control, and automobile transmission [Pas97] Fuzzy logic theory was firstapplied successfully to control systems by Mamdani in 1974 [Mam75, Mam77] In these applica-tions, soft computing overrides the classical control methods in many aspects, such as algorithmsimplicity and system robustness Fuzzy control can effectively combat the noisy and impreciseenvironment The knowledge from a human operator is embedded into the initial design stage of thefuzzy controllers, which efficiently strengthens their robustness against noise and parameter varia-tion It has been demonstrated that neural networks are well suited for the control of complex dy-namical systems [Mil87, Mil90b] The principle of neuro-control is based on learning The learningcharacteristics of neuro controllers distinguish them from classical controllers with invariant struc-tures and parameters in a changing operating environment, and can thus provide better results Goodoverviews of the recent research work on neuro-control are given by Miller et al [Mil90a], Hunt et

al [Hun92], and Narendra [Nar96] Moreover, the study of combining fuzzy logic and neural works to form more intelligent control systems remains to be a popular and highly potential topic[Bro94] In addition, genetic algorithms are widely used in optimizing the parameters of diversekinds of controllers [Wan94, Tan96b]

net-1.3 Aim of This Dissertation

The general aim of this dissertation is to explore and advance the theory and applications of softcomputing Although it has been studied intensively, soft computing has some severe drawbacks,which prevent it from being applied to time-critical applications For example, neural networks areproven to be powerful approximation tools; however, it typically takes a long training time andmany iteration steps for a neural network to converge This disadvantage apparently hinders neuralnetworks from meeting the strict demand of some real-time applications, such as on-line dynamicalsystem identification and control Even with the appearance of commercial neural network proces-sor chips, this difficulty is only partly overcome Nevertheless, hardware implementation of neuralnetworks will easily lead to expensive systems The same problem also exists in the field of rein-forcement learning, a branch of neural networks In fact, slow convergence speed is the principalreason why there are not so many practical applications of reinforcement learning Hence, one of themain topics of this dissertation, the theoretical research part, is to develop new and faster methods,

as well as to enhance the available soft computing techniques

Neural networks were originally proposed for the purpose of mimicking and further studyingthe working principle of the human brain They are, however, not suitable to apply directly foridentification and control applications For instance, the most commonly used static back-propagation neural network does not have the necessary dynamical characteristics needed for identi-fying dynamical systems Thus, some structure and learning algorithm modifications must be made

on the original neural networks to make them more flexible and applicable This kind of ment is important for increasing the efficiency and feasibility of neural networks, and will, therefore,broaden the corresponding application potential In the theoretical part of this dissertation, based onthe same thinking, we propose some new variants of the existing soft computing methods Figure1.3 illustrates the elements of the theoretical study

Fast Reinforcement Learning

Modified Elman Neural Network

New Fuzzy Logic Filter

Theoretical Study

Figure 1.3 Elements of the theoretical study of soft computing in this dissertation

More precisely, we propose a new fast reinforcement learning algorithm inspired by the idea ofMuler’s method in order to get a more accurate approximation of the desired control actions, whichwould be appropriate for the neural network to learn The training procedure of the reinforcementlearning is accelerated in this way As mentioned above, dynamical system identification and control

require the necessary internal dynamics in the neural networks Consequently, we propose a fied Elman neural network, which has these enhanced dynamical characteristics This modified El-man neural network is constructed by adding additional weights connecting the context nodes withthe output nodes We derive the corresponding learning algorithm for the network as well With thisfeature, the convergence speed of the modified Elman neural network is increased greatly so that itcould be applied for on-line identification and control By using the self-organizing map to obtainthe membership function parameters (the center locations of the membership functions), we intro-duce a new fuzzy logic-based filter This new fuzzy filter behaves better than the conventionalfuzzy filters [Wan93b] with respect to the noise filtering in motion control systems The theoreticalstudy of soft computing methods sets up the foundation for the following application study in thisdissertation In that part, the effectiveness of these new soft computing methods proposed is veri-fied by numerical simulation experiments with various backgrounds.

modi-The second topic of this dissertation is to investigate the applicability of soft computing tosome real-world problems We illustrate the structure of the application study of this dissertation inFigure 1.4 There are three principal elements in the control and instrumentation fields in the appli-cation study part Neural networks, reinforcement learning, and fuzzy logic have been applied to theprediction and control of fading power signal in mobile communications systems The power signalprediction and regulation problem in mobile communications systems is a challenging testbed forsoft computing methods We explore the properties of the neuro power controller and predictor, aswell as the novel fuzzy power command enhancement unit with a simplified radio channel model

We also propose a reinforcement learning-based power regulation configuration Simulation parison reveals that soft computing can provide better system performance than the conventionalapproaches Note that the mobile communications system is used here purely for validation pur-poses Only the simplified mobile channel model is taken into consideration Discussions of thecommunications-related technical details are beyond the scope of this study Under the topic of ve-locity and acceleration acquisition in motion control systems, the new fuzzy logic filter is applied toprovide an estimated acceleration signal for the feedback controller From the motor control point ofview, accurate acceleration is desirable in obtaining robust speed and position regulation In addition,

com-we also study the general dynamical system identification and control problems with our modifiedElman neural network All the application research is based on computer simulations using simpli-fied system models including the mobile channel, inverted pendulum, and motor drive We employthe straightforward mathematical models derived from the underlying principles of the plants Thepossible implementation of the new algorithms together with these presented schemes is, on the

other hand, not considered, because the main goal of this dissertation is to develop and investigatethe theory and applications of soft computing methods rather than design practical implementa-tions However, the work in this thesis should be of interest to those working in soft computingtheory research as well as control and instrumentation applications areas The simulation resultsreported will be beneficial in the building of realizable and reliable solutions to real-world problems.

Mobile Phone Power Prediction and Control

Velocity and Acceleration Acquisition

Dynamical Systems Identification and Control

Application Study

Figure 1.4 Elements of the application study of soft computing in this dissertation

2 Introduction to Soft Computing Methods

In this chapter, we review three essential techniques of soft computing; neural networks, fuzzylogic, and reinforcement learning These three methods are used in the original publications [P1]—[P10] This chapter provides the readers with necessary background information on soft computingmethods The basic knowledge of neural networks is first presented in Section 2.1 Three typicalneural networks, i.e., Back-Propagation (BP) neural network, Elman Neural Network (ENN), andSelf-Organizing Map (SOM) are discussed We describe their structures as well as the correspond-ing learning algorithms The fuzzy logic theory is summarized in Section 2.2 Specifically, we reviewthe working principle of fuzzy logic control systems in that section Finally, in Section 2.3, the rein-forcement learning method is investigated Two reinforcement learning schemes, single-step aheadprediction-based Actor-Critic and multi-step ahead prediction-based Temporal Difference (TD)learning are discussed We apply the above three soft computing methods to the control and instru-mentation fields, which will be discussed in Chapter 3 and Chapter 4

2.1 Neural Networks

Artificial neural networks [Rum86, Hec90], which are commonly referred to as ‘neural networks’,were first studied by a desire to understand and imitate the function of the human brain [Min69].Although significant advance has been achieved in the area of conventional expert systems for mim-icking human intelligence, there is still a long way to go for the current computational techniquesbefore realizing the capability of carrying out certain man-dependent tasks Nowadays, when siliconchips are many times faster than the operation speed of biological cells, a typical human activity,e.g., face recognition with a noisy background, which only requires the order of 100 ms to be ac-complished in the brain will still run on a serial-programming computer for days The reason for thiscan be explained by several factors: the massively connected synapses among the biological neurons,the highly parallel computing structure, and the imprecise information processing capability of thebrain [Rus79] Therefore, neural networks are constructed as simplified mathematical models, whichcan resemble the organizational principles of the human brain on the level of microscopic biologicalmodels By taking advantage of these principles, neural networks are considered as a kind of newgeneration intelligent information processing systems [Hus93] They have the advantageous capa-bilities of learning from training data, recalling memorized information, and generalizing to the un-seen patterns These capabilities do show great potential in such application areas as control[Hun92], signal processing [Wid88], and pattern recognition [Bis95]

There are altogether more than one hundred neural network structures and algorithms proposed

by people from varying standpoints [Her91] However, the most widely used neural networks arelimited to just a few We only present three typical examples here, all used later in this thesis Theyare the Back-Propagation (BP) neural network, Elman Neural Network (ENN), and Self-OrganizingMap (SOM) These three neural networks will be applied to the applications of power predictionand control in the mobile communications systems, as well as the design of a new fuzzy logic-basedfilter for the motion control systems

2.1.1 Back-Propagation Neural Network

The BP neural network, which is also called feedforward or multi-layer perceptron network, is animportant class of neural networks due to its simple topology and powerful approximation capabil-

ity It is well known that simple perceptron can only solve linearly separable or linearly

independ-ent problems [Wid90] For those linearly nonseparable problems, such as the XOR problem, it is,however, required that the neural networks should have an appropriate intermediate representation

of the input patterns by introducing nonlinear hidden layers The construction of the BP neuralnetwork is inspired by this idea A simplified BP neural network is illustrated in Figure 2.1 Weshow the single hidden layer case here, although it is possible to have more hidden layers in the BPneural network

The invention of the back-propagation learning algorithm for the BP neural network is a mark in the development history of neural networks [Wer74] In fact, only after the introduction ofthis learning algorithm, have the powerful properties of neural networks been well recognized, andthe research work of neural networks has attracted the attention of people from the scientific andengineering communities Without loosing the generality, we deduce the BP learning algorithm based

land-on the feedforward network with land-only land-one hidden layer [Lin96, pp 236-240] In Figure 2.1, let

v qj

present the weight connecting node j in the input layer with node q in the hidden layer, and

w iq

pre-sent the weight that connects node q in the hidden layer with node i in the output layer There are

m, l, and n nodes in the input layer, hidden layer, and output layer, respectively Assume

( )x d, resents a pair of training samples;

=

= 1, (2.1)

and it gives the transformed output as:

j

m j

a( ) is denoted as the node activation function of the BP neural network We calculate the input of

node i in the output layer:

m j

m j

The above equations show the feedforward propagation procedure from the input to the output of

the BP neural network The basic BP learning algorithm is based on these equations as well as the

following error back-propagation procedure Next, we define a cost function E( ) W for the BP neural

n

12

12

122

1

2

2 1

iq

i i i i iq

= E = ( )a ( ) = (2.7)

a ( ) is the first order derivative of function a( ) We define, from the above equation, the general

back-propagation error term oi for the output layer by:

oi

i i

net v

i

n iq

Comparing (2.12) with (2.8), we conclude that

hq is determined by oi, which is fed from theoutput layer to the hidden layer Therefore, it is apparent that these general back-propagation er-

rors, oi and

hq, are propagated through the layers to implement the learning algorithm The aboveprocedure can be generalized for more than one hidden layer case Note that we only demonstrate

the pattern training version of the BP learning algorithm in (2.6) to (2.12), which means the BP

neu-ral network updates its weights immediately after a pair of training patterns is provided However,

another alternative training scheme is named batch learning In the batch learning mode, the weights

are adjusted only after all the training patterns have been presented Pattern training occupies the

incremental property that is suitable to apply in on-line applications, while batch training usually

offers better convergence characteristics [Lip87]

It has been proven that a BP neural network with sufficient hidden nodes can approximate anynonlinear function to arbitrary accuracy [Cyb89, Hor89] Therefore, the BP neural network is re-garded as a universal function approximator This makes it a good candidate for signal prediction andsystem modeling In publication [P7], a hybrid neuro predictor consisting of an Adaptive LinearElement (Adaline) and a BP neural network (multi-layer perceptron) is proposed for the prediction

of fading power signals in cellular phone systems The structures of the Adaline and multi-layernetworks are optimized by applying the Predictive Minimum Description Length (PMDL) method

In addition, we introduce a BP neural network-based predictive filter in publication [P4] to acquireaccurate and delayless acceleration in motion control systems

Many factors, on the other hand, can affect the performance of the BP neural network, for ample, the initial weights [Wes92], the number of hidden nodes [Hua91] and hidden layers [Bis95,

ex-pp 121-126], and the learning constant [Jac88] The main shortcoming of the BP neural network isits slow convergence speed Thus, many accelerated algorithms such as fast learning algorithm withadaptive learning rate [Tes88] and conjugate-gradient method-based approach [Kra89] have beenproposed However, the strictly feedforward neural network lacks the dynamical characteristics,because it does not have any memory neurons inside To modeling dynamical systems, it is appro-priate for the neural network to have some recurrent connections, e.g., self-loops and backward con-nections We will discuss such a topology, the Elman neural network, in the next section A TappedDelay Line (TDL) to the input layer, on the other hand, may help in some cases when only a shortmemory is needed

2.1.2 Elman Neural Network

The Elman Neural Network (ENN) is one kind of globally feedforward locally recurrent network

model proposed by Elman [Elm90] It occupies a set of context nodes to store the internal states.

Thus, it has certain unique dynamic characteristics over static neural networks, such as the BP ral network and radial-basis function networks [Moo89] The structure of the Elman neural network

neu-is illustrated in Figure 2.2 z 1 is a unit delay It is easy to observe that the Elman network consists

of four layers: input layer, hidden layer, context layer, and output layer There are adjustableweights connecting each two adjacent layers Generally, it can be considered as a special type offeedforward neural network with additional memory neurons and local feedback [Sas94] The dis-tinct self-connections of the context nodes in the Elman network make it sensitive to the history ofinput data, which is essentially useful in dynamical system modeling [Elm90]

Figure 2.2 Structure of the Elman neural network model.

The training algorithm for the ENN is similar to the BP learning algorithm, which are both based

on the gradient descent principle However, the role that the context nodes play in the error propagation procedure must be taken into consideration in the derivation of the learning algorithm

back-From Figure 2.2, at iteration k, we have the following relationship:

k

i k

_ ( ) = _ ( ), (2.13)

where o c _ and net c i _ are the output and input of context node i, respectively The node activa- i

tion function for the context node is linear We denote

w1i j, as the weight that connects node i in the input layer to node j in the hidden layer,

w2i j, the weight that connects node i in the hidden layer to node j in the output layer, and

w3i j, the weight that connects context node i to node j in the hidden layer m, n, l are the number of nodes in the input, output, and hidden layers, respectively For the input and output of the hidden node j, we have

_ ( )=a( _ ( )) (2.15)

hidden layer is represented by a( ) Therefore, the output of node j in the output layer of the Elman

neural network,

y j k

( ), is given by:

=

=

21

, (2.16)where j=1 2, ,L ,n

Notice that the output of the context node i at the kth training iteration is the one-step-delayed output of the corresponding hidden node i, i.e.,

E( )w (Y i( )k y i( )k )

i n

2 1

w3i j, with the derivative chain rules, we have:

w

o h

o h w

,

E_

E

( ) ( )

( ) ( )

, ( )

y

j k

i k i k

j k i

n

i k i k

j i k i

n

= =1 = =1[ 2 ] (2.21)and

_

( ) , ( )

( )

( ) , ( )

i n

k

T

1 1 ,

, ( )

= = = [ ( ) ], (2.23)where o h_ i( )0 (i =1 2, ,L , )l are the initial states of the ENN Normally, they can just be assumed as:

o h_ i( )0 =0,(i=1 2, ,L , )l (2.24)for simplicity It is clear that the outputs of the context nodes play an important role in the Elmanneural network, and the dynamical characteristics of the ENN could be even improved, if we makefull use of them

Although the Elman neural network has found intensive applications in speech recognition[Elm91] and system modeling [Pha92], its converge speed is usually very slow, and therefore notsuitable for real time applications, such as on-line adaptive control and system identification Later

in this dissertation, we introduce a Modified Elman Neural Network (MENN) by adding new nections between the context nodes and output nodes to increase the convergence speed as well asenhance the dynamical characteristics The algorithm of the MENN with applications in dynamicalsystem identification, inverted pendulum trajectory control, and power regulation in the mobilecommunications systems will be discussed in publications [P1], [P2], and [P8], respectively

con-2.1.3 Self-organizing Map

The Self-Organizing Map (SOM) is an unsupervised learning neural network model, which was firstproposed by Kohonen [Koh82] By ‘unsupervised’, we here mean that differing from the super-vised learning neural network, such as the BP and Elman neural networks, there is no explicit teach-ing signal for the SOM to learn In the SOM, the neurons are placed at the nodes of a lattice, which

is usually one- or two-dimensional The neurons become selectively tuned to various input patterns

or classes of input patterns in the course of a competitive learning process The locations of thetuned neurons tend to become ordered with respect to each other in such a way that a meaningfulcoordinate system for different input features is created The self-organizing map is, therefore, char-acterized by the formation of a ‘topographic map’ of the input patterns The major goal of theSOM learning is to convert patterns of arbitrary dimensionality into the responses of one or twodimensional arrays of neurons, and still preserve the neighborhood relations of the input patterns inthe feature map In other words, the similarity in the input patterns is reflected in the topologicalordering structure of the self-organizing map

An illustrative structure of the SOM network is shown in Figure 2.3, where

neurons The corresponding output of neuron i is denoted as y i y i is, however, classified as either

‘0’ or ‘1’ Note that each component of the input vector x is connected to every node in the SOM.

Figure 2.3 Structure of a two-dimensional self-organizing map network

The SOM network uses the Kohonen’s learning rule [Koh82] to adjust its weights, which can be

described as follows The degree of matching between the training pattern x and neuron i is, in

gen-eral, referred to the Euclidean distance between these two vectors as defined in (2.25):

The ‘winner’ denoted with the output ‘1’ among all the competitive neurons is the one that has the

shortest distance d i On the other hand, the value ‘0’ is assigned to the remaining neurons:

= , , , = , , ,

, (2.27)

where ( ) k is the learning rate To ensure the convergence of training, the size of N k c( ) needs to bemade wide to cover most neurons at the beginning Nevertheless, it should shrink monotonically

with the elapsing time Figure 2.4 illustrates an example of the dynamical variation of N k c( )

Simi-larly with N k c ( ) , ( ) k starts with a value that is very close to unity, thereafter also decreasing

monotonically In addition, ( ) k needs to attain small values over a long training period Since the

self-organizing learning is a stochastic process, the final statistical accuracy of the mapping depends

on the number of steps in the final convergence phase, which must be long enough, for example,10,000 steps Unfortunately, at present there is no way to circumvent this requirement The re-sulting SOM, i.e., the topological ordering of the competitive neurons, reflects the probability den-sity function of the input data correspondingly

N c ( k )

Figure 2.4 An example of evolving N k c( ) in the self-organizing map

The SOM has been widely applied in areas such as machine vision [Oja92], speech analysis andrecognition [Beh93], as well as process control [Ski93] An outstanding application of the SOM isthe neural phonetic typewriter [Koh88] It is capable of transcribing speech into written text from

an unlimited vocabulary We have applied [Gao96] the SOM to optimize the input quantization in a

Cerebellar Model Articulation Controller (CMAC) neural network [Alb75] More detailed sion of successful application examples can be found in [Koh90] and [Koh95] In publication [P5],the self-organizing map is used to obtain appropriate fuzzy membership function parameters in thefuzzy filter This results in a new fuzzy filter, which has better noise attenuation than conventionalfuzzy filters in a motion control application.

discus-2.2 Fuzzy Logic

Although the modern sciences have made great advances based on the analysis of exact mathematicalmodels, some aspects of real world problems cannot be efficiently handled under the framework ofprecise models As mentioned previously, the well-known truck backer-upper benchmark is diffi-cult for conventional methods, and could be solved by using the fuzzy technique [Kon92] The con-cept of fuzzy logic was first introduced by Dr Zadeh to present vagueness in linguistics, and fur-ther implement and express human knowledge and inference capability in a natural way [Zad73] It

is a scheme for representing the information processing and communication procedure in the naturalhuman mind Early applications of fuzzy logic include industrial process control [Mam77] Nowa-days, there are many other applications available in diverse areas such as reliability engineering[Sin90], consumer electronics products [Ter94], pattern recognition [Ped90], signal processing[Rus96], and fault diagnosis [Kwo95] In conclusion, fuzzy logic has been applied to such problemsthat are either hard to tackle with precise mathematical tools or where the use of fuzzy logic canprovide desirable robustness, significantly improved performance, or easier implementation

2.2.1 Basic Theory of Fuzzy Logic Systems

Figure 2.5 shows a basic configuration of a fuzzy logic system Normally, there are four

compo-nents in this fuzzy reasoning system They are a fuzzification interface, a fuzzy rule base (knowledge base), an inference engine (decision-making logic), and a defuzzification interface We will give a brief

introduction to all these four components

FuzzificationInterface

InferenceEngine

Fuzzy RuleBase

DefuzzificationInterfaceCrisp

Input

CrispOutputRules

FuzzyInput

FuzzyOutput

Figure 2.5 Basic architecture of a fuzzy logic system