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TitleA First Course in Fuzzy and Neural Control - H. Nguyen et al., (Chapman and Hall, 2003) WW
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LanguageEnglish
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Total Pages305
Table of Contents
                            Title Page
Contents
Preface
Chapter 1: A PRELUDE TO CONTROL THEORY
	1.1 An ancient control system
	1.2 Examples of control problems
		1.2.1 Open-loop control systems
		1.2.2 Closed-loop control systems
	1.3 Stable and unstable systems
	1.4 A look at controller design
	1.5 Exercises and projects
Chapter 2: MATHEMATICAL MODELS IN CONTROL
	2.1 Introductory examples: pendulum problems
		2.1.1 Example: fixed pendulum
		2.1.2 Example: inverted pendulum on a cart
	2.2 State variables and linear systems
	2.3 Controllability and observability
	2.4 Stability
		2.4.1 Damping and system response
		2.4.2 Stability of linear systems
		2.4.3 Stability of nonlinear systems
		2.4.4 Robust stability
	2.5 Controller design
	2.6 State-variable feedback control
		2.6.1 Second-order systems
		2.6.2 Higher-order systems
	2.7 Proportional-integral-derivative control
		2.7.1 Example: automobile cruise control system
		2.7.2 Example: temperature control
		2.7.3 Example: controlling dynamics of a servomotor
	2.8 Nonlinear control systems
	2.9 Linearization
	2.10 Exercises and projects
Chapter 3: FUZZY LOGIC FOR CONTROL
	3.1 Fuzziness and linguistic rules
	3.2 Fuzzy sets in control
	3.3 Combining fuzzy sets
		3.3.1 Minimum, maximum, and complement
		3.3.2 Triangular norms, conorms, and negations
		3.3.3 Averaging operators
	3.4 Sensitivity of functions
		3.4.1 Extreme measure of sensitivity
		3.4.2 Average sensitivity
	3.5 Combining fuzzy rules
		3.5.1 Products of fuzzy sets
		3.5.2 Mamdani model
		3.5.3 Larsen model
		3.5.4 Takagi-Sugeno-Kang (TSK) model
		3.5.5 Tsukamoto model
	3.6 Truth tables for fuzzy logic
	3.7 Fuzzy partitions
	3.8 Fuzzy relations
		3.8.1 Equivalence relations
		3.8.2 Order relations
	3.9 Defuzzification
		3.9.1 Center of area method
		3.9.2 Height-center of area method
		3.9.3 Max criterion method
		3.9.4 First of maxima method
		3.9.5 Middle of maxima method
	3.10 Level curves and alpha-cuts
		3.10.1 Extension principle
		3.10.2 Images of alpha-level sets
	3.11 Universal approximation
	3.12 Exercises and projects
Chapter 4: FUZZY CONTROL
	4.1 A fuzzy controller for an inverted pendulum
	4.2 Main approaches to fuzzy control
		4.2.1 Mamdani and Larsen methods
		4.2.2 Model-based fuzzy control
	4.3 Stability of fuzzy control systems
	4.4 Fuzzy controller design
		4.4.1 Example: automobile cruise control
		4.4.2 Example: controlling dynamics of a servomotor
	4.5 Exercises and projects
Chapter 5: NEURAL NETWORKS FOR CONTROL
	5.1 What is a neural network?
	5.2 Implementing neural networks
	5.3 Learning capability
	5.4 The delta rule
	5.5 The backpropagation algorithm
	5.6 Example 1: training a neural network
	5.7 Example 2: training a neural network
	5.8 Practical issues in training
	5.9 Exercises and projects
Chapter 6: NEURAL CONTROL
	6.1 Why neural networks in control
	6.2 Inverse dynamics
	6.3 Neural networks in direct neural control
	6.4 Example: temperature control
		6.4.1 A neural network for temperature control
		6.4.2 Simulating PI control with a neural network
	6.5 Neural networks in indirect neural control
		6.5.1 System identification
		6.5.2 Example: system identification
		6.5.3 Instantaneous linearization
	6.6 Exercises and projects
Chapter 7: FUZZY-NEURAL AND NEURAL-FUZZY CONTROL
	7.1 Fuzzy concepts in neural networks
	7.2 Basic principles of fuzzy-neural systems
	7.3 Basic principles of neural-fuzzy systems
		7.3.1 Adaptive network fuzzy inference systems
		7.3.2 ANFIS learning algorithm
	7.4 Generating fuzzy rules
	7.5 Exercises and projects
Chapter 8: APPLICATIONS
	8.1 A survey of industrial applications
	8.2 Cooling scheme for laser materials
	8.3 Color quality processing
	8.4 Identification of trash in cotton
	8.5 Integrated pest management systems
	8.6 Comments
Bibliography
                        
Document Text Contents
Page 1

A First Course in
FUZZY

and
NEURAL

CONTROL

© 2003 by Chapman & Hall/CRC

Page 2

CHAPMAN & HALL/CRC
A CRC Press Company

Boca Raton London New York Washington, D.C.

Hung T. Nguyen • Nadipuram R. Prasad
Carol L. Walker • Elbert A. Walker

A First Course in
FUZZY

and
NEURAL

CONTROL

© 2003 by Chapman & Hall/CRC

Page 152

142 CHAPTER 4. FUZZY CONTROL

each having value 1 on one of the pieces of the mapping and 0 on the other.

0-3 -2 -1 1 2 3x

A1 (x) solid line, A2 (x) dashed line
and rules

R1 : If x is A1 then f1 (x) = 1 + x
R2 : If x is A2 then f2 (x) = 2 + x

Now

A1 (x) f1 (x) +A2 (x) f2 (x) =




2 + 2x if x ≤ −1
1
2
+ 3

2
x+ x2 if −1 ≤ x ≤ 1

−1 + 4x if 1 ≤ x

and
A1 (x) +A2 (x) = 1

giving the following plot:

-20

-10

10

-4 -2 2 4x

y =
P2
j=1Aj (x) fj (xj)

. P2
j=1Aj (x)

These models can also be used as a nonlinear interpolator between linear
systems. Sugeno proposes rules of the form

Ri: If z1 is Ci1 and ... and zp is Cip then úxi (t) = Ai (x (t)) +Biu ((t)) (4.5)

for i = 1, 2, ..., r. In this rule, Sugeno uses a canonical realization of the
system known in classical control theory as the �controller canonical form.�
Here, x (t) = (x1 (t) , . . . , xn (t)) is the n-dimensional state vector, u (t) =
(u1 (t) , . . . , um (t)) is the m-dimensional input vector, Ai, Bi, i = 1, 2, ..., r,

© 2003 by Chapman & Hall/CRC

Page 153

4.2. MAIN APPROACHES TO FUZZY CONTROL 143

are state and input matrices, respectively, and z (t) = (z1 (t) , . . . , zp (t)) is the
p-dimensional input to the fuzzy system. The output is

úx (t) =

Pr
i=1 [Aix (t) +Biu (t)] τ i (z (t))Pr

i=1 τ i (z (t))

=

Pr
i=1Aiτ i (z (t))Pr
i=1 τ i (z (t))

x (t) +

Pr
i=1Biτ i (z (t))Pr
i=1 τ i (z (t))

u (t)

where
τ i (z (t)) = 4pk=1Cik (zk (t))

for some appropriate t-norm 4. In the special case r = 1, the antecedent is a
standard linear system:

úx (t) = Ax (t) +Bu (t)

In the general case, such a fuzzy system can be thought of as a nonlinear inter-
polator between r linear systems.

Example 4.2 Suppose that z (t) = x (t), p = n = m = 1, and r = 2. Take the
two fuzzy sets

C1 (z) =




1 if z ≤ −1
1−z
2

if −1 ≤ z ≤ 1
0 if 1 ≤ z

and

C2 (z) =




0 if z ≤ 0
1+z
2

if −1 ≤ z ≤ 1
1 if 1 ≤ z

0-3 -2 -1 1 2 3x

C1 (z) solid line, C2 (z) dashed line
and rules

R1: If z is C1 then úx1 = −x1 + 2u1
R2: If z is C2 then úx2 = −2x2 + u2

so A1 = −1, B1 = 2, A2 = −2, and B2 = 1. Since τ1 (z) + τ1 (z) = C1 (z) +
C2 (z) = 1, the output of the system is

úx = (−C1 (z (t))− C2 (z (t)))x+ (2C1 (z (t)) + C2 (z (t)))u
Thus, we have

úx =




−x+ 2u if z ≤ −1
−x+

¡
3−z
2

¢
u if −1 ≤ z ≤ 1

−2x+ u if 1 ≤ z

© 2003 by Chapman & Hall/CRC

Page 304

BIBLIOGRAPHY 295

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© 2003 by Chapman & Hall/CRC

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