A First Course in FUZZY and NEURAL CONTROL

242 CHAPTER 7. FUZZY-NEURAL AND NEURAL-FUZZY CONTROL

capability of ANFIS. However, in real-world applications where the control law
is unknown, these choices belong to ìengineering skill.î Because the intended
controlled system can be tested, a goodapproximation can be obtained with
time and patience. The point is this: The universal approximation property
of ANFIS, as a mathematical theorem, is the theoretical guideline for using
ANFIS.

Example 7.5In this example, we use ANFIS to approximate a function that
we know (but pretend not to know). We take for our ìunknownî function,
sin 10xsin 10y. The surface determined by this function looks like this:

0.2^0

0.4

0.6

1 0.8

x

(^0) 0.2
0.4
0.6
0.8 1
y
-1
-0.5
0
0.5
1
z
Plot ofsin 10xsin 10y
The training data was obtained from this function by evaluating 100 random
pairs(x, y)withx, y∈[0,1],creatingatextfile,sinxsiny.dat,withthree
columns of numbers.
ïOpenMatlab, and at the prompt, enteranfisedit
This brings up the following dialog. (The training data box will be empty
at this point.)