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In-Depth Information
1:
Controller initialization
:
2:
for
j
=
1
..
m
do
r
=
1
3:
for
i
=
1
..
n
do
4:
for
l
=
1
..
M
i
do
5:
for
k
=
1
..
n
do
6:
C
kj
=
A
l
ki
{
Initialization of the antecedents
⇒
ω
r
j
(
x
)
}
7:
c
kj
=
0
{
Initialization of the consequents
}
8:
end for
9:
c
0
j
=
0
{
Initialization of the affine terms of the consequents
}
10:
r
=
r
+
1
11:
12:
end for
13:
end for
14:
end for
15:
for
q
=
1
..
s
do
P
q
=
I
{
Initializing of the
P
q
matrices
}
16:
j
=
1
17:
for
i
=
1
..
n
do
18:
q
ij
q
1
Ψ
iq
=
Φ
Definition of regions
Θ
q
,resulting
ϕ
q
(
x
)=
ω
(
x
)
}
19:
{
20:
end for
21:
end for
Fig. 4.4
Initialization algorithm
1:
target
=
0
2:
for all
points
do
3:
Calculate the closed-loop fuzzy system using (4.26)
Calculate
J
(
x
)
, using (A.46)
4:
q
j
, using (4.18)
Calculate ϕ
q
(
x
)=
ω
5:
Calculate d
ϕ
q
(
x
)
/
d
x
, using (4.49)
6:
Calculate
F
(
x
)
, using (4.28)
7:
(
F
(
x
))
> −
ε
then
8:
if
max eigenvalue
target
=
target
+
max eigenvalue
(
F
(
x
))+
ε
9:
{
ε
>
0 is a small value ensures that
F
(
x
)
10:
is strictly negative definite.
}
11:
end if
12:
end for
Fig. 4.5
Objective function
4.3.2.3 Final Adjust Phase
Since the stability condition of the Theorem 4.1 does not apply continuously, the
equilibrium state obtained can be offset from the origin. To correct this situation,
the minimization algorithm is rerun, but using (
4.51
) as the new objective function.
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