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r
o
l
alg
o
r
i
th
m
l
ik
e
∞
m
e
th
o
d
[
9
]
,
l
i
n
e
a
r
q
u
a
d
r
a
ti
c
c
o
n
t
r
o
l
le
r
(
L
GQ
)
[
1
0
]
,
a
n
d
p
r
e
d
i
c
tiv
e
c
o
n
t
r
o
l
l
e
r
[
1
1
]
.
N
u
m
e
r
o
u
s
s
tu
d
i
e
s
h
av
e
al
s
o
b
ee
n
c
o
n
d
u
c
t
e
d
o
n
th
e
o
p
t
im
al
co
n
t
r
o
l
o
f
a
d
y
n
am
i
c
s
y
s
t
em
u
s
in
g
v
a
r
i
o
u
s
m
e
th
o
d
s
w
ith
t
h
e
i
r
a
d
v
an
ta
g
e
s
a
n
d
d
i
s
a
d
v
an
t
ag
e
s
av
a
il
a
b
l
e
in
t
h
e
li
t
e
r
at
u
r
e
.
On
e
o
f
th
e
m
et
h
o
d
s
u
s
e
d
t
o
s
o
lv
e
o
p
t
im
i
z
a
ti
o
n
p
r
o
b
l
em
s
w
ith
u
n
c
e
r
t
a
in
p
a
r
am
et
e
r
s
i
s
th
e
li
n
e
a
r
q
u
a
d
r
a
ti
c
g
au
s
s
i
an
(
L
Q
G
)
[
1
2
]
.
T
h
e
r
e
a
r
e
s
e
v
e
r
a
l
r
e
p
o
r
t
s
in
v
a
r
y
in
g
f
ie
l
d
s
r
eg
a
r
d
in
g
th
e
a
d
v
a
n
t
ag
e
s
o
f
u
s
in
g
th
is
c
o
n
t
r
o
l
m
e
th
o
d
:
f
o
r
e
x
am
p
le
,
p
o
w
e
r
s
y
s
tem
[
1
3
]
,
[
1
4
]
,
m
e
ch
a
n
ic
a
l
c
o
n
t
r
o
l
p
r
o
b
l
em
[
1
5
]
,
[
1
6
]
,
p
o
w
e
r
f
l
o
w
[
1
7
]
,
u
n
m
an
n
e
d
a
e
r
i
a
l
v
eh
i
cl
e
[
1
8
]
,
s
im
p
l
if
i
e
d
c
a
r
[
1
9
]
,
a
c
q
u
is
it
i
o
n
p
r
o
c
e
s
s
[
2
0
]
,
s
lu
n
g
t
r
an
s
p
o
r
t
a
t
i
o
n
[
2
1
]
,
v
eh
i
cl
e
au
t
o
m
a
tio
n
[
2
2
]
,
[
2
3
]
,
b
u
c
k
c
o
n
v
e
r
t
e
r
c
o
n
t
r
o
ll
in
g
[
2
4
]
,
r
o
b
o
t
i
c
&
e
l
e
ct
r
o
n
i
c
s
y
s
t
em
s
[
2
5
]
,
[
2
6
]
,
a
n
d
o
p
t
i
c
s
s
y
s
t
em
[
2
7
]
.
S
i
m
u
l
a
t
i
o
n
s
a
r
e
n
e
e
d
e
d
t
o
b
e
c
a
r
r
i
e
d
o
u
t
t
o
d
e
t
e
r
m
i
n
e
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
a
c
o
n
t
r
o
l
m
e
t
h
o
d
f
o
r
a
s
p
e
c
i
f
i
c
d
y
n
a
m
i
c
a
l
s
y
s
t
em
.
T
h
e
r
e
f
o
r
e
,
t
h
i
s
s
t
u
d
y
e
m
p
l
o
y
e
d
t
h
e
L
Q
G
m
e
t
h
o
d
t
o
i
n
v
e
n
t
o
r
y
d
y
n
a
m
i
c
a
l
s
y
s
t
e
m
s
t
o
d
e
t
e
r
m
i
n
e
t
h
e
o
p
t
i
m
a
l
d
e
c
i
s
i
o
n
s
f
o
r
a
s
i
n
g
l
e
p
r
o
d
u
c
t
i
n
v
e
n
t
o
r
y
s
y
s
t
em
w
it
h
u
n
c
e
r
t
a
i
n
d
e
m
a
n
d
s
a
n
d
p
r
o
d
u
c
t
d
a
m
a
g
e
s
d
u
r
i
n
g
d
e
l
i
v
e
r
y
.
T
h
i
s
c
o
n
t
r
o
l
a
i
m
s
t
o
d
e
c
i
d
e
t
h
e
o
p
t
i
m
a
l
am
o
u
n
t
o
f
t
h
e
p
r
o
d
u
c
t
t
h
a
t
n
e
e
d
s
t
o
b
e
o
r
d
e
r
e
d
t
o
t
h
e
s
u
p
p
l
i
e
r
,
w
h
e
r
e
t
h
e
i
n
v
e
n
t
o
r
y
l
e
v
e
l
i
s
c
o
n
t
r
o
l
l
e
d
t
o
f
o
l
l
o
w
a
s
e
t
-
p
o
i
n
t
o
r
t
r
a
j
e
c
t
o
r
y
.
I
n
t
h
e
d
i
s
c
u
s
s
e
d
i
n
v
e
n
t
o
r
y
m
o
d
e
l
,
t
h
e
r
e
i
s
a
n
u
n
c
e
r
t
a
i
n
p
a
r
a
m
e
t
e
r
r
e
p
r
e
s
e
n
t
i
n
g
t
h
e
p
e
r
c
e
n
t
a
g
e
o
f
t
h
e
o
r
d
e
r
e
d
p
r
o
d
u
c
t
,
w
h
i
c
h
c
a
n
n
o
t
e
n
t
e
r
t
h
e
w
a
r
e
h
o
u
s
e
d
u
e
t
o
d
a
m
a
g
e
d
u
r
i
n
g
t
h
e
d
e
l
i
v
e
r
y
p
r
o
c
e
s
s
.
T
h
e
r
e
f
o
r
e
,
t
o
o
b
s
e
r
v
e
t
h
i
s
c
o
n
t
r
o
l
m
e
t
h
o
d
'
s
p
e
r
f
o
r
m
a
n
c
e
,
c
o
m
p
u
t
a
t
i
o
n
a
l
s
i
m
u
l
a
t
i
o
n
s
w
e
r
e
c
a
r
r
i
e
d
o
u
t
a
n
d
c
o
m
p
a
r
e
d
t
o
s
o
m
e
e
x
i
s
t
i
n
g
l
i
t
e
r
a
t
u
r
e
r
e
s
u
l
t
s
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Dy
na
m
ica
l sy
s
t
e
m
I
n
an
in
v
e
n
to
r
y
s
y
s
te
m
w
i
th
o
n
e
p
r
o
d
u
ct
ty
p
e
s
to
r
ed
in
t
h
e
w
ar
eh
o
u
s
e,
t
h
e
n
u
m
b
er
s
o
f
ite
m
s
ar
e
o
b
s
er
v
ed
p
er
i
o
d
ically
,
f
o
r
in
s
t
an
ce
,
d
ail
y
is
k
n
o
w
n
a
s
th
e
r
ev
ie
w
ti
m
e
p
er
io
d
.
L
et
∈
N
b
e
th
e
r
ev
ie
w
ti
m
e
,
w
h
er
e
(
)
≥
0
th
e
i
n
v
en
to
r
y
le
v
el
i.e
.
,
th
e
n
u
m
b
er
o
f
ite
m
s
s
to
r
ed
i
n
t
h
e
w
ar
e
h
o
u
s
e
at
r
e
v
ie
w
t
i
m
e
k,
(
)
is
t
h
e
n
u
m
b
er
o
f
th
e
p
r
o
d
u
cts
d
em
a
n
d
ed
at
r
e
v
ie
w
ti
m
e
k
wh
ich
is
u
n
ce
r
tai
n
a
n
d
is
tr
ea
ted
as
a
d
is
tu
r
b
an
ce
o
f
th
e
s
y
s
te
m
,
an
d
(
)
is
t
h
e
n
u
m
b
er
o
f
ite
m
s
o
r
d
er
ed
to
th
e
s
u
p
p
lier
at
r
e
v
ie
w
ti
m
e
k
.
I
n
th
e
p
r
o
b
le
m
d
is
cu
s
s
ed
h
er
e,
th
e
o
r
d
er
e
d
p
r
o
d
u
ct
at
r
ev
ie
w
ti
m
e
k
d
o
es
n
o
t
en
ter
th
e
w
ar
eh
o
u
s
e
at
th
e
s
a
m
e
r
ev
ie
w
ti
m
e
k
.
Ho
w
e
v
er
,
th
er
e
is
a
p
o
s
s
ib
ili
t
y
o
f
a
ti
m
e
g
ap
b
et
w
ee
n
o
r
d
er
in
g
an
d
r
ec
eiv
i
n
g
ite
m
s
.
T
h
is
ti
m
e
g
ap
,
also
k
n
o
w
n
as
d
ela
y
ti
m
e,
is
d
en
o
ted
b
y
̄
∈
N
.
T
h
is
m
ea
n
s
t
h
at
th
e
ite
m
s
o
r
d
er
ed
at
r
ev
ie
w
ti
m
e
k
ar
r
iv
es
th
e
w
ar
e
h
o
u
s
e
at
r
e
v
ie
w
ti
m
e
+
̄
.
I
n
p
ar
ticu
lar
,
n
o
t
all
ite
m
s
o
r
d
er
ed
t
o
th
e
s
u
p
p
lier
ar
e
r
e
ce
iv
ed
d
u
e
to
d
am
a
g
es
i
n
c
u
r
r
ed
d
u
r
in
g
d
eliv
er
y
.
L
et
(
)
b
e
th
e
n
u
m
b
er
o
f
d
a
m
ag
ed
ite
m
s
f
r
o
m
th
e
to
tal
a
m
o
u
n
t
o
f
th
e
o
r
d
er
ed
p
r
o
d
u
cts
at
r
e
v
ie
w
ti
m
e
k
.
T
h
i
s
v
a
lu
e
is
n
o
t
k
n
o
w
n
w
i
th
ce
r
tai
n
t
y
;
t
h
er
e
f
o
r
e,
it
is
tr
ea
ted
as
t
h
e
d
is
t
u
r
b
an
ce
o
f
t
h
e
s
y
s
te
m
.
T
h
e
co
n
tr
o
l
p
r
o
b
lem
i
s
as
s
o
ciate
d
w
i
th
s
elec
ti
n
g
t
h
e
n
u
m
b
er
o
f
ite
m
s
t
h
at
n
ee
d
to
b
e
o
r
d
er
ed
to
th
e
s
u
p
p
lier
at
ev
er
y
r
ev
ie
w
ti
m
e
to
en
s
u
r
e
t
h
e
o
n
-
h
a
n
d
p
r
o
d
u
ct
s
to
ck
lev
e
l
f
o
llo
w
s
a
s
et
p
o
in
t
o
r
tr
a
j
ec
t
o
r
y
.
L
et
(
<
0
)
=
0
,
th
en
t
h
e
ev
o
l
u
tio
n
o
f
th
e
i
n
v
e
n
to
r
y
le
v
el
y
f
o
r
an
y
r
ev
ie
w
ti
m
e
≥
0
is
ex
p
r
ess
ed
as
f
o
llo
w
s
:
(
)
=
(
0
)
−
(
0
)
+
(
1
)
−
(
1
)
+
⋯
+
(
−
̄
−
1
)
−
(
−
̄
−
1
)
−
(
0
)
−
(
1
)
−
(
2
)
−
⋯
−
(
−
1
)
th
is
ca
n
also
b
e
r
e
w
r
itte
n
as
f
o
llo
w
s
:
(
)
=
∑
(
)
−
̄
−
1
=
0
−
∑
(
)
−
̄
−
1
=
0
−
∑
(
)
−
1
=
0
,
(
1
)
T
ak
e
:
=
̄
+
1
,
(
)
=
:
1
(
)
,
an
d
(
)
:
=
(
−
̄
+
)
f
o
r
=
2
,
3
,
.
.
.
,
̄
+
1
.
T
h
e
(
1
)
ca
n
al
s
o
b
e
r
e
w
r
itte
n
a
s
f
o
llo
w
s
:
{
(
+
1
)
=
(
)
+
1
(
)
+
2
(
)
(
)
=
(
)
−
(
)
(
2
)
w
h
er
e
(
)
=
[
1
(
)
,
2
(
)
,
.
.
.
,
(
)
]
⊤
is
u
s
ed
to
d
en
o
te
th
e
s
t
ate
v
ec
to
r
,
=
[
1
1
0
⋯
0
0
0
1
⋯
0
0
0
0
⋯
⋮
⋮
⋮
⋮
⋱
1
0
0
0
⋯
0
]
,
1
=
[
0
0
⋮
1
]
,
2
=
[
−
1
0
⋮
0
]
,
=
[
1
,
0
,
0
,
⋯
,
0
]
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2502
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4752
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n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
22
,
No
.
3
,
J
u
n
e
2
0
2
1
:
1
7
4
8
-
1
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3
1750
ar
e
co
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s
tan
t
m
atr
ice
s
.
T
h
is
is
a
lin
ea
r
s
tate
s
p
ac
e
eq
u
atio
n
w
it
h
t
w
o
d
is
tu
r
b
an
ce
s
i.e
.
,
(
)
an
d
(
)
.
Ma
n
y
co
n
tr
o
l
m
et
h
o
d
s
ar
e
s
u
itab
le
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[1
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P
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Ig
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T
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0
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[2
6
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L
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7
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8
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[2
9
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5
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I
O
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RAP
H
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S O
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AUTH
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S
u
tr
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m
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n
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,
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d
o
n
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w
it
h
M
a
ste
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c
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c
e
d
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re
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tain
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f
ro
m
Un
iv
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s
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a
d
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a
(In
d
o
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)
in
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2
.
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o
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tain
e
d
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c
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lo
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g
re
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a
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m
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s
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ro
m
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a
s
Dip
o
n
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g
o
ro
(In
d
o
n
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)
in
2
0
0
9
.
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re
se
a
rc
h
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s
a
re
in
f
ield
s o
f
m
a
th
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m
a
ti
c
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l
m
o
d
e
li
n
g
,
sy
ste
m
&
c
o
n
tro
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a
n
d
o
p
ti
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iza
ti
o
n
b
o
t
h
in
t
h
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o
ry
a
n
d
a
p
p
li
c
a
ti
o
n
s.
F
u
rt
h
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r
in
f
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c
a
n
b
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f
o
u
n
d
o
n
h
is
h
o
m
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p
a
g
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:
h
tt
p
:
//
m
a
th
.
f
s
m
.
u
n
d
ip
.
a
c
.
i
d
/su
tri
s
n
o
.
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d
o
w
a
ti
is
a
p
r
o
f
e
ss
o
r
a
t
th
e
De
p
a
rtme
n
t
o
f
M
a
th
e
m
a
ti
c
s,
Dip
o
n
e
g
o
ro
Un
iv
e
rsity
,
In
d
o
n
e
sia
.
S
h
e
o
b
tain
e
d
d
o
c
to
ra
te
d
e
g
re
e
f
ro
m
In
stit
u
t
T
e
k
n
o
lo
g
i
Ba
n
d
u
n
g
(In
d
o
n
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sia
)
in
2
0
0
5
.
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r
re
se
a
rc
h
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s
a
re
in
f
ield
s
o
f
m
a
t
h
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m
a
ti
c
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l
m
o
d
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li
n
g
,
s
y
ste
m
&
c
o
n
tro
l,
b
o
th
i
n
th
e
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ry
a
n
d
a
p
p
li
c
a
ti
o
n
s.
F
u
rt
h
e
r
in
f
o
c
a
n
b
e
f
o
u
n
d
o
n
h
e
r
h
o
m
e
p
a
g
e
:
h
tt
p
:/
/m
a
t
h
.
f
s
m
.
u
n
d
i
p
.
a
c
.
id
/w
id
o
w
a
ti
R.
H
e
r
u
Tja
h
ja
n
a
is
a
lec
tu
re
r
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n
d
re
se
a
rc
h
e
r
a
t
t
h
e
De
p
a
rtm
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n
t
o
f
M
a
th
e
m
a
ti
c
s,
Dip
o
n
e
g
o
r
o
Un
iv
e
rsit
y
,
In
d
o
n
e
sia
.
He
o
b
t
a
in
e
d
d
o
c
to
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te
d
e
g
re
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f
ro
m
In
stit
u
t
T
e
k
n
o
lo
g
i
Ba
n
d
u
n
g
(In
d
o
n
e
sia
)
in
2
0
1
0
.
His
re
se
a
rc
h
e
s
a
re
in
f
ield
s
o
f
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
li
n
g
,
sy
st
e
m
&
c
o
n
tro
l,
b
o
t
h
in
t
h
e
o
ry
a
n
d
a
p
p
li
c
a
ti
o
n
s.
F
u
rt
h
e
r
in
f
o
c
a
n
b
e
f
o
u
n
d
o
n
h
is
h
o
m
e
p
a
g
e
:
h
tt
p
:
//
m
a
th
.
f
s
m
.
u
n
d
ip
.
a
c
.
i
d
/rh
e
ru
t
jah
jan
a
.
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