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[
1
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c
o
n
t
r
o
l
l
aw
s
an
d
en
e
r
g
y
f
u
n
c
t
i
o
n
ch
o
ic
e
.
T
h
e
c
o
n
t
r
o
l
l
e
r
is
n
o
t
o
n
ly
r
e
s
p
o
n
s
i
b
l
e
f
o
r
a
ch
i
ev
in
g
i
ts
in
te
n
d
e
d
g
o
al
,
w
h
e
th
e
r
t
r
a
c
k
in
g
an
d
/
o
r
r
eg
u
l
at
i
o
n
,
b
u
t
i
t
m
u
s
t
al
s
o
g
u
a
r
an
t
e
e
at
a
l
l
t
im
es
th
a
t
,
th
e
c
o
m
p
en
s
a
t
e
d
s
y
s
tem
r
em
ai
n
s
g
l
o
b
a
ll
y
a
s
y
m
p
t
o
t
i
ca
l
ly
s
t
a
b
e
.
B
a
ck
s
t
e
p
p
i
n
g
is
a
s
te
p
-
by
-
s
t
e
p
d
e
s
i
g
n
m
e
t
h
o
d
r
o
o
t
e
d
in
L
y
a
p
u
n
o
v
’
s
s
t
ab
i
l
i
ty
th
e
o
r
y
,
w
h
e
r
e
e
a
c
h
s
t
at
e
is
in
t
r
o
d
u
c
e
d
p
r
o
g
r
es
s
i
v
e
ly
a
s
a
v
i
r
tu
a
l
c
o
n
t
r
o
l
in
p
u
t
t
o
s
ta
b
i
l
iz
e
i
ts
c
o
r
r
e
s
p
o
n
d
in
g
s
u
b
s
y
s
t
em
[
2
5
]
.
I
n
teg
r
ati
n
g
an
i
n
teg
r
al
ac
tio
n
w
it
h
i
n
b
ac
k
s
tep
p
in
g
-
b
ased
co
n
tr
o
l
la
w
s
co
n
s
tit
u
tes
a
w
id
el
y
ad
o
p
ted
s
tr
ateg
y
to
en
h
an
ce
t
h
e
r
o
b
u
s
tn
es
s
o
f
th
e
ap
p
r
o
ac
h
,
en
s
u
r
i
n
g
th
e
r
e
j
ec
tio
n
o
f
d
is
tu
r
b
an
ce
s
an
d
th
e
atten
u
a
tio
n
o
f
s
tead
y
-
s
tate
tr
ac
k
in
g
er
r
o
r
s
.
T
h
e
b
lo
c
d
iag
r
am
o
f
i
n
te
g
r
ato
r
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
f
o
r
E
P
W
is
p
r
esen
ted
in
Fig
u
r
e
1
.
T
h
e
s
tep
s
f
o
llo
w
ed
f
o
r
th
e
s
y
n
t
h
esi
s
o
f
th
e
s
p
ee
d
co
n
tr
o
ller
ca
n
b
e
o
u
tlin
ed
as
f
o
l
lo
w
s
:
−
Step
1
:
R
ig
h
t
w
h
ee
l sp
ee
d
co
n
tr
o
l
First,
th
e
tr
ac
k
i
n
g
o
b
j
ec
tiv
e
d
ef
i
n
es t
h
e
tr
ac
k
i
n
g
er
r
o
r
f
o
r
th
e
r
ig
h
t
w
h
ee
l sp
ee
d
as
(
4
)
1
=
2
−
2
+
2
∫
(
2
−
2
)
0
(
4
)
T
h
e
L
y
ap
u
n
o
v
la
w
co
n
s
id
er
ed
an
d
its
d
er
iv
ate
ar
e:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
P
a
r
ticle
s
w
a
r
m
o
p
timi
z
a
tio
n
-
o
p
timiz
ed
in
teg
r
a
to
r
b
a
ck
s
tep
p
in
g
…
(
Dja
mila
B
o
u
b
ek
e
u
r
)
1649
(
1
)
=
(
1
2
)
1
2
⁄
,
̇
(
1
)
=
1
(
̇
2
−
̇
2
)
+
2
(
2
−
2
)
=
1
(
1
2
+
2
4
+
1
_
+
2
_
+
−
̇
2
+
2
(
2
−
2
)
)
(
5
)
T
o
o
b
tain
th
e
n
e
g
ati
v
e
d
er
iv
at
e
o
f
L
y
ap
u
n
o
v
f
u
n
ctio
n
,
th
e
v
i
r
tu
al
co
n
tr
o
l
w
as c
o
n
s
id
er
ed
as
(
6
)
:
(
1
)
=
−
1
1
+
̇
1
(
6
)
T
h
e
to
r
q
u
e
co
n
tr
o
l e
x
p
r
ess
io
n
w
a
s
o
b
tain
ed
as
(
7
)
:
1
_
+
2
_
=
−
2
1
−
1
2
−
2
4
−
−
2
(
2
−
2
)
(
7
)
w
it
h
:
0
=
−
2
1
−
1
2
−
2
4
−
−
2
(
2
−
2
)
T
h
er
ef
o
r
e:
̇
(
1
)
=
−
1
1
2
<
0
w
it
h
1
>
0
.
Giv
e
n
t
h
at
t
h
e
t
h
eo
r
e
m
’
s
co
n
d
itio
n
s
ar
e
s
ati
s
f
ied
;
th
e
s
tab
ilit
y
o
f
t
h
e
f
ir
s
t
s
u
b
s
y
s
te
m
i
s
en
s
u
r
e
d
i
n
th
e
s
e
n
s
e
o
f
a
s
y
m
p
to
tic
co
n
v
e
r
g
en
ce
.
Fig
u
r
e
1
.
B
lo
c
d
iag
r
am
o
f
i
n
te
g
r
ato
r
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
f
o
r
E
P
W
−
Step
2
:
L
ef
t
w
h
ee
l
s
p
ee
d
co
n
tr
o
l
Fo
r
th
e
lef
t
w
h
ee
l
s
p
ee
d
,
th
e
tr
ac
k
in
g
o
b
j
ec
tiv
e
is
f
o
r
m
u
lated
b
y
i
n
tr
o
d
u
ci
n
g
t
h
e
tr
ac
k
i
n
g
er
r
o
r
,
d
ef
in
ed
as
f
o
llo
w
s
:
2
=
4
−
4
+
4
∫
(
4
−
4
)
0
(
8
)
4
co
r
r
esp
o
n
d
s
to
th
e
p
r
ev
io
u
s
v
ir
tu
al
co
n
tr
o
l
(
1
)
T
h
e
in
cr
ea
s
ed
en
er
g
y
f
u
n
ctio
n
,
to
g
eth
er
w
it
h
its
ti
m
e
d
er
iv
at
iv
e,
ar
e
d
ef
in
ed
as
f
o
llo
w
s
:
(
1
,
2
)
=
1
2
1
2
+
1
2
⁄
⁄
2
2
,
̇
(
1
,
2
)
=
1
̇
1
+
2
̇
2
2
̇
2
=
2
(
̇
4
−
̇
4
+
4
(
4
−
4
)
)
(
9
)
=
3
2
+
4
4
+
3
_
+
4
_
+
−
̇
4
+
4
(
1
0
)
T
h
e
to
r
q
u
e
co
n
tr
o
l
ex
p
r
ess
io
n
w
a
s
o
b
tain
ed
:
3
_
+
4
_
=
−
4
2
−
3
2
−
4
4
−
−
4
(
4
−
4
)
(
1
1
)
w
it
h
:
5
=
−
4
2
−
3
2
−
4
4
−
−
4
(
4
−
4
)
T
h
u
s
:
̇
(
1
,
2
)
=
−
1
1
2
−
2
2
2
<
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
23
,
No
.
6
,
Dec
em
b
er
20
25
:
1
6
4
6
-
1
656
1650
W
ith
:
1
,
2
>
0
,
th
e
s
tab
ilit
y
p
r
o
p
er
ties
o
f
b
o
th
s
u
b
s
y
s
te
m
s
w
er
e
f
o
r
m
all
y
v
er
i
f
ied
.
T
h
e
u
n
k
n
o
w
n
co
n
tr
o
l s
y
s
te
m
i
s
s
u
m
m
ar
ized
as:
{
1
_
+
2
_
=
0
3
_
+
4
_
=
5
(
1
2
)
T
h
e
r
ef
er
en
ce
in
p
u
t
to
r
q
u
es
f
o
r
th
e
r
ig
h
t
an
d
le
f
t
w
h
ee
ls
w
er
e
d
er
iv
ed
b
y
s
o
l
v
i
n
g
th
e
f
i
n
al
t
w
o
eq
u
atio
n
s
,
y
ield
in
g
:
_
=
0
1
⁄
−
2
1
_
⁄
(
1
3
)
_
=
1
5
−
3
0
4
1
−
3
2
⁄
(
1
4
)
−
Step
3
:
R
ig
h
t
w
h
ee
l
e
lectr
o
m
a
g
n
et
ic
to
r
q
u
e
co
n
tr
o
l
Fo
r
th
is
s
tep
,
t
h
e
er
r
o
r
is
d
ef
in
ed
as
:
3
=
−
_
+
3
∫
(
−
_
)
0
(
1
5
)
̇
3
=
̇
−
̇
_
+
3
(
−
_
)
(
1
6
)
T
h
e
ad
o
p
ted
L
y
ap
u
n
o
v
f
u
n
cti
o
n
an
d
its
co
r
r
esp
o
n
d
in
g
ti
m
e
d
er
iv
ativ
e
ar
e
g
i
v
e
n
b
y
:
(
1
,
2
,
3
)
=
1
2
1
2
+
1
2
2
2
+
1
2
3
2
̇
(
1
,
2
,
3
)
=
1
̇
1
+
2
̇
2
+
3
̇
3
T
h
e
to
r
q
u
e
ex
p
r
ess
io
n
(
r
o
to
r
s
u
r
f
ac
e
m
ag
n
et
s
)
is
f
o
r
m
u
lated
as
(
1
7
)
.
=
(
1
7
)
B
y
r
ep
lacin
g
(
1
7
)
in
(
1
6
)
̇
3
=
⁄
[
(
−
−
−
)
−
̇
_
]
+
3
(
−
_
)
(
1
8
)
T
h
e
r
ea
l in
p
u
t
co
n
tr
o
l o
f
th
e
r
i
g
h
t
m
o
to
r
is
:
=
−
5
5
+
+
+
+
(
)
̇
_
(
1
9
)
w
it
h
̇
_
=
(
1
0
)
̇
0
−
(
2
1
)
̇
_
an
d
̇
0
=
[
2
(
1
+
2
)
+
1
2
+
2
3
+
1
2
]
2
−
[
(
2
+
1
+
4
+
2
)
2
]
4
−
[
(
2
+
1
+
2
)
1
+
2
3
]
_
−
[
(
2
+
1
+
2
)
2
+
2
4
]
_
−
[
2
+
1
+
2
+
2
]
T
h
er
ef
o
r
e
,
̇
(
1
,
2
,
3
)
=
−
1
1
2
−
2
2
2
−
3
3
2
<
0
,
1
,
2
,
3
>
0
−
Step
:
L
e
f
t
w
h
ee
l
elec
tr
o
m
a
g
n
e
tic
to
r
q
u
e
co
n
tr
o
l
L
et
4
d
en
o
te
th
e
last
er
r
o
r
:
4
=
−
_
+
4
∫
(
−
_
)
0
(
2
0
)
T
h
e
f
in
al
L
y
ap
u
n
o
v
i
n
c
r
ea
s
ed
f
u
n
ctio
n
an
d
its
d
er
i
v
ati
v
e
ar
e:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
P
a
r
ticle
s
w
a
r
m
o
p
timi
z
a
tio
n
-
o
p
timiz
ed
in
teg
r
a
to
r
b
a
ck
s
tep
p
in
g
…
(
Dja
mila
B
o
u
b
ek
e
u
r
)
1651
(
1
,
2
,
3
,
4
)
=
1
2
1
2
+
1
2
2
2
+
1
2
3
2
+
1
2
4
2
̇
(
1
,
2
,
3
,
4
)
=
1
̇
1
+
2
̇
2
+
3
̇
3
+
4
̇
4
̇
4
=
̇
−
̇
_
+
4
(
−
_
)
(
2
1
)
T
h
e
to
r
q
u
e
ex
p
r
ess
io
n
(
r
o
to
r
s
u
r
f
ac
e
m
ag
n
et
s
)
is
r
x
p
r
ess
ed
as
f
o
llo
w
s
:
=
(
2
2
)
B
y
r
ep
lacin
g
(
2
2
)
in
(
2
1
)
.
̇
4
=
[
(
−
−
−
)
−
̇
_
]
+
4
(
−
_
)
…….
(
2
3
)
T
h
e
r
ea
l in
p
u
t c
o
n
tr
o
l
:
=
−
4
4
+
+
+
+
̇
_
−
(
4
(
−
_
)
)
(
2
4
)
w
it
h
̇
_
=
(
1
4
1
−
3
2
)
(
1
̇
5
−
3
̇
0
)
an
d
̇
5
=
[
(
4
+
1
+
4
+
2
)
3
]
2
−
[
4
(
4
+
4
)
+
4
2
+
2
3
+
4
4
]
4
−
[
(
4
+
4
+
3
)
3
+
3
1
]
_
−
[
(
4
+
4
+
4
)
4
+
2
3
]
_
−
[
4
+
4
+
3
+
4
]
T
h
er
ef
o
r
e,
̇
(
1
,
2
,
3
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1
2
−
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3
2
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4
4
2
<
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T
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2
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3
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s
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n
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u
t
o
f
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s
y
s
te
m
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a
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s
1
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2
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3
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4
an
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1
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2
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3
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ts
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d
a
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i
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ter
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s
t
h
at
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il
ized
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e
d
y
n
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m
ics o
f
er
r
o
r
v
ar
iab
le
1
,
2
,
3
,
4
,
an
d
m
i
n
i
m
ized
o
r
eli
m
in
a
ted
th
e
s
ta
ti
c
er
r
o
r
.
3.
M
E
T
H
O
D
T
h
e
P
SO a
lg
o
r
ith
m
r
ef
er
s
to
ea
ch
ele
m
e
n
t a
s
a
p
ar
ticle
an
d
th
e
p
o
p
u
latio
n
as a
s
w
ar
m
.
Us
i
n
g
p
ar
ticle
an
d
g
r
o
u
p
m
e
m
o
r
y
to
s
ea
r
ch
f
o
r
o
p
tim
izatio
n
i
n
th
e
s
o
lu
t
io
n
s
p
ac
e
is
th
e
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ai
n
id
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n
d
er
l
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th
is
ap
p
r
o
ac
h
.
I
t
also
p
r
o
d
u
ce
s
a
v
er
y
h
i
g
h
p
r
o
b
a
b
ilit
y
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co
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v
er
g
e
n
ce
o
f
th
e
o
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ti
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izatio
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o
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j
ec
tiv
e
f
u
n
ctio
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to
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lo
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al
o
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tim
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l
s
o
l
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tio
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.
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h
is
p
r
o
p
er
t
y
o
f
t
h
e
P
SO
u
n
d
er
lies
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h
e
alg
o
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ith
m
’
s
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ig
n
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ica
n
t
i
m
p
ac
t
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ad
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ess
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co
m
b
i
n
ato
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ial
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n
o
n
li
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ea
r
o
p
ti
m
izatio
n
p
r
o
b
lem
s
[
1
8
]
,
[
1
9
]
.
T
h
e
m
o
v
e
m
e
n
t
o
f
ea
c
h
p
ar
ticle
in
th
e
s
ea
r
c
h
s
p
ac
e
d
ep
en
d
s
o
n
th
e
b
est
-
e
x
p
lo
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ed
p
lace
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o
f
b
o
th
it
s
f
i
n
d
in
g
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th
e
w
h
o
le
s
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m
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y
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w
h
ic
h
ar
e
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lled
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est
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g
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est.
Fo
r
th
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p
u
r
p
o
s
e
o
f
u
p
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atin
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p
b
est
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d
g
b
est,
ea
ch
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ar
ticle
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llec
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d
s
to
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es i
n
f
o
r
m
atio
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n
a
v
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to
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e
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al
y
ze
d
[
2
3
]
.
A
p
o
p
u
latio
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o
f
r
an
d
o
m
s
o
lu
t
i
o
n
s
w
as
u
s
ed
to
i
n
itialize
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h
e
“
s
w
ar
m
”
w
h
er
e
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ch
p
ar
ticle
(
f
o
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a
m
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th
e
ℎ
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h
as
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ate
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(
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…
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f
o
r
N
-
d
i
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io
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p
ac
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T
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ef
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icie
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o
f
a
s
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tio
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m
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u
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g
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a
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ates
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q
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alit
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o
f
ea
ch
p
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s
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o
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itio
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A
cc
o
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d
in
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l
y
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e
ca
n
s
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th
e
o
f
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th
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ep
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1
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2
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T
h
e
f
o
llo
w
i
n
g
(
2
5
)
an
d
(
2
6
)
r
e
p
r
esen
t h
o
w
t
h
e
al
g
o
r
ith
m
u
p
d
ates th
e
p
ar
ticle
p
o
s
itio
n
s
a
n
d
v
elo
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s
s
h
o
w
n
in
F
ig
u
r
e
2
at
ea
ch
iter
atio
n
o
f
t
h
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
,
u
t
ilizi
n
g
t
h
e
p
r
ev
io
u
s
in
f
o
r
m
atio
n
:
(
)
=
∗
(
−
1
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+
1
1
∗
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−
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−
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(
2
5
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(
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=
(
−
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+
(
)
(
2
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
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o
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p
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23
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.
6
,
Dec
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er
20
25
:
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6
4
6
-
1
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1652
w
h
er
e
r
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[
0
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cc
eler
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tio
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an
ts
φ
1
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d
φ
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co
n
tr
o
l
th
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p
ar
ticle
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s
co
g
n
iti
v
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eh
av
io
r
an
d
s
o
cial
ap
tit
u
d
e,
r
esp
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tiv
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y
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B
o
th
o
f
t
h
ese
p
ar
a
m
eter
s
ar
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p
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iti
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d
p
r
o
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id
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p
ir
icall
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ac
co
r
d
an
ce
w
it
h
th
e
r
elatio
n
s
h
ip
φ
1
+
φ
2
≤
4
.
Fig
u
r
es
2
an
d
3
p
r
esen
t
th
e
p
ar
ticle
m
o
v
e
m
en
t
s
ch
e
m
atic
i
n
th
e
P
SO
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d
th
e
al
g
o
r
ith
m
f
lo
w
ch
ar
t
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r
esp
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A
s
af
o
r
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m
en
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ch
p
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etain
s
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m
e
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o
r
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al
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o
f
t
h
e
s
w
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m
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g
i
v
e
n
as g
b
e
s
t
[
2
3
]
.
Fig
u
r
e
2
.
P
ar
ticle
m
o
v
e
m
e
n
t s
ch
e
m
a
tic
in
t
h
e
P
SO
Fig
u
r
e
3
.
P
SO a
lg
o
r
ith
m
f
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n
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e
s
q
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ased
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it
n
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f
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n
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n
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as d
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i
n
ed
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ex
p
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ess
ed
b
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(
2
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(
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h
er
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(
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l sch
e
m
e
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s
tr
ated
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Fi
g
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Fig
u
r
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4
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T
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e
(
−
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2
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1
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T
E
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1653
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
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N
T
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ev
alu
ate
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ab
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:
th
e
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P
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ter
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t
(
φ
1
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2
G
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a
n
t
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φ
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2
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i
a
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3
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e
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V
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C1
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C4
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3
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4
]
H
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5
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F
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’
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6
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.
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[
7
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.
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[
8
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[
9
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M
.
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mm
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J
EAIS
)
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1
1
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(
I
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[
1
2
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K
.
A
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a
m
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l
.
,
“
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me
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T
ELKO
MN
I
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A
(
T
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[
1
3
]
M
.
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.
,
“
R
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AI
MS
M
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.
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[
1
4
]
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.
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.
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T
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:
Pro
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[
1
5
]
M
.
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