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a
1.
I
NT
RO
D
UCT
I
O
N
C
y
b
er
-
p
h
y
s
ical
s
y
s
tem
s
(
C
P
S)
co
m
b
in
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c
o
m
p
lex
p
h
y
s
ical
p
r
o
ce
s
s
es
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co
m
p
u
t
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d
n
etwo
r
k
ed
co
n
t
r
o
l,
e
n
ab
lin
g
a
p
p
licatio
n
s
s
u
ch
as
au
to
n
o
m
o
u
s
v
eh
icles,
s
m
ar
t
g
r
id
s
,
an
d
i
n
d
u
s
tr
ial
au
to
m
atio
n
[
1
]
–
[
3
]
.
C
PS
b
len
d
co
m
p
lex
d
y
n
am
ics
with
r
ea
l
-
tim
e
f
ee
d
b
ac
k
th
at
ca
ll
f
o
r
r
ig
o
r
o
u
s
s
t
ab
ilit
y
an
aly
s
is
an
d
co
n
tr
o
l
s
y
n
th
esis
to
en
s
u
r
e
p
er
f
o
r
m
a
n
ce
[
4
]
,
[
5
]
.
C
o
n
tr
o
l
th
eo
r
y
ad
v
a
n
ce
m
en
ts
s
u
ch
as
L
y
ap
u
n
o
v
-
b
ased
ap
p
r
o
ac
h
es
an
d
t
h
e
u
s
e
o
f
lin
ea
r
m
atr
ix
i
n
eq
u
alities
(
L
MI
s
)
in
r
ec
en
t
y
ea
r
s
h
a
v
e
in
cr
ea
s
ed
s
tab
ilit
y
g
u
ar
an
tees
u
n
d
e
r
n
o
n
lin
ea
r
ities
an
d
u
n
ce
r
tain
ty
in
C
PS
[
6
]
–
[
1
0
]
.
T
h
e
m
u
lti
-
in
p
u
t,
m
u
lti
-
o
u
tp
u
t
(
MI
MO
)
n
atu
r
e
o
f
C
PS
r
eq
u
ir
es m
o
r
e
a
d
v
an
ce
d
an
d
s
o
p
h
is
ticated
m
ath
em
atica
l to
o
ls
to
co
n
tr
o
l
[
1
1
]
–
[
1
3
]
.
W
h
en
th
er
e
ar
e
n
o
n
lin
ea
r
d
y
n
am
ics,
ex
ter
n
al
d
is
tu
r
b
an
ce
s
,
an
d
p
ar
am
ete
r
u
n
ce
r
tain
ties
,
it
is
d
if
f
icu
lt
to
k
ee
p
C
PS
s
tab
le,
p
ar
ticu
lar
ly
wh
en
we
ar
e
d
ea
lin
g
with
MI
MO
s
y
s
tem
s
[
1
]
,
[
4
]
.
C
lass
ical
l
in
ea
r
izatio
n
o
f
ten
ca
n
n
o
t
tak
e
in
to
ac
co
u
n
t
th
e
co
m
p
lex
b
e
h
av
io
r
s
[
6
]
,
w
h
ils
t
th
e
n
etwo
r
k
its
elf
is
lik
el
y
to
in
v
o
lv
e
d
elay
s
o
r
v
u
l
n
er
ab
ilit
ies
[
3
]
,
[
1
4
]
.
T
h
e
b
ig
g
est
ch
allen
g
e
is
d
esig
n
i
n
g
co
n
t
r
o
ller
s
th
at
ca
n
ac
h
iev
e
b
o
th
s
tab
ilizatio
n
an
d
p
er
f
o
r
m
an
ce
at
th
e
s
am
e
tim
e
[
6
]
,
[
1
5
]
.
T
h
ese
c
h
allen
g
es
ar
e
o
f
p
a
r
ticu
lar
c
o
n
s
eq
u
e
n
ce
in
ap
p
licatio
n
s
lik
e
au
to
n
o
m
o
u
s
v
eh
icles
wh
er
e
p
r
ec
is
io
n
co
n
tr
o
l
m
atter
s
[
1
6
]
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
r
es
ea
r
ch
is
to
c
r
ea
te
a
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I
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2088
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r
e
,
we
p
r
o
v
i
d
ed
n
u
m
er
ical
an
aly
s
es
an
d
f
o
u
n
d
b
etter
s
tab
ilit
y
an
d
p
er
f
o
r
m
an
c
e
wh
ile
p
r
o
p
o
s
in
g
a
m
eth
o
d
th
at
ca
n
b
e
h
elp
f
u
l
to
s
ca
lin
g
in
C
P
S
ap
p
licatio
n
s
.
F
in
ally
,
th
e
f
lex
ib
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
f
r
am
ewo
r
k
allo
ws ex
ten
s
io
n
s
to
o
th
er
d
o
m
ain
s
in
clu
d
in
g
s
m
ar
t i
n
f
r
astr
u
ctu
r
e.
T
h
is
p
ap
er
is
o
r
g
an
ized
in
th
e
f
o
llo
win
g
way
:
r
elate
d
wo
r
k
in
s
ec
tio
n
2
;
m
eth
o
d
o
l
o
g
y
in
s
ec
tio
n
3
;
r
esu
lts
in
s
ec
tio
n
4
;
d
is
cu
s
s
io
n
o
f
f
in
d
i
n
g
s
an
d
lim
itatio
n
s
i
n
s
ec
tio
n
5
;
an
d
th
en
r
ec
o
m
m
en
d
atio
n
s
f
o
r
f
u
tu
r
e
wo
r
k
in
s
ec
tio
n
6
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
R
ec
en
t
wo
r
k
co
n
ce
r
n
in
g
cy
b
e
r
-
p
h
y
s
ical
s
y
s
tem
s
(
C
PS
)
,
o
n
t
o
p
ics
o
f
s
tab
ilit
y
an
d
co
n
tr
o
l
o
f
C
PS
f
o
r
p
u
r
p
o
s
es
lik
e
au
to
n
o
m
o
u
s
v
eh
icle
an
d
s
m
ar
t
g
r
id
s
y
s
tem
s
(
2
0
2
2
-
2
0
2
5
)
,
co
n
tin
u
es
to
d
ev
elo
p
.
R
u
b
io
-
Her
n
an
et
a
l.
[
1
7
]
a
p
p
l
ied
L
y
ap
u
n
o
v
m
eth
o
d
s
f
o
r
s
t
ab
ilit
y
o
f
C
PS
with
r
eg
ar
d
s
t
o
d
elay
s
,
an
d
C
h
esi
[
1
8
]
ap
p
lied
th
em
C
AD
o
n
th
r
esh
o
ld
s
to
r
ec
o
v
er
f
r
o
m
ac
tu
at
o
r
f
a
u
lts
[
1
]
,
[
5
]
.
J
o
u
y
b
ar
y
et
a
l.
[
1
9
]
a
p
p
lied
th
e
J
ac
o
b
ian
m
eth
o
d
th
r
o
u
g
h
lin
ea
r
izatio
n
to
r
o
b
o
tic
C
PS
'
s
li
n
ea
r
ized
d
y
n
am
ics
wh
ile
Sh
eik
h
s
am
ad
an
d
Pu
ig
[
2
0
]
e
x
ten
d
e
d
f
ee
d
b
ac
k
lin
e
ar
izatio
n
to
UAVs,
b
u
t
b
o
t
h
g
r
o
u
p
s
f
o
u
n
d
it
d
if
f
icu
lt
to
r
ep
r
esen
t
C
PS
p
er
f
o
r
m
an
ce
s
,
wh
ich
lay
in
a
s
et
o
f
co
m
p
lex
n
o
n
lin
ea
r
ities
[
4
]
,
[
9
]
.
Ph
an
et
a
l.
[
2
1
]
p
r
o
p
o
s
ed
th
at
ad
ap
tiv
e
lin
ea
r
izatio
n
ca
n
b
e
u
s
ed
to
d
e
al
with
th
ese
is
s
u
es
[
1
2
]
.
T
r
an
et
a
l.
[
2
2
]
ap
p
lie
d
L
QR
co
n
tr
o
l
t
o
au
t
o
n
o
m
o
u
s
v
e
h
icles
f
o
r
b
etter
o
p
er
atio
n
,
wh
ile
A
o
u
an
i
a
n
d
Olalla
[
2
3
]
ass
o
ciate
d
L
QR
with
m
ac
h
in
e
lear
n
in
g
as
a
s
m
ar
t
in
f
r
astru
ctu
r
e
co
n
tr
o
l
m
eth
o
d
[
6
]
,
[
1
0
]
.
J
ian
g
et
a
l.
[
2
4
]
a
n
d
So
n
g
et
a
l.
[
2
5
]
u
s
ed
L
MI
-
b
ased
L
QR
g
u
ar
a
n
tees
to
p
r
o
tect
C
PS
ag
ain
s
t
cy
b
er
-
attac
k
s
,
an
d
to
d
ev
el
o
p
m
u
lti
-
o
b
jectiv
e
co
n
tr
o
l,
r
esp
ec
tiv
ely
[
7
]
,
[
1
6
]
.
Yan
g
et
a
l.
[
2
6
]
i
n
co
r
p
o
r
ate
d
L
MI
s
with
r
o
b
u
s
t
co
n
tr
o
l
f
o
r
th
e
ca
s
e
o
f
MI
MO
C
PS
[
2
7
]
.
Z
h
ao
et
a
l.
[
2
8
]
an
d
Yan
g
et
a
l.
[
2
6
]
r
e
p
o
r
ted
ad
ap
tiv
e
co
n
t
r
o
l
an
d
s
ec
u
r
e
esti
m
atio
n
f
o
r
C
PS
s
ec
u
r
ity
[
2
]
,
[
3
]
.
Alca
la
et
a
l.
[
2
9
]
,
T
r
an
an
d
Vu
[
3
0
]
u
s
ed
L
QR
an
d
L
y
ap
u
n
o
v
m
eth
o
d
s
to
co
n
tr
o
l a
u
to
n
o
m
o
u
s
v
eh
icles
[
6
]
,
[
3
1
]
.
R
ev
iew
an
aly
s
is
:
Ma
n
y
r
ec
en
t
wo
r
k
s
ad
v
an
ce
C
PS
s
tab
ilit
y
an
d
c
o
n
tr
o
l
b
ased
p
r
im
ar
ily
o
n
L
y
ap
u
n
o
v
,
lin
ea
r
izatio
n
,
L
Q
R
,
an
d
L
MI
s
.
Desp
ite
th
ese
ad
v
an
ce
s
,
s
tu
d
ies
h
av
e
n
o
t
y
et
cr
ea
ted
a
u
n
if
ied
f
r
am
ewo
r
k
s
f
o
r
n
o
n
lin
ea
r
MI
MO
s
y
s
tem
s
.
T
h
is
p
ap
er
co
m
b
in
es
J
ac
o
b
ian
lin
ea
r
izatio
n
,
L
y
ap
u
n
o
v
s
tab
ilit
y
,
an
d
L
MI
b
ased
L
QR
in
th
e
co
n
tex
t o
f
a
ca
s
e
s
tu
d
y
with
an
a
u
to
n
o
m
o
u
s
v
eh
icle;
ad
d
r
ess
in
g
th
e
n
o
ted
g
ap
s
f
o
r
s
ca
lab
le
C
PS
ap
p
licatio
n
s
.
3.
M
E
T
H
O
D
T
h
is
s
tu
d
y
cr
ea
tes
an
d
d
em
o
n
s
tr
ates
a
co
n
tr
o
l
f
r
am
ewo
r
k
f
o
r
c
y
b
er
-
p
h
y
s
ical
s
y
s
tem
s
(
C
PS
)
u
s
in
g
th
e
f
o
llo
win
g
th
r
ee
m
eth
o
d
s
:
J
ac
o
b
ian
lin
ea
r
izatio
n
,
L
y
a
p
u
n
o
v
s
tab
ilit
y
an
aly
s
is
,
an
d
lin
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
(
L
QR
)
co
n
tr
o
l
v
ia
l
in
ea
r
m
atr
ix
in
eq
u
alities
(
L
MI
)
in
th
e
co
n
tex
t
o
f
a
n
au
to
n
o
m
o
u
s
v
eh
icle
ca
s
e
s
tu
d
y
.
T
h
e
s
tu
d
y
in
v
o
lv
es
th
r
e
e
co
m
p
o
n
en
ts
:
s
y
s
tem
lin
ea
r
izatio
n
,
s
tab
ilit
y
an
aly
s
is
an
d
co
n
tr
o
ller
s
y
n
th
esis
,
an
d
th
e
ca
s
e
s
tu
d
y
to
d
em
o
n
s
tr
ate
s
u
itab
ilit
y
.
3
.
1
.
Sy
s
t
e
m
lin
ea
riza
t
io
n
T
o
en
a
b
le
lin
ea
r
co
n
tr
o
l
tec
h
n
iq
u
es,
n
o
n
lin
ea
r
C
PS
d
y
n
a
m
ics
ar
e
lin
ea
r
ized
u
s
in
g
th
e
J
ac
o
b
ian
m
atr
ix
m
eth
o
d
.
T
h
e
n
o
n
lin
ea
r
s
y
s
tem
is
g
iv
en
in
s
tate
-
s
p
ac
e
f
o
r
m
:
˙
(
)
=
(
(
)
,
)
,
(
)
=
ℎ
(
(
)
,
)
(
1
)
wh
er
e:
−
(
)
∈
ℝ
is
th
e
s
tate
v
ec
to
r
,
−
(
(
)
,
)
∈
ℝ
r
ep
r
esen
ts
th
e
n
o
n
lin
ea
r
s
y
s
te
m
d
y
n
a
m
ics,
−
(
)
∈
ℝ
is
th
e
o
u
tp
u
t
v
ec
to
r
,
a
n
d
−
ℎ
(
(
)
,
)
∈
ℝ
is
th
e
n
o
n
lin
ea
r
o
u
tp
u
t f
u
n
ctio
n
.
T
h
e
J
ac
o
b
ia
n
lin
ea
r
izatio
n
a
p
p
r
o
x
im
ates
t
h
e
s
y
s
tem
a
r
o
u
n
d
an
eq
u
ilib
r
iu
m
p
o
i
n
t
(
0
,
0
)
u
s
in
g
a
f
ir
s
to
r
d
er
T
a
y
lo
r
ex
p
an
s
io
n
.
T
h
is
lin
ea
r
izatio
n
p
r
o
c
ess
y
ield
s
th
e
f
o
llo
win
g
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
7
6
-
5
2
8
5
5278
(
(
)
,
(
)
)
≈
(
0
,
0
)
+
|
(
0
,
0
)
(
(
)
−
0
)
+
|
(
0
,
0
)
(
(
)
−
0
)
ℎ
(
(
)
,
(
)
)
≈
ℎ
(
0
,
0
)
+
ℎ
|
(
0
,
0
)
(
(
)
−
0
)
+
ℎ
|
(
0
,
0
)
(
(
)
−
0
)
(
2
)
T
h
e
r
esu
ltin
g
J
ac
o
b
ia
n
m
atr
ic
es a
r
e:
=
|
(
0
,
0
)
,
=
|
(
0
,
0
)
(
3
)
At
th
e
eq
u
ilib
r
iu
m
p
o
in
t,
we
h
av
e
(
0
,
0
)
=
0
an
d
ℎ
(
0
,
0
)
=
0
,
lead
in
g
to
th
e
lin
ea
r
ized
s
y
s
tem
:
Δ
(
)
=
Δ
(
)
+
Δ
(
)
,
Δ
(
)
=
Δ
(
)
+
Δ
(
)
(
4
)
wh
er
e:
−
Δ
(
)
=
(
)
−
0
,
−
Δ
(
)
=
(
)
−
0
,
−
Ma
tr
ices
an
d
ar
e
d
er
iv
ed
s
im
ilar
ly
[
1
2
]
,
[
1
3
]
.
3
.
2
.
St
a
bil
it
y
a
na
ly
s
is
a
nd
co
ntr
o
ller
des
ig
n
Stab
ilit
y
is
en
s
u
r
ed
u
s
in
g
a
L
y
ap
u
n
o
v
f
u
n
ctio
n
,
an
d
an
o
p
tim
al
L
QR
co
n
tr
o
ller
is
s
y
n
t
h
esized
u
s
in
g
L
MI
s
.
Fo
r
th
e
lin
ea
r
ized
s
y
s
tem
:
Δ
=
⋅
Δ
+
⋅
Δ
(
5
)
A
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
d
ef
in
e
d
as:
(
Δ
)
=
Δ
⊤
Δ
(
6
)
wh
er
e
is
a
s
y
m
m
etr
ic
p
o
s
itiv
e
d
ef
in
ite
m
atr
ix
s
atis
f
y
in
g
:
(
Δ
)
>
0
f
o
r
all
Δ
≠
0
,
(
0
)
=
0
T
h
e
tim
e
d
er
iv
ativ
e
alo
n
g
th
e
s
y
s
tem
tr
ajec
to
r
ies is
:
˙
(
Δ
)
=
Δ
⊤
(
⊤
+
)
Δ
+
2Δ
⊤
Δ
(
7
)
Su
b
s
titu
tin
g
th
e
L
QR
co
n
tr
o
l l
aw
Δ
=
−
Δ
:
˙
(
Δ
)
=
Δ
⊤
(
⊤
+
−
2
)
Δ
(
8
)
Fo
r
asy
m
p
to
tic
s
tab
ilit
y
,
we
r
e
q
u
ir
e
˙
(
Δ
)
<
0
f
o
r
all
Δ
≠
0
.
T
h
e
L
QR
co
n
tr
o
ller
m
in
im
izes th
e
q
u
a
d
r
atic
co
s
t f
u
n
ctio
n
:
=
∫
∞
0
(
Δ
⊤
Δ
+
Δ
⊤
Δ
)
(
9
)
wh
er
e
is
s
y
m
m
etr
ic
p
o
s
itiv
e
s
em
i
-
d
ef
in
ite
(
≥
0
)
an
d
is
s
y
m
m
etr
ic
p
o
s
itiv
e
d
ef
in
ite
(
>
0
).
T
h
e
o
p
tim
al
co
n
tr
o
l la
w
is
g
iv
en
b
y
:
Δ
=
−
Δ
(
1
0
)
with
g
ain
g
iv
en
b
y
:
=
−
1
⊤
(
1
1
)
wh
er
e
s
o
lv
es th
e
Alg
eb
r
aic
R
icca
ti
eq
u
atio
n
(
AR
E
)
:
⊤
+
−
−
1
⊤
+
=
0
(
1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
S
ta
b
ilit
y
a
n
a
lysi
s
a
n
d
r
o
b
u
s
t c
o
n
tr
o
l o
f c
yb
er
-
p
h
ysica
l sys
te
ms:
in
teg
r
a
tin
g
…
(
R
a
c
h
id
B
o
u
ts
s
a
id
)
5279
Su
b
s
titu
tin
g
in
to
th
e
L
y
ap
u
n
o
v
d
er
iv
ativ
e:
˙
(
Δ
)
=
Δ
⊤
(
−
−
−
1
⊤
)
Δ
(
1
3
)
Sin
ce
≥
0
an
d
>
0
,
we
co
n
clu
d
e
th
at
˙
(
Δ
)
≤
0
,
an
d
if
>
0
,
we
ac
h
iev
e
asy
m
p
to
ti
c
s
tab
ilit
y
.
L
MI
s
ar
e
u
s
ed
to
f
o
r
m
u
late
t
h
e
co
n
tr
o
ller
d
esig
n
as
a
co
n
v
ex
o
p
tim
izatio
n
p
r
o
b
lem
.
T
h
e
s
tab
ilit
y
co
n
d
itio
n
is
:
Δ
⊤
(
⊤
+
−
2
)
Δ
<
0
(
1
4
)
Def
in
e
=
,
s
o
=
−
1
.
T
h
e
L
MI
b
ec
o
m
e
s
:
⊤
+
−
−
⊤
⊤
<
0
(
1
5
)
I
n
co
r
p
o
r
atin
g
p
er
f
o
r
m
a
n
ce
,
th
e
L
MI
b
ec
o
m
es:
⊤
+
−
−
⊤
⊤
+
<
0
(
1
6
)
with
co
n
s
tr
ain
ts
>
0
.
T
h
e
co
n
tr
o
l
g
ain
is
r
ec
o
v
er
e
d
as:
=
−
1
(
1
7
)
T
h
is
L
MI
is
s
o
lv
ed
u
s
in
g
n
u
m
er
ical
to
o
ls
lik
e
MA
T
L
AB
's
C
VX
s
o
lv
er
[
7
]
,
[
1
8
]
.
3
.
3
.
Ca
s
e
s
t
ud
y
s
et
up
:
a
uto
n
o
m
o
us
v
ehicle
m
o
del
T
h
e
f
r
am
ewo
r
k
is
ap
p
lied
to
an
au
to
n
o
m
o
u
s
v
eh
icle,
m
o
d
e
led
d
y
n
a
m
ically
to
ac
co
u
n
t
f
o
r
tire
-
s
lip
u
s
in
g
Pace
jk
a’
s
tire
m
o
d
el
[
2
4
]
.
T
h
e
d
y
n
am
ic
m
o
d
el,
d
er
iv
e
d
f
r
o
m
New
to
n
’
s
s
ec
o
n
d
law,
is
g
iv
en
b
y
:
{
̇
=
−
.
s
i
n
(
)
−
.
.
+
.
+
̇
=
.
co
s
(
)
+
−
.
̇
=
.
.
co
s
(
)
−
.
(
1
8
)
I
n
th
ese
e
q
u
atio
n
s
,
l
o
n
g
itu
d
i
n
al,
later
al,
a
n
d
r
o
tatio
n
al
v
elo
cities
in
th
e
v
e
h
icle’
s
f
r
a
m
e
ar
e
r
ep
r
esen
ted
,
r
esp
ec
tiv
ely
,
b
y
th
e
v
a
r
iab
les
,
,
an
d
in
th
ese
f
o
r
m
u
las.
T
h
e
co
n
tr
o
l in
p
u
ts
ar
e
δ a
n
d
a,
wh
ich
s
tan
d
f
o
r
th
e
f
r
o
n
t
tire
’
s
s
teer
in
g
a
n
g
l
e
an
d
lo
n
g
itu
d
in
al
ac
ce
ler
ati
o
n
,
r
esp
ec
tiv
ely
.
,
,
,
an
d
s
tan
d
f
o
r
t
h
e
v
eh
icle’
s
m
ass
,
in
er
tia,
an
d
th
e
s
ep
ar
atio
n
b
etwe
en
th
e
f
r
o
n
t
an
d
r
ea
r
w
h
ee
l
ax
is
f
r
o
m
t
h
e
ce
n
ter
o
f
g
r
av
ity
,
r
esp
ec
tiv
ely
.
an
d
in
d
icate
th
e
later
al
f
o
r
ce
s
ac
tin
g
o
n
th
e
f
r
o
n
t
an
d
r
ea
r
tire
s
.
Mo
r
eo
v
er
,
g
s
tan
d
s
f
o
r
th
e
g
r
av
itatio
n
al
ac
ce
ler
ati
o
n
co
n
s
tan
t,
an
d
µ
f
o
r
th
e
f
r
ictio
n
co
ef
f
icien
t.
an
d
ca
n
b
e
m
o
d
eled
u
s
in
g
Pa
ce
jk
a’
s
tire
m
o
d
el
[
3
1
]
as f
o
llo
ws:
{
=
3
.
s
in
(
2
.
−
1
(
1
.
)
)
;
=
−
−
1
(
+
.
)
=
3
.
s
in
(
2
.
−
1
(
1
.
)
)
;
=
−
−
1
(
+
.
)
(
1
9
)
I
n
th
is
ca
s
e,
th
e
co
n
s
tan
ts
1
,
2
,
a
n
d
3
m
u
s
t
b
e
ascer
tain
e
d
em
p
ir
ically
.
T
h
e
tire
m
o
d
el
s
h
o
ws
t
h
at
an
d
v
ar
y
n
o
n
lin
ea
r
with
α
,
o
r
t
h
e
s
lip
an
g
le.
On
th
e
o
t
h
er
h
an
d
,
t
h
e
eq
u
ati
o
n
s
ca
n
b
e
m
ad
e
s
im
p
ler
b
y
ass
u
m
in
g
tin
y
α
,
th
e
eq
u
atio
n
s
ca
n
b
e
r
e
d
u
ce
d
to
:
{
=
.
(
−
−
.
)
=
.
(
−
+
.
)
(
2
0
)
w
h
er
e
an
d
r
ep
r
esen
t th
e
s
tiff
n
ess
o
f
th
e
f
r
o
n
t a
n
d
r
ea
r
w
h
e
el
tire
s
,
r
esp
ec
tiv
ely
.
T
a
b
le
1
d
is
p
la
y
s
t
h
e
d
eta
ils
o
f
th
e
r
ac
i
n
g
v
e
h
i
cle
a
n
d
t
h
e
r
o
u
t
e
t
h
at
we
r
e
e
m
p
lo
y
e
d
in
t
h
is
p
r
o
je
ct
[
6
]
.
T
h
e
s
y
s
tem
is
lin
ea
r
ized
at
a
n
o
p
er
atin
g
p
o
in
t
=
[
0
,
0
,
0
]
an
d
=
[
0
,
0
]
,
y
ield
in
g
m
atr
ices
an
d
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
7
6
-
5
2
8
5
5280
=
|
,
=
|
(
2
1
)
T
h
e
lin
ea
r
ized
s
tate
-
s
p
ac
e
r
ep
r
esen
tatio
n
is
:
Δ
=
⋅
Δ
+
⋅
Δ
Δ
=
⋅
Δ
(
2
2
)
wh
er
e:
Δ
=
[
Δ
Δ
Δ
]
⊤
an
d
Δ
=
[
Δ
Δ
]
⊤
.
T
ab
le
1
.
T
h
e
d
etails o
f
th
e
r
ac
i
n
g
v
eh
icle
V
a
r
i
a
b
l
e
V
a
l
u
e
U
n
i
t
I
f
0
.
9
0
2
m
Ir
0
.
6
3
8
m
m
1
9
6
Kg
I
93
K
g
.
m
2
C
f
1
7
9
7
4
N
/
r
a
d
Cr
2
4
1
8
1
N
/
r
a
d
µ
0
.
5
-
-
-
-
-
-
-
-
g
9
.
8
1
m/
s
2
3
.
4
.
Sim
ula
t
i
o
n
s
et
up
T
h
e
s
im
u
latio
n
en
v
ir
o
n
m
en
t f
o
r
th
e
au
to
n
o
m
o
u
s
v
eh
icle
m
o
d
el
was r
ea
lized
in
MA
T
L
A
B
2
0
1
6
.
T
h
e
C
VX
s
o
lv
er
was
u
tili
ze
d
in
s
o
lv
in
g
th
e
lin
ea
r
m
atr
ix
in
e
q
u
alities
(
L
MI
)
f
o
r
d
esig
n
in
g
t
h
e
lin
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
(
L
QR
)
co
n
t
r
o
ller
to
g
u
ar
an
tee
s
tab
ilit
y
an
d
o
p
ti
m
u
m
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
e
v
eh
icle
d
y
n
a
m
ics
wer
e
r
ep
r
esen
ted
with
n
o
n
lin
ea
r
an
d
lin
ea
r
ized
s
y
s
tem
s
,
w
h
er
e
th
e
lin
ea
r
ized
s
y
s
tem
wa
s
o
b
tain
ed
a
b
o
u
t
a
n
o
p
er
atin
g
p
o
in
t.
a.
Simu
latio
n
d
u
r
atio
n
:
T
h
e
s
im
u
latio
n
was
ca
r
r
ied
o
u
t
o
n
a
ti
m
e
h
o
r
izo
n
o
f
2
0
s
ec
o
n
d
s
,
with
a
tim
e
s
tep
o
f
0
.
0
1
s
ec
o
n
d
s
i
n
o
r
d
er
to
s
tr
ik
e
a
b
alan
ce
b
etwe
en
c
o
m
p
u
tatio
n
al
s
p
ee
d
a
n
d
ac
cu
r
ac
y
o
f
th
e
n
u
m
er
ical
s
o
lu
tio
n
.
b.
C
o
n
tr
o
l
i
n
p
u
ts
:
T
h
e
v
eh
icle
s
y
s
tem
was
p
er
tu
r
b
ed
with
s
tep
in
p
u
ts
f
o
r
s
teer
in
g
an
g
le
(
δ)
a
n
d
lo
n
g
itu
d
i
n
al
ac
ce
ler
atio
n
(
a)
i
n
tr
o
d
u
ce
d
at
s
p
ec
if
ic
tim
e
in
ter
v
als to
s
im
u
late
r
ea
l
-
wo
r
ld
co
n
tr
o
l d
is
tu
r
b
an
ce
s
.
c.
Nu
m
e
r
ic
al
i
n
t
eg
r
a
tio
n
:
T
h
e
tr
a
je
cto
r
y
o
f
th
e
n
o
n
li
n
ea
r
s
y
s
tem
s
ta
te
w
a
s
in
t
eg
r
a
ted
n
u
m
er
ica
l
ly
b
y
MA
T
L
A
B
's
o
d
e4
5
s
o
lv
er
,
wh
i
ch
i
s
s
u
i
tab
le
f
o
r
in
teg
r
at
in
g
s
t
if
f
d
i
f
f
er
en
t
ia
l
eq
u
at
i
o
n
s
.
T
h
e
s
o
lv
e
r
ca
l
cu
l
at
ed
th
e
tr
a
jec
to
r
y
o
f
th
e
v
eh
ic
le
s
ta
te
s
(
,
,
)
b
a
s
ed
o
n
th
e
co
n
t
r
o
l
in
p
u
t
s
an
d
v
eh
i
cl
e
d
y
n
am
i
c
s
.
d.
C
o
n
tr
o
l
d
esig
n
:
T
h
e
L
QR
co
n
tr
o
ller
was
d
esig
n
ed
b
y
m
in
i
m
izin
g
a
q
u
ad
r
atic
c
o
s
t
f
u
n
cti
o
n
,
u
s
in
g
L
MI
to
en
f
o
r
ce
s
tab
ilit
y
co
n
s
tr
ain
ts
.
T
h
e
co
n
tr
o
l
g
ai
n
m
atr
ix
K
was
co
m
p
u
ted
to
r
eg
u
late
th
e
s
y
s
tem
’
s
r
esp
o
n
s
e
an
d
s
tab
ilize
th
e
v
eh
icle’
s
m
o
tio
n
b
ased
o
n
th
e
lin
ea
r
ized
s
y
s
tem
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
c
o
n
tr
o
ller
was
ev
alu
ated
b
ased
o
n
v
ar
i
o
u
s
m
etr
ics,
wh
ich
i
n
clu
d
e
th
e
tr
ac
k
in
g
er
r
o
r
(
th
e
d
if
f
e
r
en
ce
b
etwe
en
th
e
tar
g
et
an
d
ac
tu
al
v
eh
icle
s
tates),
co
n
tr
o
l
in
p
u
t
ef
f
o
r
ts
(
th
e
s
teer
in
g
an
d
ac
ce
ler
atio
n
)
,
an
d
clo
s
ed
-
l
o
o
p
p
e
r
f
o
r
m
an
ce
(
s
u
ch
as settl
in
g
tim
e,
o
v
er
s
h
o
o
t,
an
d
s
tead
y
-
s
tated
er
r
o
r
)
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
Resul
t
s
B
ef
o
r
e
th
e
n
u
m
er
ical
r
esu
lts
,
i
t
is
wo
r
th
m
en
tio
n
i
n
g
th
at
we
ap
p
lied
th
e
r
o
b
u
s
t
co
n
tr
o
l
f
r
a
m
ewo
r
k
to
th
e
ca
s
e
s
tu
d
y
o
f
a
n
au
to
n
o
m
o
u
s
v
eh
icle
th
at
was
d
escr
i
b
ed
in
(
1
8
)
.
T
h
e
L
QR
co
n
tr
o
ller
was
f
o
r
m
u
lated
with
L
MI
an
d
s
u
b
s
eq
u
e
n
tly
s
o
lv
ed
with
MA
T
L
AB
u
s
in
g
th
e
s
em
i
-
d
ef
in
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(
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[
1
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w
h
o
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5
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v
ex
Alg
e
b
r
aic
R
icca
ti
E
x
am
p
le
p
r
o
b
lem
ca
n
b
e
r
ed
u
ce
d
t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
7
6
-
5
2
8
5
5282
a
co
n
v
ex
o
p
tim
izatio
n
p
r
o
b
le
m
f
o
r
im
p
r
o
v
ed
co
m
p
u
tatio
n
tim
e
[
7
]
.
T
h
is
is
esp
ec
ially
b
e
n
ef
icial
in
r
ea
l
-
tim
e
C
PS
ap
p
licatio
n
s
with
q
u
ick
co
n
v
er
g
en
ce
(
2
0
s
ec
o
n
d
s
s
ettlin
g
tim
e)
,
as
s
ee
n
in
th
e
tr
aj
ec
to
r
y
tr
ac
k
in
g
o
f
au
to
n
o
m
o
u
s
v
eh
icles.
Ho
wev
er
,
th
e
f
r
am
ewo
r
k
h
as lim
itatio
n
s
.
T
h
e
ar
b
itra
r
y
s
elec
t
io
n
o
f
Qan
d
R
,
wh
ile
ef
f
ec
tiv
e
,
m
ay
n
o
t
b
e
o
p
tim
al
f
o
r
all
C
PS
d
y
n
am
ics.
As
m
en
tio
n
ed
i
n
J
ian
g
et
a
l.
[
2
4
]
,
f
u
r
th
e
r
tu
n
in
g
o
f
Q
a
n
d
R
with
r
esp
ec
t
t
o
th
e
s
y
s
tem
ca
n
f
u
r
th
e
r
d
ec
r
ea
s
e
o
v
er
s
h
o
o
t
an
d
en
e
r
g
y
co
n
s
u
m
p
tio
n
.
Ad
d
itio
n
all
y
,
J
ac
o
b
i
an
lin
ea
r
izatio
n
is
v
alid
o
n
ly
f
o
r
s
m
all
p
er
tu
r
b
a
tio
n
s
ab
o
u
t
th
e
o
p
er
atin
g
p
o
i
n
t
an
d
s
o
it
is
o
n
ly
u
s
ef
u
l
i
n
h
ig
h
ly
n
o
n
lin
ea
r
s
itu
atio
n
s
in
v
er
y
s
m
all
n
ei
g
h
b
o
r
h
o
o
d
ab
o
u
t
th
e
o
p
e
r
atin
g
p
o
in
t
[
1
3
]
.
T
h
e
au
to
n
o
m
o
u
s
v
e
h
icle
m
o
d
el,
b
ased
o
n
Pace
jk
a'
s
tire
m
o
d
el
[
3
1
]
,
ass
u
m
es
s
m
all
s
lip
an
g
les
,
wh
ich
ca
n
n
o
t
b
e
ass
u
m
ed
d
u
r
in
g
ag
g
r
ess
iv
e
m
an
eu
v
er
s
.
T
h
e
co
n
clu
s
io
n
s
o
f
th
is
s
tu
d
y
g
e
n
er
alize
n
o
t
o
n
ly
to
a
u
to
n
o
m
o
u
s
v
eh
icles
b
u
t
also
to
o
th
er
C
PS
d
o
m
ain
s
—
s
u
ch
as
in
d
u
s
tr
ial
a
u
to
m
atio
n
o
r
s
m
ar
t
in
f
r
astru
ct
u
r
e
—
wh
er
e
MI
MO
s
y
s
tem
s
e
n
co
u
n
ter
th
e
s
am
e
s
tab
ilit
y
is
s
u
es
[
2
]
.
B
ec
au
s
e
o
f
its
g
en
er
al
f
r
am
ew
o
r
k
,
we
u
s
ed
L
MI
s
an
d
co
u
l
d
q
u
ick
l
y
ap
p
ly
it
to
o
t
h
er
ap
p
licatio
n
s
ju
s
t
b
y
m
o
d
if
y
in
g
th
e
s
y
s
tem
m
atr
ices
an
d
p
er
f
o
r
m
a
n
ce
r
eq
u
i
r
em
en
ts
.
Fo
r
ex
am
p
le,
ap
p
l
y
in
g
ad
ap
tiv
e
co
n
tr
o
l
m
eth
o
d
s
,
as
p
r
o
p
o
s
ed
b
y
L
u
an
d
Yan
g
[
3
]
,
m
ay
im
p
r
o
v
e
r
esil
ien
ce
ag
ain
s
t
cy
b
er
-
attac
k
s
with
in
n
etwo
r
k
ed
C
PS
.
Fig
u
r
e
1
.
C
o
m
p
a
r
is
o
n
o
f
lin
ea
r
ized
an
d
n
o
n
lin
ea
r
v
e
h
icle
d
y
n
am
ics:
lo
n
g
itu
d
in
al
v
elo
city
,
later
al
v
elo
city
,
an
d
y
aw
r
ate
d
ev
iatio
n
s
Fig
u
r
e
2
.
State
tr
ajec
to
r
ies,
co
n
tr
o
l in
p
u
ts
,
an
d
tr
ac
k
in
g
e
r
r
o
r
f
o
r
th
e
L
QR
-
co
n
tr
o
lled
s
y
s
te
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
S
ta
b
ilit
y
a
n
a
lysi
s
a
n
d
r
o
b
u
s
t c
o
n
tr
o
l o
f c
yb
er
-
p
h
ysica
l sys
te
ms:
in
teg
r
a
tin
g
…
(
R
a
c
h
id
B
o
u
ts
s
a
id
)
5283
Fu
tu
r
e
wo
r
k
will
ex
am
in
e
d
e
v
elo
p
in
g
o
p
tim
al
Q
a
n
d
R
m
atr
ices
b
ased
o
n
th
e
s
p
ec
if
ics
o
f
a
g
iv
en
s
y
s
tem
,
p
o
ten
tially
u
s
in
g
iter
ativ
e
alg
o
r
ith
m
s
[
2
4
]
.
Similar
ly
,
ad
ap
tiv
e
o
r
n
o
n
lin
ea
r
co
n
tr
o
l
ap
p
r
o
ac
h
es
co
u
ld
b
e
co
n
s
id
er
ed
f
o
r
m
an
ag
i
n
g
s
u
b
s
tan
tially
h
ig
h
p
er
t
u
r
b
at
io
n
s
f
o
r
en
h
an
cin
g
r
o
b
u
s
tn
e
s
s
,
p
ar
ticu
lar
ly
f
o
r
v
eh
icles
with
h
ig
h
-
s
p
ee
d
tr
av
el
[
2
5
]
.
Fin
ally
,
th
e
ac
tu
al
p
h
y
s
ical
C
P
S
p
latf
o
r
m
s
s
h
o
u
ld
r
u
n
th
e
f
r
a
m
ewo
r
k
g
iv
en
th
at
im
p
lem
en
tatio
n
will
allo
w
f
o
r
test
in
g
th
e
im
p
lem
en
tatio
n
p
r
ac
ticality
a
n
d
a
d
d
r
e
s
s
s
o
m
e
o
f
th
e
r
ea
l
-
tim
e
co
n
s
tr
ain
ts
an
d
h
ar
d
war
e
lim
itatio
n
s
th
at
em
er
g
e
in
a
C
PS
.
I
n
s
u
m
m
ar
y
,
th
is
s
tu
d
y
u
n
if
ies
J
ac
o
b
ia
n
lin
ea
r
izatio
n
,
L
y
a
p
u
n
o
v
m
eth
o
d
s
,
an
d
L
M
I
-
b
ased
L
QR
co
n
tr
o
l
to
p
r
o
v
i
d
e
a
r
o
b
u
s
t
an
d
ef
f
icien
t
f
r
am
ewo
r
k
f
o
r
C
PS
s
tab
ilit
y
an
d
p
er
f
o
r
m
an
ce
.
T
h
e
r
esu
lts
u
n
d
e
r
s
co
r
e
i
ts
p
o
ten
tial
f
o
r
au
to
n
o
m
o
u
s
v
eh
icles
an
d
b
r
o
a
d
er
C
PS
ap
p
licatio
n
s
,
wh
ile
h
ig
h
lig
h
tin
g
ar
ea
s
f
o
r
f
u
r
th
er
r
ef
in
e
m
en
t.
5.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
f
u
n
ctio
n
e
d
as
a
r
ig
o
r
o
u
s
ly
d
ev
elo
p
e
d
co
n
tr
o
l
f
r
am
ewo
r
k
f
o
r
C
PS
th
at
s
u
cc
ess
f
u
lly
u
tili
ze
d
J
ac
o
b
ian
li
n
ea
r
izatio
n
,
L
y
ap
u
n
o
v
s
tab
ilit
y
,
a
n
d
L
QR
co
n
tr
o
l
b
y
u
s
in
g
L
MI
.
I
n
t
h
e
ap
p
licatio
n
o
f
th
e
au
to
n
o
m
o
u
s
v
eh
icle
ca
s
e
s
tu
d
y
,
th
is
co
n
tr
o
l
f
r
am
ewo
r
k
y
ield
ed
a
s
ettlin
g
tim
e
o
f
2
0
s
ec
o
n
d
s
,
an
o
v
er
s
h
o
o
t
o
f
3
.
8187%
,
an
d
a
s
tead
y
-
s
tate
er
r
o
r
o
f
2
.
688
×
10
−
7
d
em
o
n
s
tr
atin
g
g
o
o
d
tr
ac
k
in
g
o
f
tr
ajec
to
r
y
an
d
r
o
b
u
s
t
s
tab
ilit
y
.
T
h
e
ap
p
r
o
ac
h
was
d
esig
n
ed
to
o
v
er
c
o
m
e
th
e
ch
allen
g
es
o
f
n
o
n
lin
ea
r
MI
MO
s
y
s
tem
s
,
an
d
s
till
co
n
v
er
g
e
o
p
tim
ally
to
th
e
d
esire
d
tr
ajec
to
r
y
with
s
m
all
p
er
t
u
r
b
atio
n
.
T
h
e
r
esu
lts
ex
h
ib
ite
d
p
r
o
v
id
e
th
e
in
ten
t
o
f
d
e
v
elo
p
in
g
th
e
f
r
am
ewo
r
k
f
o
r
au
t
o
n
o
m
o
u
s
v
e
h
icles
an
d
p
er
h
ap
s
o
t
h
er
C
PS
ap
p
licatio
n
s
,
s
u
ch
as
in
d
u
s
tr
ial
au
to
m
atio
n
a
n
d
s
m
ar
t in
f
r
astru
ctu
r
e,
alth
o
u
g
h
,
th
er
e
was so
m
e
ar
b
itra
r
in
ess
o
f
Q
a
n
d
R
m
atr
ices;
th
u
s
,
s
y
s
tem
s
p
ec
if
ic
tu
n
in
g
wo
u
ld
n
ee
d
to
tak
e
p
lace
to
en
h
an
ce
o
p
tim
iz
atio
n
.
Fu
tu
r
e
wo
r
k
s
h
o
u
ld
ex
p
lo
r
e
m
eth
o
d
s
to
o
p
tim
ize
th
e
m
atr
i
ce
s
to
im
p
r
o
v
e
p
er
f
o
r
m
a
n
ce
f
o
r
d
if
f
er
en
t
C
PS
d
y
n
am
ics,
as
well
as
m
e
th
o
d
s
f
o
r
ad
ap
tiv
e
co
n
tr
o
l
wh
ich
m
ig
h
t
p
r
o
v
i
d
e
lar
g
er
r
esil
ien
ce
to
u
n
ce
r
tain
ty
th
r
o
u
g
h
r
ea
l
-
tim
e
ad
a
p
tin
g
.
T
h
is
f
r
am
ewo
r
k
estab
lis
h
es
a
s
af
eg
u
ar
d
ed
b
asis
f
o
r
e
n
h
an
ce
m
en
t
in
C
PS
co
n
tr
o
l,
an
d
o
f
f
er
s
n
ew
av
e
n
u
es f
o
r
im
p
lem
en
tatio
n
an
d
ap
p
lied
wo
r
k
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
is
co
n
d
u
cted
in
d
ep
en
d
en
tly
an
d
is
f
u
n
d
e
d
b
y
th
e
r
esear
ch
er
s
th
em
s
elv
es.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT
)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
R
ac
h
id
B
o
u
ts
s
aid
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Said
Kr
ir
im
✓
✓
✓
✓
✓
✓
✓
Ab
d
eljab
ar
Ab
o
u
lk
ass
im
✓
✓
E
l H
an
af
i A
r
jd
al
✓
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Yo
u
s
s
ef
Mo
u
m
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i
✓
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✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
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Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
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Evaluation Warning : The document was created with Spire.PDF for Python.