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20
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p
p
.
2758
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2
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6
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I
SS
N:
2088
-
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7
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DOI
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1
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v
15
i
3
.
pp
2
7
5
8
-
2
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2758
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ters
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k
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e
s.
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h
e
a
d
a
p
ti
v
e
b
a
c
k
ste
p
p
in
g
m
e
th
o
d
d
e
sig
n
s
t
h
e
c
o
n
tr
o
l
f
u
n
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ti
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n
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d
e
m
o
n
stra
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g
it
s
a
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o
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ize
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h
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m
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p
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rd
s
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n
traje
c
to
ry
u
sin
g
L
y
a
p
u
n
o
v
sta
b
il
i
ty
.
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o
tes
t
th
e
ro
b
u
stn
e
ss
o
f
th
e
p
r
o
p
o
se
d
c
o
n
tro
l
m
e
th
o
d
,
sim
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lati
o
n
s
we
re
c
o
n
d
u
c
ted
with
v
a
rio
u
s
sc
e
n
a
rio
s,
in
c
l
u
d
i
n
g
d
istu
rb
a
n
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e
s
t
o
th
e
ste
a
d
y
-
sta
te
sy
ste
m
.
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imu
latio
n
re
su
lt
s
s
h
o
w
th
a
t
th
e
c
o
n
tro
ll
e
r
su
c
c
e
ss
fu
ll
y
d
r
o
v
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th
e
sy
ste
m
o
u
t
p
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lo
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traje
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in
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e
v
e
n
with
sig
n
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c
a
n
t
d
ist
u
rb
a
n
c
e
s.
K
ey
w
o
r
d
s
:
Ad
ap
tiv
e
co
n
tr
o
l
B
ac
k
s
tep
p
in
g
m
eth
o
d
J
er
k
eq
u
atio
n
T
r
ac
k
in
g
c
o
n
tr
o
l
Un
ce
r
tain
s
y
s
tem
co
n
tr
o
l
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Kh
o
zin
Mu
’
tam
a
r
C
o
m
p
u
tatio
n
al
Ma
th
em
atics R
esear
ch
Gr
o
u
p
,
Dep
ar
tm
e
n
t o
f
Ma
th
em
atics,
Facu
lty
o
f
Ma
t
h
em
atics a
n
d
Natu
r
al
Scien
ce
s
,
Un
iv
er
s
itas
R
iau
B
in
a
W
id
y
a
C
am
p
u
s
KM
1
2
.
5
,
T
am
p
an
,
Pek
an
b
a
r
u
2
8
2
9
3
,
I
n
d
o
n
esia
E
m
ail: k
h
o
zin
.
m
u
tam
ar
@
u
n
r
i.
ac
.
id
1.
I
NT
RO
D
UCT
I
O
N
Ma
th
em
atica
l
m
o
d
els
ar
e
f
o
r
m
u
lated
b
y
tr
an
s
latin
g
n
atu
r
al
p
h
en
o
m
e
n
a
in
to
m
ath
e
m
atica
l
eq
u
atio
n
s
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
v
ar
iab
les
an
d
th
eir
p
r
o
g
r
ess
io
n
i
s
r
elian
t
o
n
p
ar
am
eter
s
,
wh
ic
h
ca
n
b
e
o
b
tain
ed
th
r
o
u
g
h
d
ir
ec
t
m
ea
s
u
r
em
en
ts
o
r
d
ata
p
r
o
ce
s
s
in
g
.
Ho
we
v
er
,
im
p
r
ec
is
e
m
ea
s
u
r
em
en
t
tech
n
i
q
u
es
o
r
m
e
asu
r
in
g
d
ev
ices
ca
n
lead
to
u
n
s
u
itab
le
p
ar
am
eter
v
alu
es,
as
ca
n
th
e
m
eth
o
d
s
u
s
ed
to
esti
m
ate
p
ar
am
eter
s
th
r
o
u
g
h
d
ata
p
r
o
ce
s
s
in
g
.
E
v
en
th
e
s
lig
h
te
s
t
er
r
o
r
in
p
ar
am
eter
v
alu
es
ca
n
s
ig
n
if
ican
tly
im
p
ac
t
th
e
ac
cu
r
ac
y
o
f
th
e
m
ath
em
atica
l
m
o
d
el.
T
ak
e,
f
o
r
ex
am
p
le,
th
e
ep
id
e
m
ic
m
o
d
el
u
s
ed
to
an
al
y
ze
th
e
s
p
r
ea
d
o
f
co
r
o
n
av
ir
u
s
d
is
ea
s
e
(
C
OVI
D
-
19
)
in
[
1
]
–
[
4
]
.
T
h
e
m
o
d
el
em
p
lo
y
s
a
f
i
x
ed
in
cu
b
atio
n
v
al
u
e
o
b
tain
e
d
b
y
d
iv
id
in
g
th
e
in
cu
b
atio
n
tim
e
b
y
th
e
m
ass
in
y
ea
r
s
.
T
h
is
v
alu
e
d
o
es
n
o
t
r
ef
lect
th
e
r
ea
lity
t
h
at
th
e
i
n
cu
b
atio
n
p
e
r
io
d
v
ar
ies
f
o
r
ea
ch
in
d
iv
id
u
al,
as
h
ig
h
lig
h
ted
in
[
5
]
–
[
8
]
.
I
t
was
k
n
o
wn
th
at
th
e
in
cu
b
atio
n
p
er
io
d
is
n
o
t
co
n
s
tan
t
an
d
ch
an
g
es o
v
e
r
tim
e
o
r
at
ce
r
tai
n
in
ter
v
als.
T
h
e
J
er
k
eq
u
atio
n
is
a
th
ir
d
-
o
r
d
er
o
r
d
in
ar
y
d
if
f
er
en
tial
eq
u
atio
n
th
at
ca
n
ex
h
ib
it
ch
ao
s
,
p
er
th
e
Po
in
tcar
e
-
B
en
d
ix
s
o
n
th
eo
r
em
[
9
]
.
I
t
is
ex
p
r
ess
ed
as
(
3
)
(
)
=
(
(
2
)
(
)
,
(
1
)
(
)
,
(
)
)
,
wh
er
e
(
)
d
en
o
tes
th
e
jer
k
ter
m
an
d
(
)
(
)
=
(
)
.
T
h
e
s
im
p
le
s
t
f
o
r
m
ex
p
er
ien
ce
s
ch
ao
s
is
(
3
)
(
)
+
(
2
)
(
)
–
(
(
1
)
)
2
(
)
+
(
)
=
0
,
d
escr
ib
ed
in
[
1
0
]
,
[
1
1
]
.
An
o
th
er
f
o
r
m
is
th
e
Gen
esio
-
T
esi
eq
u
atio
n
,
wh
ich
in
clu
d
es
a
q
u
ad
r
atic
f
o
r
m
in
th
e
f
ir
s
t
o
r
d
er
.
I
ts
g
en
er
al
f
o
r
m
is
ex
p
r
ess
ed
as
(
3
)
(
)
+
(
2
)
(
)
+
(
1
)
(
)
+
(
)
−
2
(
)
=
0
,
as
s
ee
n
in
[
1
2
]
,
[
1
3
]
.
T
h
e
J
e
r
k
eq
u
atio
n
is
wid
ely
u
s
ed
i
n
an
aly
zin
g
wav
e
b
eh
av
i
o
r
in
elec
tr
o
n
ic
cir
cu
its
.
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
Tr
a
ck
in
g
co
n
tr
o
l o
f u
n
ce
r
ta
in
th
ir
d
o
r
d
er jerk
eq
u
a
tio
n
Gen
esio
-
Tes
i u
s
in
g
…
(
K
h
o
z
in
Mu
’
ta
ma
r
)
2759
Ho
wev
er
,
th
e
r
esis
to
r
v
alu
e
d
eter
m
in
es
its
p
ar
am
eter
v
alu
e
,
wh
ich
h
as
a
s
p
ec
if
ic
v
alu
e
a
n
d
to
ler
an
ce
lim
it,
r
esu
ltin
g
in
u
n
ce
r
tain
ty
in
t
h
e
p
ar
am
eter
v
al
u
e,
as m
en
tio
n
ed
in
[
1
3
]
,
[
1
4
]
.
A
r
eliab
le
ap
p
r
o
ac
h
to
d
es
ig
n
in
g
c
o
n
tr
o
ller
s
f
o
r
n
o
n
li
n
ea
r
s
y
s
tem
s
with
u
n
ce
r
tai
n
ty
is
th
e
b
ac
k
s
tep
p
in
g
m
eth
o
d
.
Desp
ite
its
iter
ativ
e
n
atu
r
e,
th
is
tec
h
n
iq
u
e
p
r
o
v
id
es
im
p
r
ess
iv
e
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
d
u
e
to
its
f
o
cu
s
o
n
s
y
s
tem
s
tab
ilit
y
at
ea
ch
s
tag
e
u
s
in
g
L
y
a
p
u
n
o
v
s
tab
ilit
y
cr
iter
ia.
Giv
en
its
r
o
b
u
s
tn
ess
,
it
is
n
o
s
u
r
p
r
is
e
th
at
th
e
b
ac
k
s
tep
p
in
g
m
eth
o
d
is
wid
ely
em
p
l
o
y
ed
ac
r
o
s
s
v
ar
io
u
s
f
ield
s
.
So
m
e
s
tu
d
ies,
s
u
ch
as
[
1
5
]
,
[
1
6
]
,
h
a
v
e
s
u
cc
ess
f
u
lly
d
ep
lo
y
e
d
th
e
b
ac
k
s
tep
p
in
g
m
eth
o
d
to
s
et
u
p
co
n
tr
o
ller
s
f
o
r
th
e
DC
-
DC
b
u
ck
co
n
v
er
ter
.
T
h
e
b
ac
k
s
tep
p
in
g
m
eth
o
d
h
as
also
p
r
o
v
ed
h
el
p
f
u
l
in
m
o
tio
n
co
n
tr
o
ller
s
f
o
r
u
n
m
an
n
ed
ae
r
ial
v
eh
icles
(
UAVs)
in
[
1
7
]
–
[
2
1
]
an
d
s
h
ip
m
o
tio
n
m
a
n
eu
v
er
s
in
[
2
2
]
–
[
2
4
]
.
Mo
r
eo
v
er
,
Hajji
et
a
l.
[
2
4
]
h
av
e
im
p
lem
en
ted
th
e
b
ac
k
s
tep
p
in
g
m
eth
o
d
to
d
esig
n
co
n
tr
o
lle
r
s
f
o
r
in
d
u
ctio
n
m
o
to
r
is
s
u
es.
T
h
e
b
ac
k
s
tep
p
in
g
m
eth
o
d
h
as
also
tack
led
n
o
n
-
m
in
im
u
m
p
h
ase
n
o
n
lin
ea
r
co
n
tr
o
l
p
r
o
b
lem
s
in
C
STR
an
d
p
ap
er
-
c
u
ttin
g
m
ac
h
in
es,
as
d
em
o
n
s
tr
ated
i
n
[
2
5
]
–
[
2
7
]
.
T
h
e
iter
ativ
e
p
r
o
ce
d
u
r
e
o
f
th
e
b
ac
k
s
tep
p
in
g
m
eth
o
d
is
h
ig
h
ly
ef
f
ec
tiv
e
in
s
tab
ilizin
g
u
n
s
tab
le
in
ter
n
al
d
y
n
am
ics,
m
ak
in
g
it
a
v
alu
ab
le
to
o
l.
Me
an
wh
il
e,
s
ev
er
al
p
r
ev
i
o
u
s
s
tu
d
ies
h
av
e
ca
r
r
ied
o
u
t
th
e
co
n
tr
o
l
d
esig
n
o
f
th
e
jer
k
e
q
u
a
tio
n
an
d
th
e
Gen
esio
-
T
esi
s
y
s
tem
.
I
n
s
tu
d
y
[
2
8
]
,
th
e
J
er
k
eq
u
atio
n
is
co
n
tr
o
lled
u
s
in
g
a
lin
ea
r
co
n
tr
o
l
b
ased
o
n
f
ee
d
b
ac
k
.
I
n
s
tu
d
y
[
2
9
]
,
t
h
e
s
tab
ilizatio
n
o
f
th
e
Gen
esio
-
T
esi
was
ca
r
r
ied
o
u
t
u
s
in
g
th
e
s
lid
in
g
-
m
o
d
e
m
eth
o
d
.
I
n
s
tu
d
y
[
3
0
]
,
th
e
ac
tiv
e
co
m
p
en
s
atio
n
m
ec
h
an
is
m
m
eth
o
d
is
ap
p
lied
to
Gen
esio
-
T
esi,
wh
ich
co
n
tain
s
d
is
tu
r
b
an
ce
.
I
n
s
tu
d
ies
[
3
1
]
an
d
[
3
2
]
,
th
e
Gen
esio
-
T
esi
was
an
aly
ze
d
u
s
in
g
a
f
r
ac
tio
n
al
m
o
d
el
a
n
d
th
e
co
n
tr
o
l
d
esig
n
was
ca
r
r
ied
o
u
t
u
s
in
g
t
h
e
p
r
o
p
o
r
tio
n
-
i
n
teg
r
al
(
PI)
m
eth
o
d
an
d
lin
ea
r
f
ee
d
b
ac
k
c
o
n
tr
o
l.
T
h
is
ar
ticle
ex
am
in
es
th
e
d
y
n
am
ics
o
f
th
e
Gen
esio
-
T
esi,
wh
ich
co
n
tain
s
u
n
ce
r
tain
p
a
r
am
eter
s
,
an
d
th
e
d
esig
n
o
f
a
co
n
tr
o
ller
to
s
tab
ilize
it.
T
h
e
s
y
s
tem
in
th
is
a
r
ticle
d
if
f
er
s
f
r
o
m
th
e
s
y
s
tem
i
n
s
tu
d
y
[
1
4
]
,
wh
ich
u
s
es
a
s
y
s
tem
with
u
n
ce
r
tain
p
ar
am
eter
s
in
th
e
f
o
r
m
o
f
v
a
r
iatio
n
s
in
s
y
s
tem
p
ar
am
eter
v
alu
es.
T
h
e
m
ag
n
itu
d
e
o
f
th
is
v
ar
iatio
n
is
ass
u
m
ed
to
b
e
co
n
s
tan
t
b
u
t
th
e
v
alu
e
an
d
lim
its
ar
e
u
n
k
n
o
wn
.
As
a
r
es
u
lt
o
f
th
e
u
n
ce
r
tai
n
p
ar
am
eter
s
,
b
esid
es
d
eter
m
in
i
n
g
th
e
co
n
tr
o
ls
th
at
s
tab
ilize
th
e
s
y
s
tem
,
p
ar
a
m
eter
esti
m
atio
n
is
n
ee
d
ed
to
d
eter
m
in
e
th
e
ac
t
u
al
s
y
s
tem
co
n
d
itio
n
s
.
T
h
er
ef
o
r
e,
th
e
c
o
n
tr
o
ller
d
esig
n
is
ca
r
r
ied
o
u
t
u
s
in
g
an
a
d
ap
tiv
e
b
ac
k
s
tep
p
in
g
m
et
h
o
d
th
at
d
if
f
er
s
f
r
o
m
th
e
m
et
h
o
d
s
in
s
tu
d
ies
[
1
4
]
,
[
2
9
]
,
[
3
0
]
.
Nex
t,
t
h
e
ef
f
ec
t
o
f
c
o
n
tr
o
l
p
ar
am
eter
s
an
d
esti
m
ato
r
p
ar
am
eter
s
o
n
co
n
tr
o
l
p
er
f
o
r
m
an
ce
is
in
v
esti
g
ated
.
C
o
n
tr
o
l
p
er
f
o
r
m
an
ce
i
s
ca
lcu
lated
b
ased
o
n
th
e
ab
s
o
l
u
te
d
if
f
er
en
ce
b
etwe
en
th
e
s
y
s
tem
o
u
tp
u
t
an
d
th
e
g
i
v
en
tr
a
jecto
r
y
,
in
th
is
ca
s
e
th
e
tr
ajec
to
r
y
is
a
co
n
s
tan
t
an
d
a
f
u
n
ctio
n
.
Statis
tical
test
s
i
n
th
e
f
o
r
m
o
f
co
r
r
elatio
n
a
n
d
r
eg
r
ess
io
n
test
s
wer
e
g
iv
en
to
d
eter
m
in
e
th
e
n
atu
r
e
an
d
weig
h
t
o
f
th
e
e
f
f
ec
t o
f
ea
c
h
p
ar
am
eter
o
n
c
o
n
tr
o
l
p
er
f
o
r
m
an
ce
.
2.
M
E
T
H
O
D
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
p
r
o
b
lem
s
an
d
m
eth
o
d
u
s
ed
in
t
h
is
s
tu
d
y
.
T
h
e
d
is
cu
s
s
io
n
b
e
g
in
s
with
th
e
in
tr
o
d
u
ctio
n
o
f
th
e
Gen
esio
-
T
esi
eq
u
atio
n
s
f
o
llo
we
d
b
y
a
lo
ca
l
s
tab
ilit
y
an
aly
s
is
.
Fin
ally
,
a
co
n
tr
o
l
d
esig
n
f
o
r
th
e
Gen
esio
-
T
esi s
y
s
tem
with
u
n
ce
r
tain
p
a
r
am
eter
s
u
s
in
g
a
d
ap
tiv
e
b
ac
k
s
tep
p
in
g
is
p
r
esen
t
ed
.
2
.
1
.
G
enesio
-
T
esi eq
ua
t
io
n
Gen
esio
an
d
T
esi
[
4
]
in
tr
o
d
u
c
ed
a
th
ir
d
-
o
r
d
er
o
r
d
i
n
ar
y
d
if
f
e
r
en
tial e
q
u
atio
n
,
wh
ich
is
p
ar
t o
f
th
e
J
er
k
eq
u
atio
n
with
q
u
ad
r
atic
ter
m
s
in
th
e
f
o
r
m
(
3
)
(
)
+
(
2
)
(
)
+
(
1
)
(
)
+
(
)
−
(
)
=
0
(
1
)
w
h
e
r
e
(
)
(
)
=
(
)
f
o
r
=
1
,
2
,
3
.
E
q
u
a
t
i
o
n
(
1
)
ca
n
b
e
c
o
n
v
e
r
t
e
d
i
n
t
o
a
s
y
s
t
e
m
o
f
d
i
f
f
e
r
e
n
t
i
a
l
e
q
u
a
t
i
o
n
s
b
y
t
r
a
n
s
f
o
r
m
a
t
i
o
n
{
1
(
)
=
(
)
,
2
(
)
=
(
1
)
(
)
,
3
(
)
=
(
2
)
(
)
}
t
o
o
b
t
a
i
n
s
y
s
t
e
m
o
f
d
i
f
f
e
r
e
n
t
ia
l
e
q
u
a
t
i
o
n
s
i
n
(
2
)
.
{
̇
1
(
)
=
2
(
)
̇
2
(
)
=
3
(
)
̇
3
(
)
=
−
1
(
)
−
2
(
)
−
3
(
)
+
(
1
)
(
2
)
I
n
Gen
esio
-
T
esi,
th
e
f
u
n
ctio
n
(
1
)
is
a
q
u
ad
r
atic
f
o
r
m
,
th
at
is
(
1
)
=
1
2
(
)
[
1
2
]
.
I
f
th
e
g
iv
e
n
v
al
u
es
o
f
(
,
,
)
h
av
e
a
to
ler
a
n
ce
r
an
g
e
o
f
(
,
,
)
f
o
r
ea
ch
p
ar
a
m
eter
,
th
en
(
2
)
ca
n
b
e
wr
itten
as
a
Gen
esio
-
T
esi
with
u
n
ce
r
tain
p
a
r
am
eter
s
.
{
̇
1
(
)
=
2
(
)
̇
2
(
)
=
3
(
)
̇
3
(
)
=
(
+
)
(
)
+
(
1
)
(
3
)
wh
er
e
=
〈
,
,
〉
is
th
e
p
a
r
am
eter
v
alu
e
wh
o
s
e
v
al
u
e
is
p
o
s
itiv
e
an
d
k
n
o
wn
,
=
〈
,
,
〉
is
th
e
v
a
r
ian
t
v
alu
e
o
n
p
ar
am
eter
wh
o
s
e
v
alu
e
is
u
n
k
n
o
wn
,
a
n
d
(
)
=
〈
1
,
2
,
3
〉
is
th
e
b
asis
f
u
n
ctio
n
.
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
.
3
,
J
u
n
e
20
25
:
2
7
5
8
-
2
7
6
8
2760
2
.
2
.
L
o
ca
l
s
t
a
bil
it
y
a
na
ly
s
is
o
f
un
ce
rt
a
in
G
enesio
-
T
esi
T
h
e
lo
ca
l
s
tab
ilit
y
o
f
th
e
Gen
esio
-
T
esi
will
b
e
an
al
y
z
ed
ar
o
u
n
d
th
e
eq
u
ilib
r
iu
m
p
o
in
t.
T
h
e
eq
u
ilib
r
iu
m
p
o
in
t
(
1
∗
,
2
∗
,
3
∗
)
is
an
o
r
d
er
ed
tr
ip
le
p
air
th
at
s
atis
f
ies
(
1
∗
,
2
∗
,
3
∗
)
=
0
wh
er
e
(
1
,
2
,
3
)
is
a
v
ec
to
r
-
v
al
u
ed
f
u
n
ctio
n
o
n
th
e
r
ig
h
t
-
h
a
n
d
s
id
e
o
f
(
2
)
an
d
(
3
)
.
Fro
m
(
2
)
,
we
h
av
e
(
4
)
.
{
2
(
)
=
0
3
(
)
=
0
−
(
+
)
1
(
)
−
(
+
)
2
(
)
−
(
+
)
3
(
)
+
(
1
)
=
0
(
4
)
T
h
e
f
ir
s
t two
eq
u
atio
n
s
in
(
4
)
s
h
o
w
th
at
th
e
o
n
ly
v
alu
es
(
2
∗
,
3
∗
)
th
at
s
atis
f
y
ar
e
2
∗
=
0
an
d
3
∗
=
0
.
Su
b
s
titu
te
th
e
v
alu
es
(
2
∗
=
0
,
3
∗
=
0
)
in
to
th
e
th
ir
d
eq
u
atio
n
to
g
et
1
2
(
)
−
(
+
)
1
(
)
=
0
.
T
h
e
1
∗
v
alu
es
th
at
s
atis
f
y
ar
e
1
∗
=
0
an
d
1
∗
=
+
.
So
,
th
e
e
q
u
ili
b
r
iu
m
p
o
in
ts
o
f
th
e
Ge
n
esio
-
T
esi
with
u
n
ce
r
tain
p
ar
am
eter
s
in
(
3
)
a
r
e
1
=
(
0
,
0
,
0
)
an
d
2
=
(
+
,
0
,
0
)
.
T
h
e
s
ec
o
n
d
s
tep
is
to
d
eter
m
in
e
th
e
lin
ea
r
f
o
r
m
o
f
(
3
)
with
th
e
T
ay
lo
r
Ser
ies
ar
o
u
n
d
th
e
e
q
u
ilib
r
iu
m
p
o
in
t
wh
ile
s
im
u
ltan
eo
u
s
ly
d
e
ter
m
in
in
g
th
e
eig
en
v
alu
es
o
f
th
e
J
ac
o
b
ian
m
atr
ix
.
T
h
e
J
ac
o
b
ian
m
atr
ix
f
r
o
m
(
3
)
is
in
(
5
)
.
A
=
[
0
1
0
0
0
1
−
(
+
)
+
2
1
−
(
+
)
−
(
+
)
]
(
5
)
Su
b
s
titu
te
th
e
1
=
(
0
,
0
,
0
)
in
to
m
atr
ix
A
in
(
5
)
to
o
b
tain
A
1
as Jaco
b
ian
m
atr
i
x
ar
o
u
n
d
1
A
1
=
[
0
1
0
0
0
1
−
(
+
)
−
(
+
)
−
(
+
)
]
T
h
e
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial
o
f
A
1
is
A
1
=
3
+
(
+
)
2
+
(
+
)
+
(
+
)
an
d
th
e
R
o
u
th
’
s
tab
le
o
f
A
1
is
3
2
1
|
1
(
+
)
(
+
)
(
+
)
(
+
)
−
(
+
)
(
+
)
0
(
+
)
0
(
6
)
T
h
e
th
ir
d
r
o
w
an
d
f
ir
s
t
co
lu
m
n
o
f
th
e
R
o
u
th
’
s
tab
le
in
(
6
)
p
r
o
d
u
ce
t
h
e
s
y
s
tem
s
tab
ilit
y
co
n
d
itio
n
s
ar
o
u
n
d
1
,
n
am
ely
(
+
)
(
+
)
>
(
+
)
an
d
its
s
o
lu
tio
n
d
ep
e
n
d
s
o
n
th
e
v
alu
e
o
f
ea
ch
u
n
ce
r
tain
p
ar
a
m
eter
a
n
d
its
s
ig
n
.
I
f
th
e
u
n
ce
r
tain
p
ar
am
eter
v
alu
e
is
o
m
itted
,
th
e
n
th
e
s
tab
le
co
n
d
itio
n
is
>
an
d
th
er
e
is
a
co
n
d
itio
n
wh
e
r
e
=
will
ca
u
s
e
s
t
h
e
en
tr
ies
in
th
e
f
ir
s
t
co
lu
m
n
o
f
th
e
R
o
u
th
’
s
tab
le
to
b
e
ze
r
o
an
d
ca
u
s
es
s
y
m
m
etr
y
in
th
e
s
y
s
tem
.
W
e
o
m
it
d
etailed
a
n
aly
s
is
o
f
p
ar
a
m
eter
v
alu
es
a
n
d
th
ei
r
v
a
r
ian
t
s
ca
u
s
in
g
in
s
tab
ilit
y
ar
o
u
n
d
1
b
ec
au
s
e
th
er
e
ar
e
t
o
o
m
an
y
u
n
k
n
o
wn
v
alu
es.
Nex
t
is
an
aly
zin
g
th
e
lo
ca
l
s
tab
ilit
y
ar
o
u
n
d
2
.
Su
b
s
titu
te
th
e
v
alu
e
2
=
(
+
,
0
,
0
)
in
to
J
ac
o
b
ian
m
atr
ix
A
in
(
5
)
to
o
b
tain
J
ac
o
b
ian
m
atr
ix
ar
o
u
n
d
2
.
A
2
=
[
0
1
0
0
0
1
(
+
)
−
(
+
)
−
(
+
)
]
T
h
e
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial
o
f
A
2
is
A
2
=
3
+
(
+
)
2
+
(
+
)
−
(
+
)
an
d
its
R
o
u
th
’
s
tab
le
is
g
iv
en
in
(
7
)
.
3
2
1
|
1
(
+
)
(
+
)
−
(
+
)
(
+
)
+
(
+
)
(
+
)
0
−
(
+
)
0
(
7
)
T
h
e
R
o
u
th
tab
le
d
eter
m
in
es
s
y
s
tem
s
tab
ilit
y
b
y
an
aly
zin
g
s
ig
n
ch
an
g
es
in
th
e
f
ir
s
t
co
lu
m
n
o
f
(
7
)
.
An
u
n
s
tab
le
lin
ea
r
s
y
s
tem
is
in
d
i
ca
ted
b
y
s
ig
n
c
h
an
g
e
in
th
e
f
ir
s
t
co
lu
m
n
v
alu
e,
with
th
e
n
u
m
b
er
o
f
p
o
s
itiv
e
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
Tr
a
ck
in
g
co
n
tr
o
l o
f u
n
ce
r
ta
in
th
ir
d
o
r
d
er jerk
eq
u
a
tio
n
Gen
esio
-
Tes
i u
s
in
g
…
(
K
h
o
z
in
Mu
’
ta
ma
r
)
2761
eig
en
v
alu
es
eq
u
alin
g
th
e
n
u
m
b
er
o
f
s
ig
n
ch
an
g
es
in
th
e
R
o
u
th
’
s
tab
le.
T
h
e
(
,
,
)
is
p
o
s
itiv
e
an
d
(
,
)
is
s
m
all,
th
e
f
o
u
r
th
r
o
w
o
f
(
7
)
p
r
o
d
u
ce
s
a
n
eg
ativ
e
v
al
u
e.
C
o
n
s
eq
u
en
tly
,
th
e
s
y
s
tem
is
alwa
y
s
u
n
s
tab
le
ar
o
u
n
d
th
e
eq
u
ilib
r
iu
m
p
o
in
t
2
=
(
+
,
0
,
0
)
.
W
e
p
r
o
v
id
e
an
illu
s
tr
atio
n
to
s
h
o
w
th
e
e
f
f
ec
t
o
f
th
e
p
r
esen
ce
o
f
u
n
ce
r
tain
p
ar
a
m
eter
s
o
n
s
tab
ilit
y
.
T
ab
le
1
s
h
o
ws
th
e
p
ar
am
eter
v
alu
es
an
d
th
eir
v
ar
i
atio
n
s
u
s
ed
f
o
r
th
e
s
im
u
latio
n
an
d
th
eir
s
tab
ilit
y
ch
ar
ac
ter
is
tics
.
B
a
s
ed
o
n
T
ab
le
1
,
th
e
eq
u
ilib
r
iu
m
p
o
i
n
ts
ar
e
1
=
(
0
,
0
,
0
)
an
d
2
=
(
2
,
0
,
0
)
.
T
h
e
eq
u
ilib
r
iu
m
p
o
in
t
1
is
a
s
tab
le
eq
u
ilib
r
iu
m
p
o
in
t
b
ec
au
s
e
it
s
atis
f
ies
=
8
>
=
7
.
Ho
wev
er
,
th
is
p
r
o
p
er
ty
c
h
an
g
es
with
v
ar
iatio
n
s
in
p
ar
a
m
eter
v
alu
es.
Usi
n
g
th
e
v
a
r
ied
v
alu
es,
we
g
et
(
+
)
(
+
)
=
7
.
2
<
(
+
)
=
7
.
35
wh
ich
r
esu
lt
in
an
u
n
s
tab
l
e
eq
u
ilib
r
iu
m
p
o
in
t.
Gr
ap
h
i
ca
lly
,
a
co
m
p
ar
is
o
n
o
f
th
e
b
eh
a
v
io
r
o
f
th
e
two
is
s
h
o
wn
i
n
Fig
u
r
e
1
.
Fig
u
r
e
1
(
a)
d
em
o
n
s
tr
ates
th
e
o
r
b
it
b
e
h
av
io
r
o
f
b
o
th
ce
r
tain
an
d
u
n
ce
r
tain
s
y
s
tem
s
in
a
3
D
d
im
en
s
io
n
.
Star
tin
g
f
r
o
m
th
e
i
n
itial
p
o
in
t
0
=
(
0
.
1
,
0
.
4
,
0
.
2
)
in
a
s
y
s
tem
with
p
ar
am
eter
v
ar
iatio
n
s
,
th
e
o
r
b
it
g
r
ad
u
ally
m
o
v
es
awa
y
f
r
o
m
th
e
eq
u
ilib
r
iu
m
p
o
in
t
in
a
cir
cu
l
ar
m
o
tio
n
.
I
n
co
n
tr
ast,
th
e
o
r
b
i
t
o
f
ce
r
tain
s
y
s
tem
m
o
v
es
asy
m
p
to
tically
f
r
o
m
t
h
e
s
am
e
in
itial
p
o
in
t
0
=
(
0
.
1
,
0
.
4
,
0
.
2
)
to
war
d
s
th
e
eq
u
ilib
r
iu
m
p
o
in
t
1
.
Ho
wev
er
,
f
o
r
a
clea
r
er
u
n
d
er
s
tan
d
in
g
o
f
th
e
d
y
n
am
ics
o
f
an
ev
er
-
ex
p
a
n
d
in
g
u
n
ce
r
tain
s
y
s
tem
,
Fig
u
r
e
1
(
b
)
p
r
o
jects
it
o
n
to
th
e
y
z
-
p
lan
e.
T
h
e
th
ick
r
ed
lin
e
i
n
Fig
u
r
e
1
(
b
)
d
ir
ec
tly
r
esu
lts
f
r
o
m
th
e
s
y
s
tem
's
o
r
b
it.
T
h
is
o
r
b
it
is
ex
p
an
d
in
g
g
r
ad
u
ally
with
m
in
o
r
in
cr
em
en
ts
,
an
d
t
h
is
b
eh
av
io
r
is
co
n
f
ir
m
ed
b
y
Fig
u
r
e
2
.
Fig
u
r
e
2
s
h
o
ws
th
e
s
o
lu
tio
n
1
(
)
ag
ain
s
t
ti
m
e.
T
h
e
1
(
)
cu
r
v
e
in
th
e
ce
r
tain
s
y
s
tem
(
b
lu
e
lin
e)
is
asy
m
p
t
o
tically
s
tab
le
to
war
d
s
th
e
o
r
ig
in
,
wh
il
e
th
e
1
(
)
cu
r
v
e
with
p
ar
a
m
eter
v
a
r
iatio
n
s
co
n
tin
u
es to
g
r
o
w.
T
ab
le
1
.
Par
am
eter
v
alu
es o
f
t
h
e
s
y
s
tem
an
d
th
eir
v
ar
iatio
n
s
P
a
r
a
me
t
e
r
V
a
l
u
e
V
a
r
i
a
t
i
o
n
7
+
5%
4
−
5%
2
−
5%
(
a)
(
b
)
Fig
u
r
e
1
.
C
o
m
p
a
r
is
o
n
o
f
th
e
d
y
n
am
ics o
f
th
e
Gen
esio
-
T
esi s
o
lu
tio
n
in
t
h
e
p
r
esen
ce
o
f
p
a
r
a
m
eter
v
ar
iatio
n
s
(
a)
th
e
cu
r
v
e
in
3
D
co
o
r
d
in
ate
s
(
b
)
th
e
cu
r
v
e
p
r
o
jecte
d
o
n
th
e
y
z
-
p
lan
e
Fig
u
r
e
2
.
C
o
m
p
a
r
is
o
n
o
f
1
(
)
ag
ain
s
t tim
e
d
u
e
to
p
a
r
am
eter
v
ar
i
atio
n
s
th
at
r
esu
lt in
in
s
tab
ilit
y
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
.
3
,
J
u
n
e
20
25
:
2
7
5
8
-
2
7
6
8
2762
2
.
3
.
Co
ntr
o
l desig
n f
o
r
un
ce
rt
a
in G
enesio
-
T
esi u
s
ing
a
da
ptiv
e
ba
ck
s
t
eppin
g
C
o
n
s
id
er
th
e
Gen
esio
-
T
esi
with
u
n
ce
r
tain
p
ar
a
m
eter
s
in
(
3
)
.
Nex
t,
th
e
c
o
n
tr
o
l
f
u
n
ct
io
n
(
)
is
in
tr
o
d
u
ce
d
to
th
e
s
y
s
tem
co
r
r
e
s
p
o
n
d
in
g
to
th
e
d
y
n
am
ic
e
q
u
a
tio
n
s
co
n
tain
in
g
u
n
ce
r
tain
p
ar
am
eter
s
s
o
th
at
(
3
)
ca
n
b
e
wr
itten
as
(
8
)
.
{
̇
1
(
)
=
2
(
)
̇
2
(
)
=
3
(
)
̇
3
(
)
=
(
+
)
(
)
+
(
1
)
+
(
)
(
8
)
T
h
e
f
ir
s
t
s
tep
is
d
eter
m
in
in
g
th
e
co
n
t
r
o
l
f
u
n
ctio
n
s
o
th
at
th
e
s
tate
v
ar
iab
le
1
(
)
g
o
es
t
o
th
e
tr
ajec
to
r
y
(
)
u
s
in
g
v
ir
tu
al
c
o
n
tr
o
l
2
(
)
.
Vir
tu
al
co
n
t
r
o
l
is
a
s
tate
v
ar
iab
le
u
s
ed
as
an
ad
d
itio
n
al
in
p
u
t
t
o
en
s
u
r
e
th
e
L
y
ap
u
n
o
v
s
tab
ilit
y
in
th
e
b
ac
k
s
tep
p
in
g
m
eth
o
d
.
W
e
d
ef
in
ed
th
e
d
if
f
er
e
n
ce
b
et
wee
n
th
e
o
u
tp
u
t
an
d
th
e
tr
ajec
to
r
y
in
(
9
)
.
1
(
)
=
1
(
)
−
(
)
(
9
)
T
h
e
d
er
iv
ativ
e
o
f
th
e
er
r
o
r
eq
u
atio
n
in
(
9
)
with
r
esp
ec
t to
y
i
eld
s
.
̇
1
(
)
=
2
(
)
−
̇
(
)
Nex
t,
we
d
ef
in
e
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
(
1
)
=
1
2
1
2
(
)
an
d
d
if
f
e
r
en
tiate
it with
r
esp
ec
t to
to
p
r
o
d
u
ce
.
̇
(
1
)
=
1
(
)
[
2
(
)
−
̇
(
)
]
(
1
0
)
I
t
i
s
as
s
u
m
e
d
t
h
a
t
t
h
e
r
e
is
1
∈
ℝ
+
w
h
i
c
h
s
a
t
is
f
i
es
̇
(
1
)
=
−
1
1
2
(
)
s
o
t
h
a
t
f
r
o
m
(
1
0
)
w
e
o
b
t
a
i
n
v
i
r
t
u
a
l
c
o
n
t
r
o
l
2
(
)
−
̇
(
)
=
−
1
1
(
)
.
F
r
o
m
t
h
e
v
i
r
t
u
al
c
o
n
t
r
o
l
2
(
)
,
a
n
e
w
s
ta
t
e
v
a
r
ia
b
l
e
is
d
e
f
i
n
e
d
,
2
(
)
=
2
(
)
−
̇
(
)
+
1
1
(
)
,
s
o
t
h
a
t
a
n
ew
d
y
n
a
m
i
c
is
o
b
t
ai
n
e
d
,
n
a
m
e
l
y
̇
2
(
)
=
3
(
)
+
1
[
2
(
)
−
1
1
(
)
]
−
̈
(
)
.
T
h
e
s
ec
o
n
d
s
tep
is
s
tab
ilizin
g
th
e
s
tate
v
ar
iab
le
2
(
)
u
s
in
g
v
ir
tu
a
l
co
n
tr
o
l
3
(
)
.
Use
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
(
1
,
2
)
=
(
1
)
+
1
2
2
2
(
)
an
d
d
er
iv
e
(
1
,
2
)
with
r
esp
ec
t to
to
y
ield
.
̇
(
1
,
2
)
=
−
1
1
2
(
)
+
2
(
)
[
1
(
)
+
3
(
)
+
1
(
2
(
)
−
1
1
(
)
)
−
̈
(
)
]
(
1
1
)
T
h
e
3
(
)
is
u
s
ed
as
v
ir
tu
al
co
n
tr
o
l
s
o
th
at
̇
(
1
,
2
)
=
−
1
1
2
(
)
−
2
2
2
(
)
is
o
b
tain
ed
f
o
r
1
,
2
∈
ℝ
+
an
d
u
s
in
g
(
1
1
)
we
g
et
1
(
)
+
3
(
)
+
1
(
2
(
)
−
1
1
(
)
)
−
̈
(
)
=
−
2
2
(
)
.
B
ased
o
n
v
ir
tu
al
co
n
tr
o
l
3
(
)
,
a
n
ew
s
tate
v
ar
iab
le
i
s
d
ef
in
ed
;
3
(
)
=
3
(
)
+
(
1
−
1
2
)
1
(
)
+
(
2
+
1
)
2
(
)
−
̈
(
)
an
d
u
s
in
g
(
8
)
we
h
av
e
th
e
n
ew
d
y
n
am
ic
th
at
will b
e
s
tab
ilis
ed
in
(
1
2
)
.
̇
3
(
)
=
(
)
+
(
e
)
+
(
p
+
δ
)
(
e
,
,
̇
,
̈
)
−
(
3
)
+
(
2
+
1
)
(
3
−
2
2
−
1
)
+
(
1
−
1
2
)
(
2
−
1
1
)
(
12
)
T
h
e
f
in
al
s
tep
is
s
tab
ilizin
g
th
e
f
in
al
d
y
n
a
m
ic
in
(
1
2
)
w
h
ile
m
in
im
izin
g
th
e
er
r
o
r
b
e
twee
n
th
e
u
n
ce
r
tain
p
ar
a
m
eter
s
an
d
th
ei
r
esti
m
ates.
W
e
d
ef
in
e
n
ew
L
y
ap
u
n
o
v
f
u
n
ctio
n
(
1
,
2
,
3
)
b
y
in
clu
d
i
n
g
th
e
er
r
o
r
ter
m
o
f
u
n
ce
r
tain
p
ar
am
e
ter
esti
m
atio
n
in
(
1
3
)
.
(
1
,
2
,
3
)
=
2
+
1
2
3
2
(
)
+
δ
̃
Γ
δ
̃
(
1
3
)
wh
er
e
δ
̃
=
δ
−
δ
̂
is
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
u
n
ce
r
tain
p
ar
am
ete
r
s
an
d
its
e
s
tim
ated
v
alu
e.
Der
iv
ativ
e
(
1
,
2
,
3
)
r
esp
ec
t to
y
ield
s
.
̇
(
1
,
2
,
3
)
=
−
1
1
2
(
)
−
2
2
2
(
)
+
3
(
)
[
2
(
)
+
̇
3
(
)
]
+
δ
̃
Γ
δ
̃
(
1
4
)
Def
in
e
co
n
tr
o
l
(
)
in
(
1
5
)
.
(
)
=
(
3
)
−
(
e
)
−
(
p
+
δ
̂
)
(
e
,
,
̇
,
̈
)
+
[
1
(
1
−
1
2
)
+
1
+
2
]
1
+
[
1
2
+
1
2
+
2
2
−
2
]
2
−
[
1
+
2
+
3
]
3
(
1
5
)
T
h
en
s
u
b
s
titu
te
th
e
co
n
tr
o
l
(
)
in
to
(
1
2
)
an
d
(
1
4
)
to
p
r
o
d
u
ce
(
1
6
)
.
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
Tr
a
ck
in
g
co
n
tr
o
l o
f u
n
ce
r
ta
in
th
ir
d
o
r
d
er jerk
eq
u
a
tio
n
Gen
esio
-
Tes
i u
s
in
g
…
(
K
h
o
z
in
Mu
’
ta
ma
r
)
2763
̇
(
1
,
2
,
3
)
=
−
1
1
2
(
)
−
2
2
2
(
)
−
3
3
2
+
3
(
)
δ
̃
(
e
,
,
̇
,
̈
)
+
δ
̃
Γ
δ
̃
(
1
6
)
W
e
ca
n
g
et
̇
(
1
,
2
,
3
)
<
0
f
o
r
ev
er
y
≥
0
in
(
1
6
)
b
y
m
ak
in
g
ze
r
o
s
ter
m
s
co
n
t
ain
in
g
δ
̃
an
d
f
r
o
m
th
e
f
ac
t
th
at
δ
̃
≠
0
th
en
we
o
b
tain
δ
̃
=
−
3
(
)
Γ
−
1
(
e
,
,
̇
,
̈
)
.
T
h
e
δ
̂
is
u
s
ed
in
(
1
5
)
a
n
d
u
s
in
g
r
elatio
n
δ
̃
=
δ
−
δ
̂
we
h
av
e
th
e
d
y
n
a
m
ic
f
o
r
p
ar
a
m
eter
esti
m
atio
n
in
(
1
7
)
.
δ
̂
=
3
(
)
Γ
−
1
(
e
,
,
̇
,
̈
)
(
1
7
)
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
s
h
o
wca
s
es
th
e
i
m
p
lem
en
tatio
n
o
f
th
e
co
n
tr
o
l
d
esig
n
f
o
r
Gen
esio
-
T
esi
eq
u
atio
n
s
with
u
n
ce
r
tain
p
ar
am
eter
s
i
n
v
a
r
io
u
s
s
ce
n
ar
io
s
.
T
o
ev
alu
ate
th
e
co
n
tr
o
l'
s
ef
f
ec
tiv
en
ess
,
we
co
n
d
u
cted
a
s
im
u
latio
n
u
s
in
g
th
e
d
ata
p
r
o
v
id
ed
in
T
ab
le
2
.
T
h
e
f
ir
s
t
s
ce
n
ar
i
o
in
v
o
lv
e
s
a
s
in
g
le
u
n
ce
r
tain
p
ar
am
eter
.
T
h
e
p
r
im
ar
y
g
o
al
is
to
g
u
ar
an
tee
t
h
at
th
e
o
u
tc
o
m
e
ad
h
e
r
es
to
th
e
c
o
n
s
tan
t
tr
ajec
to
r
y
(
)
=
2
an
d
th
e
f
u
n
ctio
n
t
r
ajec
to
r
y
(
)
=
2
s
in
(
)
+
1
2
.
Fig
u
r
es
3
,
4
,
a
n
d
5
p
r
esen
t
th
e
s
im
u
latio
n
r
esu
lts
o
b
tain
ed
b
y
v
a
r
y
in
g
th
e
c
o
n
tr
o
l
p
ar
am
eter
s
{
1
,
2
,
3
}
in
o
r
d
e
r
to
ass
ess
its
p
er
f
o
r
m
an
ce
.
T
h
e
co
n
t
r
o
l
f
u
n
ctio
n
'
s
ef
f
ec
tiv
en
ess
in
d
ir
ec
tin
g
th
e
o
u
tp
u
t
to
wa
r
d
s
th
e
f
u
n
ctio
n
tr
ajec
to
r
y
is
u
n
e
q
u
iv
o
ca
lly
d
em
o
n
s
tr
ated
in
Fig
u
r
es
3
(
a)
a
n
d
4
(
a)
.
Fu
r
t
h
er
m
o
r
e,
Fig
u
r
e
5
(
a)
s
er
v
es
as
clea
r
e
v
id
en
ce
o
f
h
o
w
t
h
e
co
n
tr
o
l
f
u
n
ctio
n
ef
f
ec
tiv
ely
d
ir
ec
ts
th
e
o
u
tp
u
t
to
war
d
s
a
co
n
s
tan
t
tr
ajec
to
r
y
.
Ho
wev
er
,
p
ar
t
(
b
)
o
f
th
e
f
ig
u
r
es
clea
r
ly
r
ev
ea
ls
th
at
n
o
t
all
p
ar
am
eter
esti
m
ates
ca
n
ac
cu
r
ately
ca
p
tu
r
e
u
n
ce
r
tain
p
ar
am
eter
v
alu
es.
Sp
ec
if
ically
,
Fig
u
r
es
3
(
b
)
an
d
4
(
b
)
u
n
a
m
b
i
g
u
o
u
s
ly
s
h
o
w
th
at
th
e
p
ar
am
eter
esti
m
ates c
o
r
r
esp
o
n
d
to
t
h
e
u
n
ce
r
tain
p
ar
am
et
er
s
em
p
lo
y
ed
in
th
e
s
im
u
latio
n
.
C
o
n
v
er
s
ely
,
n
o
n
e
o
f
th
e
s
im
u
latio
n
p
ar
am
eter
c
o
m
b
in
atio
n
s
in
Fig
u
r
e
5
(
b
)
y
iel
d
ed
th
e
c
o
r
r
ec
t p
a
r
am
eter
esti
m
ates.
T
h
e
s
im
u
latio
n
r
esu
lts
s
h
o
w
th
at
th
e
co
n
tr
o
l
p
ar
am
eter
'
s
v
alu
e
in
f
lu
e
n
ce
s
th
e
s
y
s
tem
'
s
o
u
tp
u
t
co
n
v
er
g
en
ce
s
p
ee
d
.
T
h
er
e
f
o
r
e
,
a
s
im
u
latio
n
is
ca
r
r
ied
o
u
t
b
y
v
ar
y
i
n
g
th
e
p
ar
am
eter
v
alu
e
s
{
1
,
2
,
3
,
Γ
}
an
d
test
in
g
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
ese
v
alu
es
an
d
th
e
co
n
tr
o
l
p
er
f
o
r
m
an
ce
.
Fo
r
th
is
s
im
u
latio
n
,
th
e
f
u
n
ctio
n
tr
ajec
to
r
y
(
)
=
2
s
in
(
)
+
1
2
is
u
s
ed
an
d
tim
e
in
ter
v
al
∈
[
0
,
5
]
is
p
ar
titi
o
n
ed
b
y
=
5
×
10
3
p
ar
titi
o
n
s
.
Var
iatio
n
s
in
th
e
v
al
u
es
u
s
ed
ar
e
1
,
2
,
3
=
{
1
,
3
,
5
,
7
,
9
}
an
d
Γ
=
{
0
.
01
,
0
.
1
,
1
,
10
,
100
}
.
T
h
e
am
o
u
n
t
o
f
d
ata
g
en
er
ated
is
5
4
=
625
d
ata.
T
h
e
co
r
r
elatio
n
test
was
ca
r
r
ied
o
u
t
u
s
in
g
th
e
Sp
ea
r
m
an
m
et
h
o
d
,
an
d
th
e
r
eg
r
ess
io
n
test
u
s
ed
was
m
u
l
tip
le
lin
ea
r
r
eg
r
ess
io
n
.
T
h
e
s
i
m
u
latio
n
r
esu
lts
ar
e
s
h
o
w
n
i
n
T
ab
le
3
.
T
ab
le
3
s
h
o
ws
th
at
f
o
r
ea
ch
ca
s
e
o
f
d
ef
in
ite
p
ar
am
eter
s
,
{
1
,
2
,
3
}
v
alu
es
ar
e
n
eg
ativ
ely
co
r
r
elate
d
with
co
n
tr
o
l
p
er
f
o
r
m
an
ce
.
T
h
u
s
,
we
ca
n
r
ed
u
ce
th
e
v
alu
e
o
f
{
1
,
2
,
3
}
to
im
p
r
o
v
e
co
n
tr
o
l
p
er
f
o
r
m
an
ce
.
T
h
e
weig
h
t
o
f
ea
ch
v
alu
e
{
1
,
2
,
3
}
o
n
co
n
tr
o
l
p
e
r
f
o
r
m
an
ce
in
ea
ch
ca
s
e
is
alm
o
s
t
id
en
tical.
I
n
co
n
tr
ast
to
{
1
,
2
,
3
}
,
th
e
v
alu
e
o
f
Γ
p
o
s
itiv
ely
af
f
ec
ts
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
ev
e
n
th
o
u
g
h
it
is
tin
y
.
W
ith
a
co
r
r
elatio
n
v
alu
e
b
elo
w
0
.
3
,
th
er
e
is
n
o
co
r
r
elatio
n
Γ
o
n
c
o
n
t
r
o
l p
er
f
o
r
m
a
n
ce
,
wh
ich
is
also
s
ee
n
in
th
e
v
e
r
y
s
m
all
r
eg
r
ess
io
n
co
ef
f
icien
t.
T
h
e
s
ec
o
n
d
s
ce
n
ar
io
is
to
co
n
tr
o
l
a
s
y
s
tem
wh
er
e
all
p
ar
am
eter
s
co
n
tain
u
n
ce
r
tain
v
al
u
es.
B
ec
au
s
e
o
f
th
r
ee
u
n
ce
r
tain
p
ar
am
eter
s
,
we
n
ee
d
an
esti
m
ato
r
p
o
s
itiv
e
d
ef
in
ite
m
atr
ix
Γ
∈
ℝ
3
×
3
with
in
f
i
n
ite
f
o
r
m
s
.
A
p
o
s
itiv
e
d
ef
in
ite
m
atr
ix
is
o
n
e
in
wh
ich
all
th
e
eig
en
v
alu
es
ar
e
p
o
s
itiv
e.
W
e
ch
o
o
s
e
th
e
d
iag
o
n
al
m
atr
ix
an
d
th
e
u
p
p
e
r
tr
ian
g
u
lar
m
atr
ix
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o
r
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im
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licity
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s
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e
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en
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es c
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o
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iag
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ies.
C
h
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s
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m
atr
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Γ
1
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1106
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0
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an
d
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.
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h
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u
r
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.
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u
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6
(
a)
h
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th
e
s
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tem
's
o
u
tp
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ts
th
at
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o
llo
wed
a
co
n
s
tan
t
tr
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y
d
esp
ite
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ar
y
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g
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g
e
n
ce
r
ates.
On
th
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o
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h
an
d
,
Fig
u
r
e
6
(
b
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s
h
o
wca
s
es
th
e
s
y
s
tem
'
s
o
u
tp
u
t
f
o
llo
win
g
a
f
u
n
ctio
n
al
tr
ajec
to
r
y
.
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h
ese
f
ig
u
r
es
s
h
o
w
t
h
at
th
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s
y
s
tem
'
s
o
u
tp
u
t
q
u
ick
ly
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n
v
er
g
es
f
aster
o
n
t
h
e
f
u
n
ct
io
n
al
tr
ajec
to
r
y
th
a
n
o
n
t
h
e
c
o
n
s
tan
t
tr
ajec
to
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y
.
T
h
is
is
p
ar
ticu
lar
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id
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n
t
at
≈
2
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er
e
all
s
y
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tem
o
u
tp
u
ts
o
n
t
h
e
f
u
n
ctio
n
al
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ajec
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r
y
ar
e
clo
s
e
to
th
e
g
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t
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ajec
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.
T
ab
le
2
.
Par
am
eter
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n
d
a
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o
r
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P
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[
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
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I
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l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
5
8
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2
7
6
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2764
(
a)
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b
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u
r
e
3
.
T
h
e
b
e
h
av
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f
th
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Gen
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T
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u
n
ce
r
tain
p
ar
am
eter
s
o
n
p
a
r
am
eter
(
a)
s
y
s
tem
’
s
o
u
tp
u
t
with
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u
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n
t
r
ajec
to
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(
)
=
2
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in
(
)
+
1
2
an
d
(
b
)
esti
m
atio
n
p
ar
am
ete
r
̂
(
a)
(
b
)
Fig
u
r
e
4
.
T
h
e
b
e
h
av
io
r
o
f
th
e
Gen
esio
-
T
esi with
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n
ce
r
tain
p
ar
am
eter
s
o
n
p
a
r
am
eter
(
a)
s
y
s
tem
’
s
o
u
tp
u
t
with
f
u
n
ctio
n
t
r
ajec
to
r
y
(
)
=
2
s
in
(
)
+
1
2
an
d
(
b
)
esti
m
atio
n
p
ar
am
ete
r
̂
(
a)
(
b
)
Fig
u
r
e
5
.
T
h
e
b
e
h
av
io
r
o
f
th
e
Gen
esio
-
T
esi with
u
n
ce
r
tain
p
ar
am
eter
s
o
n
p
a
r
am
eter
(
a)
s
y
s
tem
’
s
o
u
tp
u
t
with
co
n
s
tan
t
tr
ajec
to
r
y
(
)
=
2
an
d
(
b
)
esti
m
atio
n
p
ar
am
ete
r
̂
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
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8
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Tr
a
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in
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co
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tr
o
l o
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r
ta
in
th
ir
d
o
r
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eq
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a
tio
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Gen
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Tes
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s
in
g
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(
K
h
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Mu
’
ta
ma
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)
2765
T
ab
le
3
.
C
o
r
r
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d
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eg
r
e
s
s
io
n
test
r
esu
lts
f
o
r
th
e
f
u
n
cti
o
n
tr
ajec
to
r
y
with
a
v
ar
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ar
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eter
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t
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a
t
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last
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ce
n
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test
th
e
r
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u
s
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ess
o
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th
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o
s
ed
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tr
o
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m
et
h
o
d
.
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h
e
d
is
tu
r
b
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ce
is
g
iv
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to
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e
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y
s
tem
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ile
h
as
r
ea
ch
ed
a
s
tead
y
-
s
tate
p
o
in
t.
T
h
e
d
is
tu
r
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a
n
ce
is
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to
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h
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ar
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le
{
1
(
)
,
2
(
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,
3
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)
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with
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n
o
is
e
(
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=
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r
a
n
d
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o
r
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[
2
,
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h
e
c
o
n
tr
o
l
p
a
r
am
eter
s
u
s
ed
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e
{
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2
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3
=
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an
d
th
e
m
atr
ix
esti
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ato
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Γ
=
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g
(
[
0
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01
1
10
]
)
.
T
h
e
s
im
u
latio
n
r
esu
lts
ar
e
s
h
o
wn
in
Fig
u
r
e
7
.
Fig
u
r
es
7
(
a)
an
d
7
(
b
)
s
h
o
w
th
at
at
∈
[
2
,
6
]
,
th
er
e
ar
e
ir
r
e
g
u
lar
s
p
ik
es
in
th
e
c
u
r
v
e.
T
h
e
d
is
tu
r
b
an
ce
f
u
n
ctio
n
is
ca
u
s
in
g
a
d
is
r
u
p
tio
n
in
th
e
s
y
s
tem
'
s
o
u
tp
u
t,
lead
i
n
g
t
o
a
s
ig
n
if
ican
t
s
u
r
g
e
a
n
d
d
ev
iatio
n
f
r
o
m
th
e
in
te
n
d
ed
tr
ac
k
.
Ho
wev
er
,
th
e
m
o
tio
n
o
f
t
h
e
p
er
tu
r
b
ed
s
y
s
tem
in
Fig
u
r
e
7
(
b
)
u
n
d
o
u
b
ted
l
y
alig
n
s
with
th
e
in
ten
d
ed
tr
ajec
to
r
y
p
atter
n
with
g
r
ea
t
ac
cu
r
a
cy
.
Af
ter
≥
6
,
th
e
d
is
tu
r
b
an
ce
is
r
em
o
v
ed
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l f
u
n
ctio
n
ca
n
b
r
in
g
b
ac
k
th
e
o
u
tp
u
t to
a
g
iv
e
n
tr
ajec
to
r
y
.
T
h
is
s
h
o
ws th
at
th
e
co
n
tr
o
l f
u
n
ctio
n
is
v
er
y
g
o
o
d
at
s
tab
ilizin
g
th
e
s
y
s
tem
.
T
h
e
s
y
s
tem
's
d
is
tu
r
b
an
ce
ca
n
n
o
t
b
e
elim
in
ated
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ec
au
s
e
th
e
co
n
tr
o
l
d
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n
d
o
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n
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t
in
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lv
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ts
o
f
th
e
d
is
tu
r
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ce
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u
n
ct
io
n
.
Ho
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er
,
th
e
c
o
n
tr
o
l
f
u
n
ctio
n
ca
n
q
u
ick
ly
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esto
r
e
s
y
s
tem
o
u
tp
u
t w
h
e
n
th
e
d
is
tu
r
b
an
ce
is
r
em
o
v
ed
.
(
a)
(
b
)
Fig
u
r
e
6
.
C
o
m
p
a
r
is
o
n
o
f
s
y
s
tem
d
y
n
a
m
ics with
s
ev
er
al
v
ar
ia
tio
n
s
o
f
co
n
t
r
o
l p
a
r
am
eter
s
(
a)
co
n
s
tan
t
tr
ajec
to
r
y
(
)
=
2
an
d
(
b
)
f
u
n
ctio
n
tr
a
jecto
r
y
(
)
=
2
s
in
(
)
+
1
2
(
a)
(
b
)
Fig
u
r
e
7
.
C
o
m
p
a
r
is
o
n
o
f
s
y
s
tem
d
y
n
a
m
ics with
d
is
tu
r
b
an
ce
s
at
∈
[
2
,
6
]
(
a)
co
n
s
tan
t
tr
ajec
to
r
y
(
)
=
2
an
d
(
b
)
f
u
n
ctio
n
tr
ajec
to
r
y
(
)
=
2
s
in
(
)
+
1
2
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
.
3
,
J
u
n
e
20
25
:
2
7
5
8
-
2
7
6
8
2766
4.
CO
NCLU
SI
O
N
T
h
is
ar
ticle
p
r
esen
ts
a
co
n
tr
o
l
d
esig
n
f
o
r
th
e
Gen
esio
-
T
e
s
i
with
u
n
ce
r
tain
p
ar
am
eter
s
ca
u
s
ed
b
y
v
ar
iatio
n
s
in
m
o
d
el
p
ar
am
ete
r
v
alu
es.
T
h
e
c
o
n
tr
o
l
d
esig
n
a
p
p
r
o
ac
h
u
s
es
th
e
b
ac
k
s
tep
p
i
n
g
m
eth
o
d
,
b
ased
o
n
L
y
ap
u
n
o
v
s
tab
ilit
y
,
wh
ic
h
h
as
p
r
o
v
en
to
m
ak
e
t
h
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s
y
s
tem
g
lo
b
ally
asy
m
p
to
tically
s
tab
le.
Simu
latio
n
r
esu
lts
d
em
o
n
s
tr
ate
th
at
th
e
co
n
tr
o
ller
ca
n
r
ap
id
ly
d
r
iv
e
th
e
o
u
tp
u
t i
n
to
th
e
d
esire
d
tr
ajec
to
r
y
.
B
ased
o
n
s
tatis
tical
tes
t
r
esu
lts
,
it
is
clea
r
th
at
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
p
ar
a
m
e
ter
s
ig
n
if
ican
tly
en
h
an
ce
s
co
n
tr
o
l
p
e
r
f
o
r
m
an
ce
.
Ho
wev
er
,
th
e
p
ar
am
eter
v
alu
es
f
o
r
p
ar
am
eter
esti
m
atio
n
ar
e
in
s
u
f
f
icien
t
to
s
u
p
p
o
r
t
c
o
n
tr
o
l
p
er
f
o
r
m
a
n
ce
im
p
r
o
v
em
e
n
t.
D
u
r
in
g
th
e
r
o
b
u
s
tn
ess
test
,
an
u
n
k
n
o
wn
d
is
t
u
r
b
an
ce
is
in
tr
o
d
u
ce
d
to
th
e
s
tead
y
-
s
tate
o
f
th
e
s
y
s
tem
f
o
r
a
s
p
ec
if
ic
p
er
io
d
o
f
tim
e.
T
h
is
ca
u
s
es
th
e
s
y
s
tem
o
u
tp
u
t
to
b
ec
o
m
e
d
is
r
u
p
ted
,
a
s
th
e
co
n
tr
o
l
d
esig
n
d
o
es
n
o
t
ac
co
u
n
t
f
o
r
th
e
d
is
t
u
r
b
an
ce
.
Ho
wev
e
r
,
o
n
ce
th
e
d
is
tu
r
b
an
ce
is
r
em
o
v
ed
,
th
e
c
o
n
tr
o
ller
is
ab
le
to
r
esto
r
e
th
e
o
u
tp
u
t
to
its
o
r
ig
in
al
s
tate.
I
d
en
tify
in
g
th
e
o
p
tim
al
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Evaluation Warning : The document was created with Spire.PDF for Python.