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ee
s
tate
v
ar
iab
le
s
as f
o
llo
w
s
:
̇
1
=
(
2
−
1
)
̇
2
=
(
−
)
1
−
1
3
̇
3
=
1
2
−
3
(
1
)
w
h
er
e
1
,
2
an
d
3
ar
e
th
e
s
tate
v
ar
ia
b
les
o
f
t
h
e
s
y
s
te
m
an
d
,
an
d
ar
e
th
e
t
h
r
ee
s
tate
v
ar
iab
les
o
f
th
e
T
s
y
s
te
m
.
W
h
e
n
=
2
.
1
,
=
30
an
d
=
0
.
6
,
th
e
b
eh
a
v
io
r
o
f
th
e
T
s
y
s
te
m
(
1
)
is
ch
ao
tic.
T
h
e
p
h
ase
p
o
r
tr
aits
o
f
th
e
T
ch
ao
tic
s
y
s
te
m
w
i
th
th
ese
s
y
s
te
m
p
ar
a
m
e
ter
s
a
n
d
th
e
i
n
itial
s
tate
v
ar
iab
le
s
1
=
4
.
3
,
2
=
7
.
2
an
d
3
=
5
.
8
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1.
I
n
ad
d
itio
n
,
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
ca
n
b
e
g
iv
en
a
s
f
o
llo
w
s
:
̇
1
=
−
1
+
2
̇
2
=
1
−
2
−
1
3
̇
3
=
1
2
−
3
(
2
)
w
h
er
e
1
,
2
an
d
3
ar
e
th
e
s
tate
v
ar
iab
les
o
f
th
e
L
o
r
en
z
c
h
ao
tic
s
y
s
te
m
s
.
T
h
e
ch
ao
tic
b
eh
av
io
r
o
f
th
e
L
o
r
en
z
s
y
s
te
m
(
2
)
is
ill
u
s
tr
ated
i
n
Fi
g
u
r
e
2
,
w
ith
s
y
s
te
m
p
ar
a
m
ete
r
s
an
d
in
itia
l
s
t
ate
v
ar
iab
les
a
s
:
1
=
11
,
2
=
7
an
d
3
=
9
.
3.
SYNCH
RO
NI
Z
A
T
I
O
N
Ass
u
m
e
th
e
T
ch
ao
tic
s
y
s
te
m
p
r
ese
n
ted
in
(
1
)
,
as
th
e
d
r
iv
e
s
y
s
te
m
t
h
e
n
r
esp
o
n
s
e
s
y
s
te
m
ca
n
b
e
g
iv
e
n
b
ased
o
n
t
h
e
L
o
r
en
z
c
h
a
o
tic
s
y
s
te
m
(
2
)
as f
o
llo
w
s
:
(
a)
(
b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
4
4
6
–
3
4
5
3
3448
(
c)
(
d
)
Fig
u
r
e
1
.
T
im
e
p
o
r
tr
ait
o
f
th
e
T
ch
ao
tic
s
y
s
te
m
̇
1
=
−
(
+
∆
)
1
+
(
+
∆
)
2
+
1
̇
2
=
(
+
∆
)
1
−
2
−
1
3
+
2
̇
3
=
1
2
−
(
+
∆
)
3
+
3
(
3
)
w
h
er
e
,
an
d
ar
e
th
e
p
a
r
am
et
er
s
o
f
th
e
d
r
iv
e
T
ch
ao
tic
s
y
s
te
m
(
1
)
,
an
d
∆
,
∆
an
d
∆
r
ep
r
esen
t
th
e
d
is
p
ar
it
y
a
m
o
u
n
t
o
f
s
y
s
te
m
p
a
r
a
m
eter
s
.
1
,
2
an
d
3
ar
e
th
e
f
ee
d
b
ac
k
co
n
tr
o
ller
,
w
h
ich
h
av
e
to
b
e
d
esig
n
e
d
in
s
u
c
h
w
a
y
th
a
t
r
esp
o
n
s
e
s
ta
te
v
ar
iab
les
o
f
L
o
r
en
z
c
h
ao
tic
s
y
s
te
m
(
3
)
tr
ac
k
t
h
e
tr
aj
ec
to
r
ies
o
f
t
h
e
d
r
i
v
e
T
ch
ao
tic
s
y
s
te
m
(
1
)
,
as
y
m
p
to
tic
all
y
.
T
h
en
th
e
s
y
n
c
h
r
o
n
izatio
n
er
r
o
r
s
b
et
w
ee
n
t
h
e
s
tate
v
ar
iab
l
es
o
f
th
e
T
ch
ao
tic
s
y
s
te
m
(
1
)
an
d
th
e
L
o
r
en
z
ch
ao
ti
c
s
y
s
te
m
(
3
)
ca
n
b
e
o
b
tain
b
ased
o
n
th
e
p
r
o
j
ec
t
iv
e
lag
s
y
n
c
h
r
o
n
izatio
n
er
r
o
r
s
as f
o
llo
w
s
:
1
=
1
−
1
1
(
−
)
2
=
2
−
2
2
(
−
)
3
=
3
−
3
3
(
−
)
(
4
)
w
h
er
e
1
,
2
an
d
3
ar
e
th
e
th
r
ee
m
o
d
if
ied
p
r
o
j
ec
tiv
e
s
ca
lin
g
er
r
o
r
f
ac
to
r
an
d
s
tates
th
e
ti
m
e
-
d
ela
y
o
f
th
e
s
y
s
te
m
.
T
h
e
d
y
n
a
m
ical
r
ep
r
es
en
tatio
n
o
f
s
y
s
te
m
er
r
o
r
s
ca
n
b
e
d
escr
ib
ed
b
ased
o
n
th
e
s
y
n
ch
r
o
n
izatio
n
er
r
o
r
s
(
4
)
as f
o
llo
w
s
:
̇
1
=
̇
1
−
1
̇
1
(
−
)
̇
2
=
̇
2
−
2
̇
2
(
−
)
̇
3
=
̇
3
−
3
̇
3
(
−
)
(
5
)
I
n
th
e
f
o
llo
w
in
g
t
h
e
co
n
ce
p
t o
f
ch
ao
s
s
y
n
c
h
r
o
n
izatio
n
b
et
w
e
en
t
w
o
ch
ao
tic
s
y
s
te
m
s
is
g
iv
e
n
w
it
h
a
d
ef
i
n
itio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
A
d
a
p
tive
P
r
o
jective
La
g
S
yn
c
h
r
o
n
iz
a
tio
n
o
f T
a
n
d
Lu
C
h
a
o
t
ic
S
ystems
(
Ha
med
Tir
a
n
d
a
z
)
3449
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
2
.
T
im
e
p
o
r
tr
ait
o
f
th
e
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
Def
ini
t
io
n
1
.
T
h
e
tr
iv
ial
s
o
l
u
tio
n
o
f
t
h
e
s
y
s
te
m
er
r
o
r
(
4
)
i
s
s
aid
to
b
e
s
tab
le
i
f
f
o
r
an
y
p
r
o
j
ec
tiv
e
s
ca
lin
g
f
ac
to
r
1
,
2
an
d
3
an
d
a
n
y
ti
m
e
-
d
ela
y
w
it
h
a
n
y
in
itial
s
ta
te
v
ar
iab
les
1
,
2
an
d
3
an
d
1
,
2
an
d
3
an
d
f
o
r
an
y
>
0
,
th
er
e
ex
is
t
a
>
0
s
u
ch
t
h
at
f
o
r
an
y
ti
m
e
>
,
w
e
h
a
v
e
|
|
<
.
I
n
o
th
er
w
o
r
d
s
,
l
im
→
∞
|
|
=
0
f
o
r
all
=
1
,
2
,
3
.
I
n
th
e
f
o
llo
w
i
n
g
th
eo
r
e
m
,
an
ap
p
r
o
p
r
iate
f
ee
d
b
ac
k
co
n
tr
o
l
la
w
a
n
d
a
p
ar
am
eter
es
ti
m
atio
n
la
w
ar
e
g
iv
e
n
to
ac
h
iev
e
d
r
iv
e
-
r
esp
o
n
s
e
s
y
n
c
h
r
o
n
izatio
n
an
d
to
f
o
r
c
e
th
e
tr
iv
ia
l
s
o
lu
tio
n
o
f
th
e
s
y
s
te
m
er
r
o
r
(
4
)
to
b
e
s
tab
le.
T
heo
re
m
1
.
T
h
e
d
r
iv
e
T
ch
ao
tic
s
y
s
te
m
(
1
)
an
d
t
h
e
r
e
s
p
o
n
s
e
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
(
3
)
w
o
u
ld
b
e
s
y
n
ch
r
o
n
ized
an
d
also
s
y
n
c
h
r
o
n
izatio
n
er
r
o
r
s
d
ef
i
n
ed
i
n
(
4
)
w
o
u
ld
b
e
s
tab
le,
i
f
th
e
co
n
tr
o
l
la
w
a
n
d
p
ar
a
m
e
ter
esti
m
atio
n
la
w
ar
e
ta
k
en
as
f
o
l
lo
w
s
:
1
=
(
+
∆
)
(
1
−
2
)
+
1
(
+
∆
)
(
2
(
−
)
−
1
(
−
)
)
−
1
1
2
=
−
(
+
∆
)
1
+
2
+
1
3
+
2
[
(
(
+
∆
)
−
(
+
∆
)
)
1
(
−
)
−
(
+
∆
)
1
(
−
)
3
(
−
)
]
−
2
2
3
=
−
1
2
+
(
+
∆
)
3
−
3
3
+
3
[
1
(
−
)
2
(
−
)
−
(
+
∆
)
3
(
−
)
]
(
6
)
an
d
,
∆
̇
=
1
(
2
−
1
)
−
2
1
2
−
2
2
1
(
−
)
3
(
−
)
∆
̇
=
2
1
(
−
)
2
∆
̇
=
−
3
3
(
−
)
3
(
7
)
W
h
er
e
1
,
2
,
3
,
1
,
2
an
d
3
ar
e
th
e
co
n
s
tan
t p
o
s
itiv
e
v
a
lu
e
s
.
P
ro
o
f
.
L
et
th
e
L
y
ap
u
n
o
v
s
tab
ilit
y
f
u
n
ctio
n
as
f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
4
4
6
–
3
4
5
3
3450
=
1
2
(
1
2
+
2
2
+
3
2
+
(
∆
)
2
+
(
∆
)
2
+
(
∆
)
2
)
(
8
)
I
t is cle
ar
th
at
V
is
p
o
s
iti
v
e
d
e
f
i
n
ite.
T
h
en
,
th
e
d
er
iv
at
iv
e
o
f
V
alo
n
g
t
h
e
ti
m
e
d
o
m
ai
n
w
o
u
l
d
b
e:
̇
=
1
2
(
1
̇
1
+
2
̇
2
+
3
̇
3
+
(
∆
)
(
∆
)
′
+
(
∆
)
(
∆
)
′
+
(
∆
)
(
∆
)
′
)
(
9
)
W
ith
co
n
s
id
er
in
g
t
h
e
d
y
n
a
m
i
ca
l
er
r
o
r
s
in
(
5
)
an
d
d
y
n
a
m
i
ca
l
o
f
p
ar
am
eter
esti
m
atio
n
er
r
o
r
s
in
(
7
)
,
an
d
s
u
b
s
eq
u
en
t
l
y
,
d
y
n
a
m
ical
r
ep
r
esen
tat
io
n
o
f
d
r
iv
e
s
y
s
te
m
(
1
)
an
d
r
esp
o
n
s
e
s
y
s
te
m
(
2
)
an
d
ad
ap
tiv
e
p
r
o
j
ec
tiv
e
lag
f
ee
d
b
ac
k
co
n
tr
o
ller
p
r
o
p
o
s
ed
in
(
6
)
,
th
e
d
er
iv
ativ
e
o
f
L
y
a
p
u
n
o
v
f
u
n
ct
io
n
(
9
)
ca
n
b
e
s
i
m
p
lif
ied
as f
o
llo
w
s
:
̇
=
−
1
1
2
−
2
2
2
−
3
3
2
−
1
(
∆
)
2
−
2
(
∆
)
2
−
3
(
∆
)
2
(
1
0
)
Sin
ce
t
h
e
L
y
ap
u
n
o
v
ca
n
d
id
ate
f
u
n
ctio
n
(
8
)
is
p
o
s
iti
v
e
d
ef
i
n
i
te
an
d
its
d
er
i
v
ati
v
e
is
n
e
g
ati
v
e
d
ef
in
i
te.
T
h
en
,
th
e
s
tab
ilit
y
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
la
w
6
)
a
n
d
p
ar
a
m
eter
est
i
m
a
tio
n
la
w
(
7
)
is
p
r
o
v
ed
.
T
h
u
s
,
t
h
e
an
ticip
ated
s
y
n
ch
r
o
n
izatio
n
b
et
w
ee
n
t
h
e
s
tate
v
ar
iab
les
o
f
th
e
d
r
iv
e
T
ch
ao
tic
s
y
s
te
m
(
1
)
an
d
t
h
e
r
esp
o
n
s
e
ch
ao
tic
s
y
s
te
m
(
3
)
w
o
u
ld
b
e
ac
h
iev
ed
.
F
u
r
th
er
m
o
r
e,
th
e
s
y
n
ch
r
o
n
izatio
n
er
r
o
r
s
d
ef
in
ed
in
(
4
)
ar
e
s
tab
ilized
.
4.
NUM
E
RICAL
S
I
M
UL
AT
I
O
N
S
I
n
t
h
is
s
ec
t
io
n
,
s
o
m
e
n
u
m
er
ic
al
r
esu
lts
r
elate
d
to
t
h
e
s
y
n
c
h
r
o
n
izatio
n
o
f
t
h
e
d
r
iv
e
T
ch
ao
tic
s
y
s
te
m
(
1
)
an
d
th
e
r
esp
o
n
s
e
L
o
r
en
z
c
h
ao
tic
s
y
s
te
m
(
3
)
ar
e
g
i
v
e
n
.
D
u
r
in
g
t
h
is
s
ec
tio
n
,
th
e
u
n
k
n
o
wn
p
ar
a
m
eter
s
o
f
t
h
e
d
r
iv
e
T
ch
ao
tic
s
y
s
te
m
(
1
)
ar
e
co
n
s
id
er
ed
as
=
2
,
=
2
.
3
an
d
=
1
.
5
.
Fu
r
t
h
er
m
o
r
e,
th
e
in
i
tial
e
s
ti
m
atio
n
o
f
p
ar
am
eter
s
ar
e
s
et
as
∆
=
0
.
3
,
∆
=
0
.
5
an
d
∆
=
0
.
2
.
T
h
e
in
itial
s
tate
v
ar
iab
les
o
f
th
e
d
r
iv
e
T
ch
ao
ti
c
s
y
s
te
m
(
1
)
ar
e
s
elec
ted
as:
1
=
12
,
2
=
9
an
d
3
=
11
an
d
also
th
e
r
esp
o
n
s
e
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
(
3
)
ar
e
ch
o
s
en
a
s
1
=
2
,
2
=
1
.
5
an
d
3
=
3
.
T
h
e
ef
f
ec
t
iv
e
n
es
s
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
la
w
f
o
r
s
y
n
ch
r
o
n
i
za
tio
n
o
f
th
e
d
r
iv
e
T
ch
ao
tic
s
y
s
te
m
(
1
)
an
d
th
e
f
o
llo
w
er
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
(
3
)
w
it
h
u
n
k
n
o
w
n
d
r
iv
e
s
y
s
te
m
p
ar
a
m
eter
s
a,
b
,
an
d
c
i
s
s
h
o
w
n
i
n
Fig
u
r
e
3
,
4
an
d
5
f
o
r
d
if
f
er
en
t
p
r
o
j
ec
tiv
e
s
y
n
ch
r
o
n
izatio
n
f
ac
to
r
s
Λ
=
(
1
,
2
,
3
)
as f
o
llo
w
s
:
Λ
1
=
(
1
,
1
,
1
)
Λ
2
=
(
−
1
,
−
1
,
−
1
)
Λ
3
=
(
1
.
02
,
0
.
997
,
1
.
012
)
(
1
1
)
Fig
u
r
e
3
a
s
h
o
w
s
t
h
e
p
r
o
j
ec
tv
ie
lag
s
y
n
c
h
r
o
n
izat
io
n
b
et
w
ee
n
th
e
s
tate
v
ar
iab
el
o
f
t
h
e
d
r
iv
e
T
ch
ao
tic
s
y
s
te
m
a
n
d
r
esp
o
n
s
e
L
o
r
en
z
c
h
ao
tic
s
y
s
te
m
w
i
th
co
n
s
id
er
in
g
ti
m
e
-
d
ela
y
a
s
:
=
0
.
T
h
e
esti
m
ati
o
n
er
r
o
r
s
o
f
s
y
s
te
m
p
ar
a
m
eter
s
f
o
r
th
i
s
p
r
o
j
ec
tiv
e
s
ca
lin
g
Λ
1
(
co
m
p
lete
s
y
n
c
h
r
o
n
izatio
n
)
w
ith
=
0
is
g
i
v
en
i
n
Fig
u
r
e
1
b
.
I
n
ad
d
itio
n
,
p
r
o
j
ec
tiv
e
lag
s
y
n
ch
r
o
n
izatio
n
an
d
d
i
s
p
ar
it
y
a
m
o
u
n
t
o
f
p
ar
a
m
eter
e
s
ti
m
atio
n
w
it
h
s
ca
li
n
g
f
ac
to
r
Λ
1
an
d
ass
u
m
in
g
t
h
e
ti
m
e
-
d
ela
y
s
as
=
0
.
5
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
3
c
an
d
Fig
u
r
e
3
d
,
r
esp
ec
tiv
el
y
.
An
ti
-
s
y
n
ch
r
o
n
izatio
n
p
r
o
b
le
m
i
s
ill
u
s
tr
ated
in
F
ig
u
r
e
4
,
w
i
th
p
r
o
j
ec
tiv
e
s
ca
li
n
g
Λ
2
=
(
−
1
,
−
1
,
−
1
)
.
Fig
u
r
e
4
a
an
d
4
b
s
h
o
w
th
e
an
ti
-
s
y
n
c
h
r
o
n
izat
io
n
p
r
o
b
lem
w
it
h
o
u
t
co
n
s
id
er
en
i
n
g
an
y
ti
m
e
-
d
ela
y
s
.
W
h
ile
Fi
g
u
r
e
4
c
an
d
4
d
d
ep
ict
t
h
e
a
n
ti
-
s
y
n
c
h
r
o
n
izat
io
n
p
r
o
b
le
m
w
it
h
co
n
s
id
er
i
n
g
ti
m
e
-
d
elay
a
s
as
=
0
.
5
.
Fin
all
y
,
an
o
t
h
er
p
r
o
j
ec
tiv
e
s
y
n
ch
r
o
n
izatio
n
is
d
ep
icted
in
Fig
u
r
e
5
,
w
ith
a
t
y
p
ical
s
ca
li
n
g
f
ac
to
r
s
Λ
3
=
(
1
.
02
,
0
.
997
,
1
.
012
)
.
Fig
u
r
e
5
a
an
d
5
b
s
h
o
w
th
e
p
r
o
j
ec
tiv
e
lag
s
y
n
ch
r
o
n
izat
io
n
p
r
o
b
lem
an
d
d
is
p
ar
it
y
o
f
p
ar
m
ae
ter
est
i
m
at
io
n
b
et
w
ee
n
th
e
d
r
iv
e
c
h
ao
tic
s
y
s
te
m
(
1
)
an
d
r
esp
o
n
s
e
c
h
ao
t
ic
s
y
s
te
m
(
2
)
w
it
h
a
t
y
p
ical
p
r
o
j
ec
tiv
e
s
ca
li
n
g
Λ
3
an
d
w
it
h
o
u
t
co
n
s
id
er
in
g
a
n
y
ti
m
e
-
d
ela
y
s
(
=
0
)
.
I
n
s
i
m
ilar
m
an
n
er
,
t
h
e
p
r
o
j
ec
itv
e
lag
s
y
n
c
h
r
o
n
izatio
n
an
d
d
is
p
ar
iti
y
a
m
o
u
n
t
o
f
p
ar
a
m
eter
esti
m
atio
n
s
ar
e
ac
h
i
v
ed
w
it
h
p
r
o
j
ec
tiv
e
s
ca
lin
g
Λ
3
an
d
a
s
s
u
m
in
g
t
h
e
s
y
s
te
m
t
i
m
e
-
d
ela
y
as
=
0
.
5
in
Fi
g
u
r
es
5
c
an
d
5
d
,
r
esp
ec
itv
el
y
.
As
i
t
ca
n
b
e
s
ee
n
f
r
o
m
t
h
ese
r
esu
lts
,
t
h
e
a
n
ticip
ated
s
y
n
c
h
r
o
n
izat
io
n
s
ar
e
ac
h
i
v
ed
.
Fu
r
t
h
er
m
o
r
e,
th
e
d
is
p
ar
it
y
a
m
o
u
n
t
o
f
s
y
s
te
m
p
ar
a
m
eter
s
esti
m
at
io
n
s
co
n
v
er
g
e
to
ze
r
o
,
w
it
h
all
p
r
o
j
ec
tiv
e
s
ca
lin
g
f
ac
to
r
s
Λ
1
,
Λ
2
an
d
Λ
3
.
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I
J
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C
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0
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8
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8708
A
d
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iz
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ystems
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izatio
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ar
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eter
esti
m
atio
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r
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h
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y
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h
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izatio
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r
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r
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P
ar
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eter
esti
m
atio
n
er
r
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r
w
it
h
(
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Fig
u
r
e
3
.
p
r
o
j
ec
tiv
e
lag
s
y
n
c
h
r
o
n
izatio
n
o
f
T
ch
ao
tic
s
y
s
te
m
(
1
)
an
d
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
(
3
)
w
it
h
p
r
o
j
ec
tiv
e
s
ca
lin
g
f
ac
to
r
=
(
1
,
1
,
1
)
(
a)
s
y
n
c
h
r
o
n
izatio
n
er
r
o
r
w
ith
(
=
0
)
(
b
)
P
ar
am
eter
esti
m
atio
n
er
r
o
r
w
it
h
(
=
0
)
(
c)
s
y
n
c
h
r
o
n
izatio
n
er
r
o
r
w
ith
(
=
0
.
5
)
(
d
)
P
ar
am
eter
esti
m
atio
n
er
r
o
r
w
it
h
(
=
0
.
5
)
Fig
u
r
e
4
.
p
r
o
j
ec
tiv
e
lag
s
y
n
c
h
r
o
n
izatio
n
o
f
T
ch
ao
tic
s
y
s
te
m
(
1
)
an
d
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
(
3
)
w
it
h
p
r
o
j
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tiv
e
s
ca
lin
g
f
ac
to
r
Λ
=
(
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1
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1
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)
0
1
2
3
4
5
6
7
8
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20
0
20
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2
3
4
5
6
7
8
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20
0
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0
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2
3
4
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6
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I
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er
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izatio
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izatio
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r
am
eter
est
i
m
a
tio
n
er
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o
r
w
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h
(
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Fig
u
r
e
5
.
p
r
o
j
ec
tiv
e
lag
s
y
n
c
h
r
o
n
izatio
n
o
f
T
ch
ao
tic
s
y
s
te
m
(
1
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d
L
o
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en
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ch
ao
tic
s
y
s
te
m
(
3
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it
h
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s
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lin
g
f
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r
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=
(
1
.
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.
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,
1
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)
5.
CO
NCLU
SI
O
NS
I
n
th
i
s
s
t
u
d
y
,
a
n
e
w
ad
ap
tiv
e
p
r
o
j
ec
tiv
e
lag
co
n
tr
o
l
m
et
h
o
d
f
o
r
s
y
n
c
h
r
o
n
izatio
n
o
f
T
ch
ao
tic
s
y
s
te
m
as
th
e
d
r
iv
e
s
y
s
te
m
a
n
d
th
e
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
as
t
h
e
r
esp
o
n
s
e
s
y
s
te
m
is
ac
h
iev
ed
.
T
h
e
p
ar
am
eter
s
o
f
t
h
e
d
r
iv
e
ch
ao
tic
s
y
s
te
m
ar
e
co
n
s
id
er
ed
u
n
k
n
o
w
n
.
T
h
u
s
,
ad
ap
tiv
e
co
n
tr
o
l
is
u
tili
z
ed
to
ac
h
iev
e
t
h
e
s
y
n
ch
r
o
n
izatio
n
.
P
r
o
j
ec
tiv
e
co
n
tr
o
l
m
et
h
o
d
is
g
i
v
e
n
b
ased
o
n
a
L
y
ap
u
n
o
v
ca
n
d
id
ate
f
u
n
ctio
n
to
f
o
r
ce
th
e
s
tate
v
ar
iab
les
o
f
t
h
e
r
esp
o
n
s
e
L
o
r
en
z
ch
ao
tic
s
y
s
te
m
to
f
o
ll
o
w
t
h
e
m
o
tio
n
tr
aj
ec
to
r
ies
o
f
th
e
d
r
iv
e
T
ch
ao
tic
s
y
s
te
m
.
Fu
r
t
h
er
m
o
r
e,
s
o
m
e
n
u
m
er
ical
s
i
m
u
lat
io
n
s
ar
e
p
er
f
o
r
m
ed
to
v
al
id
ate
th
e
e
f
f
ec
ti
v
e
n
ess
o
f
th
e
p
r
o
p
o
s
ed
p
r
o
j
ec
tiv
e
lag
s
y
n
c
h
r
o
n
izat
io
n
m
eth
o
d
.
T
h
e
r
esu
lts
s
h
o
w
t
h
a
t
th
e
an
t
icip
ated
d
r
iv
e
-
r
esp
o
n
s
e
s
y
n
c
h
r
o
n
izatio
n
is
d
er
iv
ed
an
d
also
th
e
d
is
p
a
r
it
y
a
m
o
u
n
t
o
f
p
ar
a
m
eter
est
i
m
atio
n
s
co
n
v
er
g
e
to
ze
r
o
as
ti
m
e
g
o
es
to
t
h
e
in
f
in
it
y
.
RE
F
E
R
E
NC
E
S
[1
]
H.
N.
A
g
iz
a
a
n
d
M
.
T
.
Ya
ss
e
n
,
“
S
y
n
c
h
ro
n
iza
ti
o
n
o
f
Ro
ss
ler
a
n
d
Ch
e
n
c
h
a
o
ti
c
d
y
n
a
m
ic
a
l
s
y
ste
m
s
u
sin
g
a
c
ti
v
e
c
o
n
tro
l
,”
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y
sic
s L
e
tt
e
rs
A
,
v
o
l/
is
su
e
:
2
7
8
(4
)
,
p
p
.
1
9
1
-
1
9
7
,
2
0
0
1
.
[2
]
M
.
T
.
Ya
ss
e
n
,
“
Ch
a
o
s s
y
n
c
h
ro
n
iz
a
ti
o
n
b
e
tw
e
e
n
t
w
o
d
iff
e
re
n
t
c
h
a
o
t
ic s
y
ste
m
s u
sin
g
a
c
ti
v
e
c
o
n
tro
l
,”
Ch
a
o
s
,
S
o
li
to
n
s
&
Fra
c
ta
ls
,
v
o
l/
issu
e
:
2
3
(1
)
,
p
p
.
131
-
1
4
0
,
2
0
0
5
.
[3
]
S.
Bh
a
lek
a
r
a
n
d
V
.
D
.
G
e
jj
i,
“
S
y
n
c
h
ro
n
iza
ti
o
n
o
f
d
iff
e
re
n
t
f
ra
c
ti
o
n
a
l
o
rd
e
r
c
h
a
o
t
ic
sy
ste
m
s
u
sin
g
a
c
ti
v
e
c
o
n
tro
l
,”
Co
mm
u
n
ica
ti
o
n
s i
n
No
n
li
n
e
a
r S
c
i
e
n
c
e
a
n
d
Nu
me
ric
a
l
S
imu
l
a
ti
o
n
,
v
o
l/
issu
e
:
1
5
(
1
1
),
p
p
.
3
5
3
6
-
3
5
4
6
,
2
0
1
0
.
[4
]
S.
Ch
e
n
a
n
d
J.
L
ü
,
“
S
y
n
c
h
ro
n
iza
ti
o
n
o
f
a
n
u
n
c
e
rtain
u
n
if
ied
c
h
a
o
ti
c
s
y
ste
m
v
i
a
a
d
a
p
ti
v
e
c
o
n
tro
l
,”
Ch
a
o
s
,
S
o
li
to
n
s
&
Fra
c
ta
ls
,
v
o
l/
issu
e
:
1
4
(4
)
,
p
p
.
643
-
6
4
7
,
2
0
0
2
.
[5
]
T
.
L
.
L
iao
a
n
d
S
.
H
.
T
sa
i,
“
A
d
a
p
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
c
h
a
o
ti
c
sy
ste
m
s
a
n
d
it
s
a
p
p
l
ica
ti
o
n
to
se
c
u
re
c
o
m
m
u
n
ica
ti
o
n
s
,”
Ch
a
o
s,
S
o
l
it
o
n
s
&
Fra
c
ta
ls
,
v
o
l/
issu
e
:
1
1
(
9
),
p
p
.
1
3
8
7
-
1
3
9
6
,
2
0
0
0
.
[6
]
S.
V
a
id
y
a
n
a
th
a
n
,
e
t
a
l
.,
“
Ba
c
k
ste
p
p
i
n
g
Co
n
tro
l
De
sig
n
f
o
r
th
e
A
d
a
p
ti
v
e
S
tab
il
iza
ti
o
n
a
n
d
S
y
n
c
h
ro
n
iza
ti
o
n
o
f
th
e
P
a
n
d
e
y
Je
r
k
Ch
a
o
ti
c
S
y
ste
m
w
it
h
Un
k
n
o
w
n
P
a
ra
m
e
ters
,”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
C
o
n
tro
l
T
h
e
o
ry
a
n
d
Ap
p
li
c
a
ti
o
n
s
,
v
o
l
/i
ss
u
e
:
9
(1
),
p
p
.
299
-
3
1
9
,
2
0
1
6
.
[7
]
M
.
C.
Ho
,
e
t
a
l
.,
“
P
h
a
se
a
n
d
a
n
t
i
-
p
h
a
se
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
tw
o
c
h
a
o
ti
c
s
y
s
te
m
s
b
y
u
sin
g
a
c
ti
v
e
c
o
n
tro
l
,”
Ph
y
sic
s
letter
s A
,
v
o
l/
issu
e
:
2
9
6
(1
),
p
p
.
43
-
48
,
2
0
0
2
.
[8
]
J.
H.
P
a
rk
,
“
S
y
n
c
h
ro
n
iza
ti
o
n
o
f
G
e
n
e
sio
c
h
a
o
ti
c
s
y
st
e
m
v
ia
b
a
c
k
ste
p
p
in
g
a
p
p
r
o
a
c
h
,”
Ch
a
o
s,
S
o
li
t
o
n
s
&
Fra
c
ta
ls
,
v
o
l/
issu
e
:
2
7
(5
),
p
p
.
1
3
6
9
-
1
3
7
5
,
2
0
0
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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C
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2
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A
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a
p
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n
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[9
]
Y.
Yu
a
n
d
S.
Z
h
a
n
g
,
“
A
d
a
p
ti
v
e
b
a
c
k
ste
p
p
in
g
sy
n
c
h
ro
n
iza
t
io
n
o
f
u
n
c
e
rtain
c
h
a
o
ti
c
sy
ste
m
,”
Ch
a
o
s,
S
o
li
to
n
s
&
Fra
c
ta
ls
,
v
o
l
/i
ss
u
e
:
2
1
(
3
),
p
p
.
6
4
3
-
6
4
9
,
2
0
0
4
.
[1
0
]
C.
L
i,
e
t
a
l
.
,
“
L
a
g
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
h
y
p
e
rc
h
a
o
s
w
it
h
a
p
p
li
c
a
ti
o
n
to
se
c
u
re
c
o
m
m
u
n
ica
ti
o
n
s
,”
Ch
a
o
s,
S
o
li
t
o
n
s
&
Fra
c
ta
ls
,
v
o
l
/i
ss
u
e
:
2
3
(
1
),
p
p
.
1
8
3
-
1
9
3
,
2
0
0
5
.
[1
1
]
B.
L
iu
,
e
t
a
l
.,
“
Ro
b
u
st i
m
p
u
lsiv
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
u
n
c
e
rtain
d
y
n
a
m
ica
l
n
e
t
w
o
rk
s
,”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
Circ
u
it
s
a
n
d
S
y
ste
ms
I:
Reg
u
la
r
Pa
p
e
rs
,
v
o
l/
issu
e
:
5
2
(
7
),
pp.
1
4
3
1
-
1
4
4
1
,
2
0
0
5
.
[1
2
]
H.
Zh
a
n
g
,
e
t
a
l
.,
“
Ro
b
u
st g
lo
b
a
l
e
x
p
o
n
e
n
t
ial
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
u
n
c
e
rtain
c
h
a
o
ti
c
d
e
la
y
e
d
n
e
u
ra
l
n
e
tw
o
rk
s
v
ia
d
u
a
l
-
sta
g
e
i
m
p
u
lsiv
e
c
o
n
tro
l
,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
y
ste
ms
,
M
a
n
,
a
n
d
Cy
b
e
rn
e
ti
c
s,
P
a
rt
B
(
Cy
b
e
rn
e
ti
c
s)
,
v
o
l/
issu
e
:
4
0
(
3
),
p
p
.
8
3
1
-
8
4
4
,
2
0
1
0
.
[1
3
]
M.
Ra
f
ik
o
v
a
n
d
J.
M
.
Ba
lt
h
a
z
a
r,
“
On
c
o
n
tr
o
l
a
n
d
sy
n
c
h
ro
n
iza
ti
o
n
in
c
h
a
o
ti
c
a
n
d
h
y
p
e
rc
h
a
o
ti
c
sy
ste
m
s
v
ia
li
n
e
a
r
f
e
e
d
b
a
c
k
c
o
n
tro
l
,”
Co
mm
u
n
ica
ti
o
n
s
in
No
n
li
n
e
a
r
S
c
ien
c
e
a
n
d
N
u
me
ric
a
l
S
imu
l
a
ti
o
n
,
v
o
l/
issu
e
:
1
3
(7
),
p
p
.
1
2
4
6
-
1
2
5
5
,
2
0
0
8
.
[1
4
]
J.
Zh
a
o
a
n
d
J.
A
.
L
u
,
“
Us
in
g
sa
m
p
led
-
d
a
ta
f
e
e
d
b
a
c
k
c
o
n
tro
l
a
n
d
li
n
e
a
r
f
e
e
d
b
a
c
k
s
y
n
c
h
ro
n
iz
a
ti
o
n
i
n
a
n
e
w
h
y
p
e
rc
h
a
o
ti
c
s
y
ste
m
,”
Ch
a
o
s,
S
o
l
it
o
n
s &
Fra
c
ta
ls
,
v
o
l/
issu
e
:
3
5
(
2
),
p
p
.
3
7
6
-
3
8
2
,
2
0
0
8
.
[1
5
]
H.
H.
Ch
e
n
,
e
t
a
l
.,
“
Ch
a
o
s
sy
n
c
h
ro
n
iza
ti
o
n
b
e
tw
e
e
n
t
w
o
d
if
f
e
r
e
n
t
c
h
a
o
ti
c
sy
ste
m
s
v
ia
n
o
n
li
n
e
a
r
f
e
e
d
b
a
c
k
c
o
n
tro
l
,”
No
n
li
n
e
a
r A
n
a
lys
is:
T
h
e
o
ry
,
M
e
t
h
o
d
s
&
Ap
p
li
c
a
ti
o
n
s
,
v
o
l/
issu
e
:
7
0
(1
2
),
p
p
.
4
3
9
3
-
4
4
0
1
,
2
0
0
9
.
[1
6
]
L
.
L
in
g
,
e
t
a
l
.
,
“
S
y
n
c
h
ro
n
iza
ti
o
n
b
e
tw
e
e
n
tw
o
d
iff
e
re
n
t
c
h
a
o
ti
c
sy
s
tem
s
w
it
h
n
o
n
l
in
e
a
r
f
e
e
d
b
a
c
k
c
o
n
tro
l
,”
Ch
i
n
e
se
Ph
y
sic
s
,
v
o
l/
issu
e
:
1
6
(
6
),
p
p.
1
6
0
3
,
2
0
0
7
.
[1
7
]
R.
M
a
in
ieri
a
n
d
J.
Re
h
a
c
e
k
,
“
P
r
o
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
i
n
th
re
e
-
d
im
e
n
sio
n
a
l
c
h
a
o
ti
c
sy
ste
m
s
,”
Ph
y
sic
a
l
Rev
iew
L
e
tt
e
rs
,
v
o
l/
issu
e
:
8
2
(1
5
),
p
p.
3
0
4
2
,
19
99
.
[1
8
]
D.
X
u
,
“
Co
n
tr
o
l
o
f
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
i
n
c
h
a
o
ti
c
sy
st
e
m
s
,”
Ph
y
sic
a
l
re
v
iew
E
,
v
o
l/
issu
e
:
6
3
(
2
),
p
p.
0
2
7
2
0
1
,
2
0
0
1
.
[1
9
]
G
.
H.
L
i,
“
M
o
d
if
ied
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
c
h
a
o
ti
c
s
y
ste
m
,”
Ch
a
o
s,
S
o
li
t
o
n
s
&
Fra
c
ta
ls
,
v
o
l/
issu
e
:
3
2
(5
)
,
pp.
1
7
8
6
-
1
7
9
0
,
2
0
0
7
.
[2
0
]
D.
Xu
a
n
d
Z.
L
i,
“
Co
n
tr
o
ll
e
d
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
i
n
n
o
n
p
a
rti
a
ll
y
-
li
n
e
a
r
c
h
a
o
ti
c
s
y
st
e
m
s
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Bi
f
u
rc
a
ti
o
n
a
n
d
C
h
a
o
s
,
v
o
l/
issu
e
:
1
2
(
0
6
),
p
p
.
1
3
9
5
-
1
4
0
2
,
2
0
0
2
.
[2
1
]
N.
Ca
i,
e
t
a
l
.,
“
M
o
d
if
ied
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
c
h
a
o
ti
c
s
y
ste
m
s
w
it
h
d
istu
rb
a
n
c
e
s
v
ia
a
c
ti
v
e
slid
in
g
m
o
d
e
c
o
n
tro
l
,”
Co
mm
u
n
ica
t
io
n
s in
No
n
li
n
e
a
r
S
c
ien
c
e
a
n
d
N
u
me
ric
a
l
S
i
mu
la
ti
o
n
,
v
o
l/
issu
e
:
1
5
(6
),
p
p
.
1
6
1
3
-
1
6
2
0
,
2
0
1
0
.
[2
2
]
X
.
W
a
n
g
,
e
t
a
l
.
,
“
M
o
d
if
ied
p
ro
je
c
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
f
ra
c
ti
o
n
a
l
-
o
rd
e
r
c
h
a
o
ti
c
sy
ste
m
s
v
ia
a
c
ti
v
e
slid
in
g
m
o
d
e
c
o
n
tro
l
,”
No
n
li
n
e
a
r Dy
n
a
mic
s
,
v
o
l/
issu
e
:
6
9
(1
)
,
p
p
.
5
1
1
-
5
1
7
,
2
0
1
2
.
[2
3
]
J.
H.
P
a
rk
,
“
A
d
a
p
ti
v
e
m
o
d
if
ie
d
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
a
u
n
if
ied
c
h
a
o
ti
c
s
y
ste
m
w
it
h
a
n
u
n
c
e
rtai
n
p
a
ra
m
e
ter
,”
Ch
a
o
s,
S
o
li
to
n
s
&
Fra
c
ta
ls
,
v
o
l
/i
ss
u
e
:
3
4
(
5
),
p
p
.
1
5
5
2
-
1
5
5
9
,
2
0
0
7
.
[2
4
]
H.
Du
,
e
t
a
l
.,
“
F
u
n
c
ti
o
n
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
in
c
o
u
p
led
c
h
a
o
ti
c
sy
st
e
m
s
,”
No
n
li
n
e
a
r
A
n
a
lys
is:
Rea
l
W
o
rl
d
Ap
p
li
c
a
ti
o
n
s
,
v
o
l
/i
ss
u
e
:
1
1
(
2
),
p
p
.
7
0
5
-
7
1
2
,
2
0
1
0
.
[2
5
]
Y.
Ch
e
n
a
n
d
X.
L
i,
“
F
u
n
c
ti
o
n
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
b
e
tw
e
e
n
tw
o
id
e
n
ti
c
a
l
c
h
a
o
t
ic
sy
ste
m
s
,”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
M
o
d
e
rn
Ph
y
sic
s C
,
v
o
l
/i
ss
u
e
:
1
8
(0
5
),
p
p
.
8
8
3
-
8
8
8
,
2
0
0
7
.
[2
6
]
P.
Zh
o
u
a
n
d
W
.
Zh
u
,
“
F
u
n
c
ti
o
n
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
f
o
r
f
ra
c
ti
o
n
a
l
-
o
r
d
e
r
c
h
a
o
ti
c
sy
ste
m
s
,”
No
n
li
n
e
a
r
An
a
lys
is:
Rea
l
W
o
rld
Ap
p
li
c
a
t
io
n
s
,
v
o
l/
issu
e
:
1
2
(
2
),
p
p
.
8
1
1
-
8
1
6
,
2
0
1
1
.
[2
7
]
H.
Du
,
e
t
a
l
.
,
“
M
o
d
if
ied
f
u
n
c
ti
o
n
p
ro
jec
ti
v
e
sy
n
c
h
r
o
n
iza
ti
o
n
o
f
c
h
a
o
ti
c
sy
ste
m
,”
Ch
a
o
s,
S
o
li
to
n
s
&
Fra
c
ta
ls
,
v
o
l/
issu
e
:
4
2
(4
),
p
p
.
2
3
9
9
-
2
4
0
4
,
2
0
0
9
.
[2
8
]
S.
V
a
i
d
y
a
n
a
th
a
n
a
n
d
S.
P
a
k
iri
sw
a
m
y
,
“
Ge
n
e
ra
li
z
e
d
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
six
-
ter
m
S
u
n
d
a
ra
p
a
n
d
ia
n
c
h
a
o
ti
c
s
y
ste
m
s b
y
a
d
a
p
ti
v
e
c
o
n
tro
l
,”
In
t
J
Co
n
tro
l
T
h
e
o
ry
Ap
p
l
,
v
o
l/
issu
e
:
6
(2
),
p
p
.
1
5
3
-
1
6
3
,
2
0
1
3
.
[2
9
]
G
.
H.
L
i,
“
G
e
n
e
ra
li
z
e
d
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
tw
o
c
h
a
o
ti
c
sy
ste
m
s
b
y
u
sin
g
a
c
ti
v
e
c
o
n
tro
l
,”
Ch
a
o
s
,
S
o
li
to
n
s
&
Fra
c
ta
ls
,
v
o
l/
issu
e
:
3
0
(1
)
,
p
p
.
77
-
82
,
2
0
0
6
.
[3
0
]
P.
S
a
ra
su
a
n
d
V
.
S
u
n
d
a
ra
p
a
n
d
i
a
n
,
“
G
e
n
e
ra
li
z
e
d
p
ro
jec
ti
v
e
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
tw
o
-
sc
ro
ll
sy
st
e
m
s
v
ia
a
d
a
p
ti
v
e
c
o
n
tro
l
,”
In
t
J
S
o
ft
C
o
mp
u
t
,
v
o
l/
issu
e
:
7
(4
)
,
p
p
.
1
4
6
-
1
5
6
,
2
0
1
2
.
[3
1
]
G
.
T
i
g
a
n
a
n
d
D.
Op
riş,
“
A
n
a
ly
sis
o
f
a
3
D
c
h
a
o
ti
c
s
y
ste
m
,”
Ch
a
o
s,
S
o
li
to
n
s
&
Fra
c
ta
ls
,
v
o
l/
issu
e
:
3
6
(5
),
p
p
.
1
3
1
5
-
1
3
1
9
,
2
0
0
8
.
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