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I
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I
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t J E
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C
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g
,
Vo
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14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
2
7
1
-
6
2
7
8
6272
T
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g
en
er
atio
n
o
f
s
tab
le
o
s
cillatio
n
s
an
d
th
e
s
u
p
p
r
ess
io
n
o
f
u
n
wan
ted
d
is
tu
r
b
a
n
ce
s
.
B
y
lev
er
ag
in
g
t
h
e
s
y
n
er
g
etic
p
r
in
cip
les
o
f
s
elf
-
o
r
g
an
izatio
n
an
d
co
n
tr
o
l,
th
e
ADACO
m
eth
o
d
o
f
f
er
s
a
p
r
o
m
is
in
g
s
o
lu
ti
o
n
f
o
r
ad
v
a
n
c
in
g
th
e
s
tate
o
f
th
e
ar
t
in
n
o
n
lin
ea
r
co
n
tr
o
l
th
eo
r
y
.
T
h
e
f
ield
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l
h
as
ev
o
lv
ed
s
i
g
n
if
ican
tly
o
v
er
th
e
y
ea
r
s
,
with
SC
T
p
r
o
v
id
in
g
a
r
o
b
u
s
t
f
r
a
m
ewo
r
k
f
o
r
t
h
e
s
y
n
th
esis
o
f
co
n
tr
o
l
laws
f
o
r
co
m
p
lex
,
m
u
lti
-
d
im
en
s
io
n
al
s
y
s
tem
s
.
T
h
is
r
ev
iew
aim
s
to
o
u
tlin
e
th
e
f
o
u
n
d
atio
n
al
th
eo
r
ies
an
d
m
eth
o
d
s
th
at
h
av
e
led
to
th
e
d
ev
elo
p
m
e
n
t o
f
t
h
e
ADACO m
eth
o
d
,
h
ig
h
lig
h
tin
g
k
e
y
co
n
tr
ib
u
tio
n
s
an
d
ad
v
a
n
ce
m
en
ts
.
T
h
e
class
ical
m
eth
o
d
s
in
co
n
tr
o
llin
g
n
o
n
lin
ea
r
o
s
cillatio
n
s
p
r
im
ar
ily
f
o
c
u
s
o
n
two
m
aj
o
r
c
h
allen
g
es:
g
en
er
atin
g
s
tab
le
n
o
n
lin
ea
r
o
s
cillatio
n
s
an
d
s
u
p
p
r
ess
in
g
u
n
wan
ted
ex
ter
n
al
o
s
cillatio
n
s
.
E
ar
ly
wo
r
k
s
in
th
is
ar
ea
,
s
u
ch
as
th
e
v
a
n
d
er
Po
l
a
n
d
R
ay
leig
h
o
s
cillato
r
s
,
laid
t
h
e
g
r
o
u
n
d
wo
r
k
f
o
r
u
n
d
er
s
tan
d
in
g
an
d
c
o
n
tr
o
llin
g
n
o
n
lin
ea
r
o
s
cillatio
n
s
in
v
ar
io
u
s
f
ield
s
,
in
clu
d
in
g
au
t
o
o
s
cillatio
n
th
eo
r
y
,
r
ad
io
en
g
in
ee
r
in
g
,
an
d
elec
tr
o
m
ec
h
an
ics
[
1
]
.
T
h
ese
tr
ad
itio
n
al
m
eth
o
d
s
p
r
o
v
i
d
ed
i
n
itial
in
s
ig
h
ts
b
u
t
wer
e
lim
ited
in
th
eir
ab
ilit
y
to
g
en
er
alize
ac
r
o
s
s
d
if
f
e
r
en
t ty
p
es o
f
n
o
n
lin
ea
r
s
y
s
tem
s
.
Sy
n
er
g
etic
co
n
tr
o
l
th
e
o
r
y
e
m
er
g
ed
as
a
p
o
we
r
f
u
l
a
p
p
r
o
ac
h
f
o
r
d
ea
lin
g
with
th
e
in
h
er
en
t
co
m
p
lex
ities
o
f
n
o
n
lin
ea
r
o
s
cillatin
g
s
y
s
tem
s
.
SC
T
em
p
h
asizes
th
e
h
a
r
m
o
n
io
u
s
in
teg
r
atio
n
o
f
s
elf
-
o
r
g
an
izatio
n
an
d
co
n
tr
o
l
p
r
o
ce
s
s
es,
en
ab
lin
g
th
e
s
y
n
th
esi
s
o
f
co
n
tr
o
l
laws
th
at
ca
n
ad
ap
t
to
th
e
d
y
n
am
ic
b
eh
av
io
r
s
o
f
m
u
lti
-
d
im
en
s
io
n
al
s
y
s
tem
s
.
On
e
o
f
th
e
cr
itical
ch
allen
g
es
in
SC
T
is
th
e
s
elec
tio
n
an
d
ju
s
tific
atio
n
o
f
in
v
ar
ian
t
m
a
n
i
f
o
ld
s
,
wh
ich
s
er
v
e
as
th
e
tar
g
et
attr
ac
to
r
s
f
o
r
th
e
s
y
s
tem
.
T
h
is
asp
ec
t
o
f
SC
T
i
s
cr
u
cial
f
o
r
en
s
u
r
in
g
th
at
th
e
co
n
tr
o
l
p
r
o
ce
s
s
es
alig
n
with
th
e
s
p
ec
if
ic
tech
n
o
lo
g
ical
r
eq
u
i
r
em
en
ts
o
f
v
ar
io
u
s
f
ield
s
,
s
u
ch
as e
lectr
ic
p
o
wer
e
n
g
in
ee
r
in
g
,
r
o
b
o
tics
,
av
iatio
n
,
an
d
astro
n
a
u
tics
[
2
]
.
T
h
e
ADAC
m
eth
o
d
,
a
p
r
ec
u
r
s
o
r
to
ADACO,
r
ep
r
esen
ts
a
s
ig
n
if
ican
t
ad
v
a
n
ce
m
en
t
in
SC
T
b
y
in
tr
o
d
u
cin
g
a
s
tr
u
ctu
r
ed
ap
p
r
o
ac
h
to
th
e
s
y
n
t
h
esis
o
f
co
n
tr
o
l
laws.
ADAC
is
b
ased
o
n
th
e
p
r
in
cip
les
o
f
an
aly
tical
m
ec
h
an
ics
an
d
in
v
o
lv
es
th
e
u
s
e
o
f
in
v
a
r
ian
t
m
an
if
o
ld
s
to
d
esig
n
co
n
tr
o
l
la
ws
th
at
ca
n
ac
h
iev
e
d
esire
d
o
s
cillato
r
y
b
e
h
av
io
r
s
.
Ho
wev
er
,
w
h
ile
ADAC
p
r
o
v
id
ed
a
s
o
lid
f
o
u
n
d
atio
n
,
it
h
ad
lim
itatio
n
s
in
ter
m
s
o
f
its
ap
p
licab
ilit
y
to
a
b
r
o
a
d
e
r
r
an
g
e
o
f
n
o
n
lin
ea
r
s
y
s
tem
s
an
d
its
ab
ilit
y
to
ef
f
icien
tly
m
a
n
ag
e
en
er
g
y
u
s
e.
B
u
i
l
d
i
n
g
o
n
t
h
e
AD
AC
m
et
h
o
d
,
t
h
e
AD
AC
O
m
et
h
o
d
i
n
t
r
o
d
u
c
e
s
s
e
v
e
r
a
l
k
e
y
i
n
n
o
v
a
t
i
o
n
s
th
a
t
a
d
d
r
e
s
s
t
h
e
s
h
o
r
t
c
o
m
i
n
g
s
o
f
i
t
s
p
r
e
d
e
ce
s
s
o
r
.
A
DAC
O
i
n
c
o
r
p
o
r
a
t
e
s
en
e
r
g
y
i
n
v
a
r
i
a
n
t
s
a
n
d
f
i
r
s
t
i
n
t
eg
r
a
l
s
o
f
m
o
t
i
o
n
i
n
t
o
t
h
e
s
y
n
t
h
es
is
o
f
c
o
n
t
r
o
l
l
a
ws
,
p
r
o
v
i
d
i
n
g
a
m
o
r
e
c
o
m
p
r
e
h
e
n
s
i
v
e
f
r
a
m
ew
o
r
k
f
o
r
e
n
e
r
g
y
-
e
f
f
i
c
i
e
n
t
c
o
n
t
r
o
l
o
f
o
s
c
i
ll
a
t
o
r
y
a
n
d
v
i
b
r
a
t
i
o
n
m
o
d
e
s
i
n
n
o
n
l
i
n
e
a
r
s
y
s
t
e
m
s
.
T
h
i
s
m
e
t
h
o
d
a
l
l
o
w
s
f
o
r
t
h
e
g
e
n
e
r
a
l
iz
at
i
o
n
o
f
c
o
n
t
r
o
l
l
a
w
s
a
c
r
o
s
s
v
a
r
i
o
u
s
a
p
p
l
i
ca
t
i
o
n
s
,
f
r
o
m
a
e
r
o
s
p
a
c
e
s
y
s
t
e
m
s
t
o
c
o
m
p
le
x
o
b
j
e
c
t
s
w
i
t
h
c
h
a
o
ti
c
d
y
n
a
m
ic
s
[
3
]
.
T
h
e
th
eo
r
etica
l
u
n
d
er
p
in
n
in
g
s
o
f
t
h
e
ADACO
m
eth
o
d
a
r
e
r
o
o
ted
in
th
e
s
y
n
er
g
etic
p
r
in
cip
les
o
f
s
elf
-
o
r
g
an
izatio
n
a
n
d
co
n
tr
o
l.
B
y
lev
er
ag
in
g
th
ese
p
r
i
n
cip
les,
ADACO
p
r
o
v
id
es
a
u
n
if
ied
ap
p
r
o
ac
h
to
b
o
th
th
e
g
en
er
atio
n
o
f
s
tab
le
o
s
cillatio
n
s
an
d
t
h
e
s
u
p
p
r
ess
io
n
o
f
u
n
w
an
ted
d
is
tu
r
b
a
n
ce
s
.
T
h
e
m
eth
o
d
h
as
d
e
m
o
n
s
tr
ate
d
s
ig
n
if
ican
t
ad
v
a
n
tag
es
in
ter
m
s
o
f
en
er
g
y
e
f
f
icien
cy
an
d
r
o
b
u
s
tn
ess
,
m
ak
in
g
it
ap
p
licab
le
to
a
wid
e
r
a
n
g
e
o
f
s
cien
tific
an
d
tech
n
o
l
o
g
ical
f
i
eld
s
.
C
o
m
p
ar
ed
to
class
ical
m
eth
o
d
s
an
d
th
e
ADA
C
ap
p
r
o
ac
h
,
th
e
ADAC
O
m
eth
o
d
o
f
f
er
s
s
ev
er
al
d
is
tin
ct
b
en
ef
its
.
I
t
p
r
o
v
id
es
a
clea
r
er
p
h
y
s
ical
in
ter
p
r
etatio
n
o
f
th
e
o
p
tim
ality
cr
iter
ia,
m
ak
in
g
it
m
o
r
e
in
tu
itiv
e
f
o
r
p
r
ac
tical
ap
p
licatio
n
s
.
A
d
d
itio
n
ally
,
th
e
ADACO
m
eth
o
d
is
f
u
lly
an
al
y
tical,
allo
win
g
f
o
r
p
r
ec
is
e
an
d
ef
f
icien
t
s
y
n
th
esis
o
f
co
n
tr
o
l
laws,
ev
en
f
o
r
u
n
s
tab
le
n
o
n
lin
ea
r
o
b
j
ec
ts
.
T
h
is
an
aly
tical
n
atu
r
e
d
is
tin
g
u
is
h
es
it
f
r
o
m
o
th
er
m
eth
o
d
s
,
s
u
ch
as
th
e
L
eto
v
-
Kalm
an
an
d
A.
A.
Kr
aso
v
s
k
y
’
s
m
eth
o
d
s
,
wh
ich
o
f
ten
r
eq
u
ir
e
n
u
m
er
ical
ap
p
r
o
ac
h
es a
n
d
h
av
e
lim
itatio
n
s
in
ter
m
s
o
f
ap
p
licab
ilit
y
an
d
p
h
y
s
ical
in
ter
p
r
etatio
n
[
4
]
.
T
h
e
ADACO
m
eth
o
d
r
ep
r
esen
ts
a
s
ig
n
if
ican
t
ad
v
an
ce
m
e
n
t
in
th
e
f
ield
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l,
b
u
ild
in
g
o
n
th
e
s
tr
en
g
th
s
o
f
class
ical
m
eth
o
d
s
an
d
s
y
n
er
g
etic
co
n
tr
o
l
th
e
o
r
y
.
I
ts
ab
ilit
y
to
in
teg
r
ate
en
er
g
y
in
v
a
r
ian
ts
an
d
f
ir
s
t in
teg
r
als o
f
m
o
tio
n
in
to
th
e
s
y
n
th
e
s
is
o
f
co
n
tr
o
l la
ws o
f
f
er
s
a
r
o
b
u
s
t f
r
am
ewo
r
k
f
o
r
th
e
en
er
g
y
-
ef
f
icien
t
co
n
tr
o
l
o
f
a
wid
e
r
an
g
e
o
f
n
o
n
lin
ea
r
s
y
s
tem
s
.
As
th
e
f
ield
co
n
tin
u
es
to
ev
o
lv
e,
th
e
ADACO
m
eth
o
d
s
tan
d
s
o
u
t
a
s
a
p
r
o
m
is
in
g
ap
p
r
o
ac
h
f
o
r
a
d
d
r
ess
in
g
th
e
co
m
p
lex
ch
allen
g
es
ass
o
ciate
d
with
n
o
n
lin
ea
r
o
s
cillatio
n
s
in
v
ar
io
u
s
s
cien
tific
an
d
tech
n
o
l
o
g
ical
d
o
m
ain
s
.
2.
P
RO
B
L
E
M
ST
A
T
E
M
E
NT
I
n
s
y
n
er
g
etic
co
n
tr
o
l
th
eo
r
y
,
wh
en
s
y
n
th
esizin
g
o
b
jecti
v
e
co
n
tr
o
l
laws
f
o
r
n
o
n
lin
e
ar
m
u
lti
-
d
im
en
s
io
n
al
an
d
m
u
lti
-
co
n
n
e
cted
o
b
jects,
o
n
e
o
f
th
e
k
ey
p
r
o
b
lem
s
is
th
e
s
elec
tio
n
a
n
d
ju
s
tific
atio
n
o
f
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
Op
tima
l c
o
n
tr
o
l o
f th
e
d
y
n
a
mi
cs o
f n
o
n
lin
ea
r
o
s
cilla
tin
g
s
ystems
u
s
in
g
…
(
S
id
d
iko
v
I
s
o
mid
d
in
X
a
kimo
vich
)
6273
in
v
ar
ian
t
m
an
if
o
ld
s
,
wh
ich
a
r
e
th
e
tar
g
et
attr
ac
to
r
s
o
f
t
h
e
s
y
s
tem
(
d
en
o
ted
as
=
0
)
[
1
]
–
[
5
]
.
T
h
is
is
an
im
p
o
r
tan
t ta
s
k
th
at
is
u
s
u
ally
s
o
lv
ed
d
ep
e
n
d
in
g
o
n
th
e
s
p
ec
if
ic
tech
n
o
lo
g
ical
r
eq
u
i
r
em
en
ts
ass
o
ciate
d
with
th
e
co
n
tr
o
l
o
f
o
b
jects
o
f
a
ce
r
tain
n
atu
r
e,
with
in
th
e
f
r
am
ewo
r
k
o
f
SC
T
[
6
]
–
[
8
]
.
Du
e
t
o
th
e
c
o
n
s
id
er
ab
le
v
a
r
iety
o
f
co
n
tr
o
l
task
s
o
f
v
ar
io
u
s
n
o
n
lin
ea
r
o
b
jects,
th
e
ch
o
ice
an
d
ju
s
tific
atio
n
o
f
in
v
a
r
ian
t
m
an
if
o
l
d
s
h
as
a
n
in
d
ep
en
d
en
t
ch
ar
ac
ter
with
in
th
e
f
r
am
ewo
r
k
o
f
SC
T
[
9
]
,
a
n
d
r
eq
u
i
r
es
a
d
ee
p
u
n
d
er
s
tan
d
in
g
o
f
th
e
c
o
n
tr
o
l
p
r
o
ce
s
s
es
o
f
th
e
co
r
r
esp
o
n
d
in
g
o
b
jects
in
v
ar
io
u
s
f
ield
s
,
s
u
ch
as
elec
tr
ic
p
o
wer
en
g
in
ee
r
i
n
g
,
elec
tr
o
m
ec
h
an
ics,
r
o
b
o
tics
,
av
iatio
n
,
astro
n
au
tics
an
d
o
th
er
s
.
I
n
o
th
er
wo
r
d
s
,
th
e
well
-
k
n
o
wn
SC
T
[
1
0
]
lack
s
a
u
n
if
ied
f
o
r
m
al
p
r
o
ce
d
u
r
e
f
o
r
s
elec
tin
g
tech
n
o
lo
g
ical
in
v
ar
ian
t
m
an
if
o
l
d
s
.
Ho
wev
er
,
it
s
h
o
u
ld
b
e
n
o
ted
th
at
in
th
e
d
y
n
a
m
ics
o
f
b
eh
a
v
io
r
o
f
a
wid
e
class
o
f
tec
h
n
ical
o
b
jects
th
er
e
ar
e
co
m
m
o
n
b
asic
p
r
o
ce
s
s
es
th
at
d
eter
m
in
e
th
e
ess
en
ce
o
f
t
h
e
m
ain
co
n
tr
o
l
p
r
o
b
le
m
-
n
o
n
lin
ea
r
o
s
cillato
r
y
p
r
o
ce
s
s
es.
T
h
e
p
r
o
b
lem
o
f
co
n
tr
o
llin
g
s
u
c
h
o
s
cillatio
n
s
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
d
ir
ec
tio
n
s
in
m
o
d
er
n
o
s
cillatio
n
th
eo
r
y
an
d
n
o
n
lin
ea
r
c
o
n
tr
o
l th
eo
r
y
[
1
1
]
–
[
1
3
]
.
T
wo
m
ain
p
r
o
b
lem
s
ca
n
b
e
d
is
tin
g
u
is
h
ed
in
th
e
co
n
tr
o
l
th
e
o
r
y
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
s
.
First,
it
is
th
e
p
r
o
b
lem
o
f
cr
ea
tin
g
s
tab
le
n
o
n
lin
ea
r
o
s
cillatio
n
s
,
i.e
.
,
th
e
p
r
o
b
lem
o
f
d
ev
elo
p
in
g
a
n
ew
class
o
f
g
en
er
ato
r
s
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
s
th
at
o
u
tp
er
f
o
r
m
a
n
d
g
en
er
alize
th
e
k
n
o
wn
g
en
er
at
o
r
s
,
s
u
ch
as
th
o
s
e
o
f
v
a
n
d
er
Po
l,
R
ay
leig
h
,
Po
in
ca
r
e
an
d
o
th
er
s
.
T
h
ese
g
en
er
ato
r
s
ar
e
wid
ely
u
s
ed
in
v
ar
io
u
s
f
ield
s
o
f
s
cien
ce
an
d
en
g
in
ee
r
in
g
,
s
u
ch
as
au
to
o
s
cillatio
n
th
eo
r
y
[
1
]
,
r
ad
io
en
g
in
ee
r
in
g
,
el
ec
tr
o
m
ec
h
an
ics
an
d
o
th
er
s
.
T
h
e
ess
en
ce
o
f
th
e
p
r
o
b
lem
is
to
cr
ea
te
g
en
er
at
o
r
s
o
f
r
eg
u
lar
o
s
cillatio
n
s
with
ce
r
tain
p
r
o
p
er
ties
.
Seco
n
d
ly
,
i
t
is
th
e
p
r
o
b
lem
o
f
s
u
p
p
r
ess
in
g
ex
ter
n
al
u
n
wan
te
d
o
s
cillatio
n
s
an
d
p
r
o
v
id
i
n
g
in
th
e
s
y
s
tem
eith
er
d
esire
d
o
s
cillatio
n
s
o
r
th
eir
co
m
p
lete
o
r
p
ar
tial
s
u
p
p
r
ess
io
n
.
T
h
is
p
r
o
b
lem
is
a
k
ey
c
h
allen
g
e
in
t
h
e
co
n
t
r
o
l
o
f
elec
tr
o
m
ec
h
an
ics,
av
iatio
n
,
v
eh
icles a
n
d
o
th
e
r
f
ield
s
.
T
h
e
ADACO
m
eth
o
d
co
n
s
id
e
r
s
th
ese
two
p
r
o
b
lem
s
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l
f
r
o
m
a
u
n
if
ied
th
eo
r
etica
l
p
o
s
itio
n
.
I
t
is
b
ase
d
o
n
th
e
g
en
er
al
p
r
o
p
er
ties
o
f
o
s
cillato
r
y
s
y
s
tem
s
o
f
an
y
n
at
u
r
e.
I
n
p
a
r
ticu
lar
,
it
is
s
h
o
wn
in
[
8
]
th
at
en
e
r
g
y
in
v
ar
ian
ts
,
n
am
ely
,
th
e
e
n
er
g
y
o
f
th
e
s
y
n
th
esized
s
y
s
tem
an
d
i
ts
f
ir
s
t
in
teg
r
als
o
f
m
o
tio
n
,
a
r
e
g
en
er
al
p
r
o
p
er
ti
es
o
f
s
u
ch
s
y
s
tem
s
.
C
o
n
s
eq
u
en
tly
,
f
o
r
th
e
s
y
n
t
h
esis
o
f
co
n
tr
o
l
s
y
s
tem
s
f
o
r
n
o
n
lin
ea
r
o
s
cillatio
n
s
,
it
is
n
ec
ess
ar
y
to
d
e
v
elo
p
a
n
ew
m
eth
o
d
b
ased
o
n
t
h
e
b
asic
c
o
n
ce
p
ts
o
f
a
n
aly
tical
m
ec
h
an
ics
[
1
4
]
,
[
1
5
]
.
I
n
o
u
r
o
p
in
io
n
,
th
e
ADACO
m
eth
o
d
r
e
p
r
esen
ts
s
u
ch
a
m
eth
o
d
an
d
o
f
f
er
s
a
n
ew
ap
p
r
o
ac
h
in
th
e
c
o
n
tr
o
l th
eo
r
y
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
s
.
I
n
o
r
d
er
t
o
d
e
v
elo
p
a
n
ew
a
p
p
r
o
ac
h
to
s
o
lv
i
n
g
th
e
p
r
o
b
l
em
s
o
f
g
e
n
er
atio
n
an
d
s
u
p
p
r
ess
io
n
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
s
,
it
is
o
b
v
io
u
s
th
at
th
e
ADAC
m
eth
o
d
b
ased
o
n
th
e
id
eo
lo
g
y
o
f
s
y
s
tem
th
eo
r
etic
co
n
tr
o
l
an
d
s
u
cc
ess
f
u
lly
ap
p
lied
i
n
v
a
r
io
u
s
f
ield
s
o
f
en
g
in
ee
r
in
g
s
h
o
u
ld
b
e
m
o
d
if
ied
o
n
th
e
b
asis
o
f
a
g
en
er
al
class
o
f
in
v
ar
ian
t
m
an
if
o
ld
s
[
1
6
]
–
[
1
8
]
.
T
h
is
class
o
f
m
an
if
o
ld
s
in
cl
u
d
es
th
e
e
n
er
g
y
o
f
t
h
e
o
s
cilla
tin
g
s
y
s
tem
,
wh
ich
ca
n
b
e
s
y
n
th
esized
,
a
n
d
th
e
f
ir
s
t
in
teg
r
als
o
f
m
o
tio
n
o
f
th
i
s
s
y
s
tem
.
T
h
at
is
wh
y
we
p
r
o
p
o
s
ed
a
m
o
d
if
ied
m
eth
o
d
ca
lled
ADACO a
cc
o
r
d
in
g
to
t
h
e
an
alo
g
y
to
t
h
e
ADAC m
eth
o
d
.
3.
M
E
T
H
O
D
B
ased
o
n
th
e
p
r
in
cip
le
o
f
p
h
a
s
e
s
p
ac
e
ex
p
an
s
io
n
-
co
m
p
r
ess
io
n
f
r
o
m
s
y
n
e
r
g
etic
co
n
tr
o
l
th
eo
r
y
,
th
is
p
ap
er
d
ev
el
o
p
s
a
n
ew
m
eth
o
d
f
o
r
th
e
an
aly
tical
d
esig
n
o
f
a
g
g
r
eg
ate
co
n
tr
o
ller
s
o
f
o
s
cillatio
n
-
ADACO.
T
h
i
s
m
eth
o
d
is
b
ased
o
n
th
e
b
asic
id
ea
o
f
th
e
well
-
k
n
o
wn
ADA
C
O
m
eth
o
d
,
wh
ich
in
tr
o
d
u
ce
s
attr
ac
tin
g
in
v
ar
ia
n
t
m
an
if
o
ld
s
(
1
,
…
,
)
=
0
,
o
n
wh
ich
th
e
n
at
u
r
al
p
r
o
p
e
r
ties
o
f
th
e
o
b
ject
(
e
n
er
g
y
,
m
ec
h
an
ical,
an
d
th
er
m
al
)
an
d
th
e
r
e
q
u
ir
em
en
ts
o
f
th
e
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l
p
r
o
b
lem
ar
e
co
n
s
is
ten
t.
Fro
m
th
e
p
o
in
t
o
f
v
iew
o
f
co
n
tr
o
l
th
e
o
r
y
,
th
e
p
ec
u
liar
ity
o
f
th
e
s
y
n
e
r
g
etic
s
y
n
th
esis
o
f
o
s
cillatin
g
s
y
s
tem
s
is
th
e
way
o
f
g
en
e
r
atin
g
a
s
et
o
f
f
ee
d
b
ac
k
s
-
co
n
tr
o
l
laws
(
)
=
(
)
,
wh
ich
allo
w
th
e
s
y
s
tem
to
f
ir
s
t
m
o
v
e
f
r
o
m
an
a
r
b
itra
r
y
in
itia
l
s
tate
n
ea
r
th
e
m
an
if
o
ld
s
(
)
=
0
,
an
d
th
e
n
en
s
u
r
e
asy
m
p
to
tically
s
tab
l
e
m
o
tio
n
o
f
t
h
e
s
y
s
tem
alo
n
g
th
ese
m
an
if
o
ld
s
u
n
til
th
e
tar
g
et
o
s
c
illato
r
y
attr
ac
to
r
s
ar
e
r
ea
ch
ed
.
At
th
ese
attr
ac
to
r
s
,
th
e
f
u
lf
ilm
en
t
o
f
s
p
ec
if
ied
r
eq
u
ir
em
e
n
ts
f
o
r
th
e
s
y
n
th
esis
ed
s
y
s
tem
,
s
u
ch
as o
s
cillatio
n
g
en
er
atio
n
o
r
s
u
p
p
r
ess
io
n
,
is
g
u
ar
an
teed
.
T
h
e
b
asic
p
r
in
cip
les
o
f
th
e
A
DACO
m
eth
o
d
ap
p
lied
i
n
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l
p
r
o
b
lem
s
ar
e
b
ased
o
n
th
e
c
o
n
ce
p
t
u
al
f
o
u
n
d
atio
n
s
o
f
s
y
s
tem
th
eo
r
etica
l
co
n
tr
o
l
[
1
]
–
[
5
]
an
d
lead
to
th
e
f
o
llo
win
g
s
tag
es.
At
th
e
f
ir
s
t
s
tag
e,
th
e
in
itial
d
if
f
er
en
tial
eq
u
atio
n
s
o
f
th
e
o
b
ject
ar
e
wr
itten
d
o
wn
,
wh
ich
ca
n
b
e
r
ep
r
esen
ted
,
f
o
r
ex
am
p
le,
in
t
h
e
f
o
r
m
(
1
)
:
̇
(
)
=
(
1
,
⋯
,
)
+
(
)
,
=
1
,
2
,
⋯
,
−
1
,
≤
,
̇
+
1
(
)
=
+
1
(
1
,
⋯
,
)
+
+
1
+
+
1
(
)
,
̇
(
)
=
(
1
,
⋯
,
)
+
+
(
)
,
(
1
)
wh
er
e
1
,
…
,
ar
e
co
o
r
d
in
ates
o
f
th
e
o
b
ject
s
tate;
1
(
)
,
…
,
(
)
ar
e
ex
ter
n
al
p
e
r
tu
r
b
in
g
in
f
lu
en
ce
s
;
an
d
u
₁,
+
1
,
…
,
ar
e
co
n
tr
o
l sig
n
als.
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.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
2
7
1
-
6
2
7
8
6274
At
th
e
s
ec
o
n
d
s
tag
e,
ad
d
itio
n
al
eq
u
atio
n
s
ar
e
a
d
d
ed
to
th
e
s
y
s
tem
(
1
)
,
wh
ich
tak
e
i
n
to
ac
co
u
n
t
in
ter
n
al
an
d
e
x
ter
n
al
p
er
tu
r
b
atio
n
s
:
̇
(
)
=
(
1
,
⋯
,
,
1
,
⋯
,
)
,
=
1
,
⋯
,
(
2)
I
t
s
h
o
u
ld
b
e
n
o
te
d
th
at
tw
o
s
e
p
ar
ate
p
r
o
b
le
m
s
a
r
is
e
i
n
th
e
f
o
r
m
u
lat
io
n
o
f
(
2
)
.
Fi
r
s
t
ly
,
i
t
is
t
h
e
tas
k
o
f
d
es
cr
ib
in
g
r
e
al
p
e
r
t
u
r
b
ati
o
n
s
as
p
ar
tia
l
s
o
lu
t
io
n
s
o
f
a
d
d
it
io
n
al
d
i
f
f
er
e
n
ti
al
e
q
u
a
ti
o
n
s
.
S
ec
o
n
d
,
i
t
is
th
e
task
o
f
esta
b
l
is
h
in
g
r
el
ati
o
n
s
b
e
twe
e
n
t
h
e
e
q
u
at
io
n
s
o
f
th
e
i
n
i
tia
l
o
b
je
ct
a
n
d
t
h
e
e
q
u
ati
o
n
s
d
esc
r
i
b
i
n
g
t
h
e
d
is
t
u
r
b
an
ce
s
.
A
t
t
h
e
t
h
i
r
d
s
tag
e,
a
f
t
er
d
ef
in
in
g
th
e
co
u
p
lin
g
eq
u
ati
o
n
s
,
we
o
b
t
ai
n
a
n
ex
t
e
n
d
e
d
s
y
s
te
m
o
f
d
i
f
f
er
en
ti
al
e
q
u
a
ti
o
n
s
.
T
h
is
s
y
s
te
m
r
ep
r
ese
n
ts
a
m
o
d
el
f
o
r
th
e
s
y
n
t
h
esis
o
f
t
h
e
c
o
n
t
r
o
l s
y
s
tem
o
f
n
o
n
l
in
ea
r
o
s
cill
ati
o
n
s
.
̇
(
)
=
(
1
,
⋯
,
,
1
,
⋯
,
)
,
=
1
,
⋯
,
;
̇
(
)
=
(
1
,
⋯
,
)
+
,
=
+
1
,
⋯
,
−
1
;
̇
+
1
(
)
=
+
1
(
1
,
⋯
,
)
+
+
1
+
+
1
;
̇
(
)
=
(
1
,
⋯
,
)
+
+
.
(
3
)
T
h
e
co
n
s
tr
u
cted
ex
ten
d
ed
m
o
d
el
(
3
)
allo
ws
u
s
to
f
o
r
m
u
l
ate
th
e
p
r
o
b
lem
o
f
s
y
n
th
esis
o
f
co
n
tr
o
l
laws
-
o
s
cillatio
n
r
eg
u
lato
r
s
.
T
h
is
p
r
o
b
lem
c
o
n
s
is
ts
in
f
in
d
in
g
th
e
co
n
tr
o
l v
ec
to
r
(
1
,
⋯
,
)
in
th
e
f
o
r
m
o
f
a
s
et
o
f
n
o
n
lin
ea
r
f
ee
d
b
ac
k
s
th
at
will
en
s
u
r
e
th
e
tr
an
s
itio
n
o
f
th
e
i
m
ag
e
p
o
in
t
o
f
th
e
e
x
ten
d
e
d
s
y
s
tem
(
3
)
f
r
o
m
an
ar
b
itra
r
y
in
itial st
ate
at
th
e
b
eg
in
n
in
g
to
th
e
tar
g
et
e
n
er
g
y
m
a
n
if
o
ld
s
.
(
1
,
⋯
,
,
1
,
⋯
,
)
,
=
1
,
2
,
⋯
,
,
(
4
)
T
h
en
,
b
y
m
o
v
in
g
alo
n
g
th
e
in
ter
s
ec
tio
n
o
f
m
an
if
o
ld
s
=
0
(
4
)
,
a
g
iv
en
f
in
al
s
tate,
th
e
tar
g
e
t
o
s
cillato
r
y
attr
ac
to
r
,
is
r
ea
ch
ed
,
wh
ich
p
r
o
v
id
es g
en
e
r
atio
n
o
r
s
u
p
p
r
ess
io
n
o
f
o
s
cillatio
n
s
.
I
t
s
h
o
u
ld
b
e
n
o
te
d
th
at
th
e
o
p
tim
al
v
alu
e
o
f
th
e
ac
co
m
p
an
y
in
g
o
p
tim
izin
g
f
u
n
ctio
n
al
(
AOF)
is
ac
h
iev
ed
o
n
th
e
tr
ajec
to
r
ies o
f
m
o
tio
n
o
f
th
e
clo
s
ed
o
s
cillato
r
y
s
y
s
tem
,
wh
ich
ca
n
h
av
e,
f
o
r
ex
am
p
le,
th
e
f
o
r
m
(
5
)
.
Σ
=
∫
[
∑
2
=
1
(
)
+
∑
2
2
(
)
=
1
]
∞
0
.
(
5
)
Acc
o
r
d
in
g
to
(
5
)
,
t
h
e
m
o
tio
n
o
f
th
e
im
ag
e
p
o
in
t
o
f
th
e
s
y
n
t
h
esized
s
y
s
tem
s
h
o
u
l
d
c
o
r
r
es
p
o
n
d
to
a
s
y
s
tem
o
f
f
u
n
ctio
n
al
e
q
u
atio
n
s
th
at
d
ep
e
n
d
o
n
m
ac
r
o
v
ar
iab
les
.
̇
(
)
+
(
)
=
0
,
=
1
,
2
,
⋯
,
.
(
6
)
E
q
u
atio
n
s
(
6
)
a
r
e
E
u
ler
-
L
ag
r
a
n
g
e
eq
u
atio
n
s
th
at
o
p
tim
ize
AOF
(
5
)
an
d
r
e
f
lect
th
e
i
n
teg
r
al
p
r
o
p
er
ties
o
f
th
e
s
y
n
th
esized
s
y
s
tem
s
.
B
ased
o
n
(
5
)
,
v
ar
io
u
s
s
y
s
tem
q
u
ality
cr
i
ter
ia
ca
n
b
e
co
n
s
tr
u
cted
[
1
9
]
–
[
2
3
]
.
I
t
is
im
p
o
r
tan
t
to
n
o
te
th
at
(
6
)
ar
e
in
v
ar
ian
t
r
elatio
n
s
wid
ely
u
s
ed
in
an
aly
tical
m
ec
h
an
ics.
I
n
[
1
0
]
,
a
d
ee
p
co
n
n
ec
tio
n
b
etwe
en
th
e
i
n
v
ar
ian
t
r
elatio
n
s
o
f
an
aly
tical
m
ec
h
an
ics
an
d
s
y
n
er
g
etic
m
e
th
o
d
s
o
f
n
o
n
lin
ea
r
s
y
s
tem
s
y
n
th
esis
was
d
em
o
n
s
tr
ated
,
in
clu
d
in
g
ADAC
an
d
ADACO
m
eth
o
d
s
,
wh
ich
ar
e
b
ased
o
n
th
e
s
y
n
er
g
etic
ap
p
r
o
ac
h
to
th
e
s
y
n
th
esis
o
f
co
n
t
r
o
l
s
y
s
tem
s
f
o
r
o
b
jects
with
d
if
f
er
e
n
t
ch
a
r
ac
ter
i
s
tics
.
I
n
th
e
th
e
o
r
y
o
f
an
aly
tical
d
esig
n
o
f
o
p
tim
a
l
co
n
tr
o
ller
s
,
wh
ich
h
as
g
ain
e
d
co
n
s
id
er
a
b
le
d
ev
elo
p
m
en
t
i
n
th
e
2
0
th
ce
n
tu
r
y
,
th
e
m
ain
m
et
h
o
d
s
o
f
r
e
g
u
lato
r
s
y
n
th
esis
ar
e
two
a
p
p
r
o
ac
h
es.
First,
it
is
th
e
L
eto
v
-
Kal
m
an
m
eth
o
d
,
w
h
er
e
q
u
ad
r
atic
q
u
ality
c
r
iter
ia
an
d
,
as
a
r
u
le,
lin
ea
r
m
o
d
els
o
f
o
b
j
ec
ts
ar
e
u
s
ed
f
o
r
o
p
tim
izatio
n
[
5
]
,
[
1
4
]
.
Seco
n
d
,
it
is
th
e
m
eth
o
d
o
f
Kr
aso
v
s
k
y
[
1
5
]
,
w
h
er
e
t
h
e
g
en
er
alize
d
wo
r
k
f
u
n
ctio
n
al
(
GW
F)
an
d
n
o
n
li
n
ea
r
o
b
ject
m
o
d
els
ar
e
u
s
ed
.
T
o
d
ate,
th
e
s
y
n
th
esis
o
f
th
e
o
p
tim
al
r
eg
u
lato
r
b
y
th
e
L
et
o
v
-
Kalm
an
m
eth
o
d
f
o
r
lin
ea
r
o
b
jects
h
as
m
ad
e
s
ig
n
if
ican
t
p
r
o
g
r
ess
d
u
e
to
n
u
m
er
ical
m
eth
o
d
s
.
Ho
wev
er
,
in
o
u
r
o
p
in
io
n
,
th
is
m
eth
o
d
h
as
s
o
m
e
d
is
ad
v
an
tag
es,
s
u
ch
as
d
if
f
ic
u
lties
in
th
e
r
ea
s
o
n
ab
le
ch
o
ic
e
o
f
weig
h
t
co
e
f
f
icien
ts
f
o
r
q
u
ad
r
atic
o
p
tim
ality
cr
iter
ia
an
d
th
eir
p
h
y
s
ical
ju
s
tific
atio
n
.
I
n
A.
A.
Kr
aso
v
s
k
y
’
s
m
eth
o
d
,
t
h
e
o
p
tim
izin
g
f
u
n
ctio
n
al
is
r
ep
r
esen
te
d
as
a
q
u
ad
r
atic
f
o
r
m
o
f
c
o
o
r
d
in
ates,
wh
ich
r
ef
lects
th
e
“
g
e
n
er
alize
d
wo
r
k
”
o
f
th
e
s
y
s
tem
b
ein
g
s
y
n
th
esized
.
T
h
is
m
eth
o
d
h
as
a
clea
r
er
p
h
y
s
ical
ju
s
t
if
icatio
n
co
m
p
ar
ed
to
th
e
L
eto
v
-
Kalm
an
m
eth
o
d
.
Ho
wev
er
,
n
u
m
er
ical
m
eth
o
d
s
ar
e
also
r
e
q
u
ir
e
d
to
s
y
n
th
esize
th
e
o
p
tim
al
r
e
g
u
lat
o
r
u
s
in
g
A.
A.
Kr
aso
v
s
k
y
’
s
m
eth
o
d
.
I
n
ad
d
itio
n
,
Kr
aso
v
s
k
y
’
s
m
eth
o
d
is
ap
p
lie
d
m
ain
l
y
to
s
tab
le
n
o
n
lin
ea
r
o
b
jects,
an
d
th
e
p
r
o
c
ed
u
r
e
f
o
r
s
y
n
th
esizin
g
c
o
n
tr
o
l
laws
i
s
n
o
t
an
aly
tical
in
th
e
m
ath
em
atica
l
s
en
s
e.
Ho
wev
er
,
it
s
h
o
u
ld
b
e
n
o
ted
th
at
Kr
aso
v
s
k
y
’
s
m
eth
o
d
is
a
s
ig
n
if
ican
t
p
r
o
g
r
ess
in
th
e
d
e
v
elo
p
m
en
t
o
f
o
p
tim
al
co
n
tr
o
l
m
eth
o
d
s
an
d
h
as
b
ee
n
s
u
cc
ess
f
u
lly
ap
p
lied
to
s
o
lv
e
im
p
o
r
tan
t
p
r
o
b
lem
s
o
f
ai
r
cr
af
t c
o
n
t
r
o
l
[
2
4
]
.
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
Op
tima
l c
o
n
tr
o
l o
f th
e
d
y
n
a
mi
cs o
f n
o
n
lin
ea
r
o
s
cilla
tin
g
s
ystems
u
s
in
g
…
(
S
id
d
iko
v
I
s
o
mid
d
in
X
a
kimo
vich
)
6275
T
h
e
ADACO
m
eth
o
d
,
in
co
m
p
ar
is
o
n
with
th
e
m
eth
o
d
o
f
Kr
aso
v
s
k
y
[
1
5
]
,
h
as
a
clea
r
er
p
h
y
s
ical
co
n
ten
t
with
r
esp
ec
t
to
th
e
cr
i
ter
ia
o
f
o
p
tim
al
co
n
tr
o
l.
I
n
t
h
e
ADACO
m
eth
o
d
,
th
e
o
p
tim
ality
cr
iter
ia
ca
n
b
e
r
ep
r
esen
ted
,
f
o
r
ex
a
m
p
le,
in
t
h
e
f
o
r
m
o
f
(
5
)
,
wh
er
e
(
)
r
ep
r
ese
n
ts
th
e
en
er
g
y
o
f
th
e
s
y
n
t
h
esis
ed
o
s
cillato
r
y
s
y
s
tem
,
an
d
th
e
co
m
p
o
n
e
n
t
̇
(
)
r
ef
lects
its
p
o
wer
.
T
h
u
s
,
th
e
o
p
tim
ality
cr
iter
io
n
in
th
e
A
DACO
m
eth
o
d
m
o
r
e
f
u
lly
r
ef
lects
th
e
s
p
ec
if
i
c
p
h
y
s
ical
co
n
ten
t
o
f
th
e
p
r
o
b
lem
s
o
f
s
y
n
th
esis
o
f
co
n
tr
o
l
l
aws
f
o
r
o
s
cillatin
g
s
y
s
tem
s
th
an
th
e
m
eth
o
d
o
f
A.
A.
Kr
aso
v
s
k
y
.
T
h
e
ADACO
m
eth
o
d
is
also
ap
p
licab
le
t
o
u
n
s
tab
le
n
o
n
lin
ea
r
o
b
jects,
an
d
th
e
p
r
o
ce
d
u
r
e
o
f
s
y
n
th
esis
o
f
co
n
tr
o
l
laws
in
th
is
m
eth
o
d
is
f
u
lly
an
aly
tical
i
n
th
e
m
ath
em
atica
l
s
en
s
e.
T
h
u
s
,
th
e
ADACO
m
eth
o
d
h
as
a
clea
r
p
h
y
s
ical
co
n
t
en
t
an
d
is
ap
p
licab
le
to
th
e
p
r
o
b
lem
s
o
f
o
p
tim
al
co
n
tr
o
l o
f
n
o
n
lin
ea
r
o
s
cillatio
n
s
.
L
et
u
s
n
o
w
co
n
s
id
er
th
e
p
r
o
ce
d
u
r
e
o
f
ap
p
ly
i
n
g
th
e
ADACO
m
eth
o
d
to
s
o
lv
e
th
e
p
r
o
b
lem
o
f
s
y
n
th
esis
o
f
co
n
tr
o
l
s
y
s
tem
s
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
s
.
T
h
is
m
eth
o
d
is
b
ased
o
n
th
e
s
y
n
er
g
etic
ap
p
r
o
ac
h
an
d
th
e
co
n
ce
p
t o
f
u
n
ity
o
f
s
elf
-
o
r
g
an
izatio
n
an
d
co
n
tr
o
l p
r
o
ce
s
s
es (
C
U
SOC
P).
Acc
o
r
d
in
g
to
th
is
ap
p
r
o
ac
h
,
u
n
d
er
th
e
ac
tio
n
o
f
“e
x
ter
n
al”
co
n
t
r
o
ls
+
1
,
⋯
,
th
e
p
o
i
n
t
r
ep
r
esen
tin
g
t
h
e
ex
ten
d
ed
s
y
s
tem
(
2
)
f
alls
in
th
e
n
eig
h
b
o
u
r
h
o
o
d
o
f
th
e
in
te
r
s
ec
tio
n
o
f
en
er
g
y
m
an
if
o
ld
s
=
0
.
T
h
e
m
o
tio
n
alo
n
g
th
ese
m
an
if
o
ld
s
is
d
escr
ib
ed
b
y
d
ec
o
m
p
o
s
ed
e
q
u
atio
n
s
o
f
“in
ter
n
al”
d
y
n
a
m
ics
.
̇
(
)
=
(
1
,
⋯
,
,
+
1
,
⋯
,
,
1
,
⋯
,
−
1
)
;
̇
(
)
=
(
1
,
⋯
,
−
1
,
+
1
,
⋯
,
)
;
=
1
,
⋯
,
;
=
+
1
,
⋯
,
−
1
.
(
7
)
wh
er
e
+
1
,
⋯
,
-
“in
ter
n
al”
c
o
n
tr
o
ls
.
T
h
en
,
u
s
in
g
th
e
d
ec
o
m
p
o
s
ed
s
y
s
tem
(
7
)
,
th
e
s
y
n
th
esis
o
f
“i
n
ter
n
al”
co
n
tr
o
ls
+
1
,
⋯
,
,
wh
ich
p
r
o
v
id
e
th
e
d
esire
d
d
y
n
am
ic
p
r
o
p
er
ties
wh
en
th
e
im
ag
in
g
p
o
in
t
m
o
v
es
al
o
n
g
th
e
en
er
g
y
m
an
if
o
l
d
s
=
0
,
is
ca
r
r
ied
o
u
t.
T
h
e
s
y
n
th
esis
o
f
th
e
c
o
n
tr
o
ls
+
1
,
⋯
,
is
a
s
ep
ar
ate
in
ter
n
a
l
co
n
tr
o
l
p
r
o
b
lem
f
o
r
s
u
b
o
b
ject
(
7
)
.
A
s
eq
u
en
tially
p
ar
allel
s
et
o
f
en
e
r
g
y
in
v
ar
ia
n
ts
-
o
s
cillato
r
y
attr
ac
to
r
s
-
is
ap
p
lied
ac
co
r
d
in
g
to
th
e
C
USOC
P
an
d
th
e
ADA
C
O
m
et
h
o
d
[
1
]
,
[
2
]
,
[
8
]
.
Acc
o
r
d
in
g
to
th
e
p
r
in
cip
le
o
f
co
n
s
er
v
atio
n
o
f
co
n
t
r
o
ls
[
2
5
]
,
th
e
“in
ter
n
al”
c
o
n
tr
o
ls
h
av
e
co
n
s
tan
t
d
im
en
s
io
n
ality
≈
,
w
h
ich
co
r
r
esp
o
n
d
s
to
th
e
d
im
en
s
io
n
ality
o
f
th
e
co
n
tr
o
l
v
ec
to
r
.
T
h
e
co
n
tr
o
ls
af
f
ec
t
th
e
s
u
b
o
b
ject
(
7
)
b
y
d
ec
o
m
p
o
s
in
g
it
in
to
th
e
n
ex
t
s
u
b
o
b
ject
with
th
eir
in
ter
n
al
co
n
tr
o
ls
.
T
h
is
p
r
o
ce
s
s
o
f
s
u
cc
ess
iv
e
d
ec
o
m
p
o
s
itio
n
co
n
tin
u
es u
n
til th
e
im
ag
in
g
p
o
in
t r
ea
ch
es th
e
s
elec
ted
f
in
is
h
i
n
g
o
s
cillato
r
y
attr
ac
to
r
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
p
r
o
ce
d
u
r
e
r
esu
lts
in
th
e
id
en
tific
atio
n
o
f
in
ter
r
elate
d
“
in
ter
n
al”
co
n
tr
o
ls
,
k
n
o
win
g
wh
ich
o
n
e
ca
n
cr
ea
te
th
e
d
esire
d
m
ac
r
o
v
ar
iab
les,
s
u
ch
as
(
8
)
.
=
1
(
+
1
−
1
)
+
⋯
+
(
,
⋯
,
)
,
=
1
,
⋯
,
.
(
8
)
C
o
n
s
eq
u
en
tly
,
b
y
u
s
in
g
f
u
n
cti
o
n
al
(
6
)
a
n
d
m
ac
r
o
v
a
r
iab
les
(
8
)
i
n
ac
co
r
d
an
ce
with
t
h
e
eq
u
atio
n
s
o
f
s
y
s
tem
(
3
)
,
th
e
“e
x
ter
n
al”
c
o
n
tr
o
l la
w
s
o
f
n
o
n
lin
e
ar
o
s
cillatio
n
s
ar
e
d
is
co
v
er
ed
[
1
]
,
[
2
]
,
[
8
]
.
+
1
=
−
+
1
(
1
,
⋯
,
)
−
+
1
−
1
;
=
−
(
1
,
⋯
,
)
−
−
(
9
)
wh
er
e
=
|
11
12
⋯
1
21
22
⋯
2
⋯
⋯
⋯
⋯
1
2
⋯
|
≠
0
,
1
=
|
1
12
⋯
1
2
22
⋯
2
⋯
⋯
⋯
⋯
2
⋯
|
≠
0
whe
n
=
0
,
=
|
11
12
⋯
1
,
−
1
21
22
⋯
2
,
−
1
⋯
⋯
⋯
⋯
1
2
⋯
,
−
1
1
2
⬚
|
≠
0
whe
n
=
0
,
T
h
e
r
elatio
n
s
p
r
esen
ted
h
e
r
e
allo
w
u
s
to
o
b
tain
s
p
ec
if
ic
v
ec
to
r
co
n
tr
o
l
laws
(
9
)
,
w
h
ich
d
ir
ec
t
th
e
im
ag
e
p
o
in
t
o
f
th
e
s
y
s
tem
in
th
e
n
eig
h
b
o
r
h
o
o
d
o
f
th
e
in
ter
s
ec
tio
n
o
f
t
h
e
tar
g
et
o
s
cillato
r
y
attr
ac
to
r
s
1
=
0
,
⋯
,
=
0
.
T
h
e
m
o
tio
n
o
f
th
e
im
ag
in
g
p
o
in
t
alo
n
g
t
h
is
in
ter
s
ec
tio
n
is
d
eter
m
in
ed
b
y
th
e
e
q
u
atio
n
s
o
f
“in
ter
n
al”
d
y
n
am
ics
(
7
)
.
T
h
e
co
n
tr
o
l
laws
(
9
)
t
o
g
eth
e
r
with
th
e
co
u
p
lin
g
eq
u
atio
n
s
co
n
s
titu
te
th
e
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.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
2
7
1
-
6
2
7
8
6276
eq
u
atio
n
s
o
f
th
e
d
y
n
am
ic
ag
g
r
eg
ated
r
eg
u
lato
r
o
f
n
o
n
lin
e
ar
o
s
cillatio
n
s
,
wh
ich
,
d
e
p
en
d
in
g
o
n
th
e
task
at
h
an
d
,
ca
n
g
e
n
er
ate
ap
p
r
o
p
r
iat
e
o
s
cillatio
n
s
w
ith
s
p
ec
if
ied
p
r
o
p
er
ties
o
r
s
u
p
p
r
ess
ex
ter
n
al
p
er
tu
r
b
atio
n
s
o
n
th
e
s
y
s
tem
,
p
r
o
v
id
in
g
th
e
d
esire
d
p
r
o
p
er
ties
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
s
.
I
t
s
h
o
u
ld
b
e
n
o
ted
t
h
at
th
e
b
as
ic
p
r
in
cip
les
o
f
th
e
ADACO
m
eth
o
d
ar
e
s
im
ilar
to
t
h
e
b
asi
c
p
r
in
ci
p
les
o
f
th
e
wid
ely
k
n
o
wn
ADAC m
eth
o
d
in
tech
n
ical
co
n
tr
o
l sy
s
tem
s
[
2
6
]
.
I
n
o
t
h
er
wo
r
d
s
,
th
e
ADACO m
eth
o
d
is
a
f
u
r
th
e
r
m
o
d
if
icatio
n
o
f
th
e
ADAC
m
eth
o
d
ap
p
lied
to
a
wid
e
class
o
f
n
o
n
lin
ea
r
o
b
jec
ts
with
r
eg
u
lar
an
d
ch
ao
tic
o
s
cillatio
n
s
.
I
n
th
e
A
DACO
m
eth
o
d
,
th
e
ch
o
ice
o
f
in
v
a
r
ian
t
m
a
n
if
o
ld
s
is
n
o
t
a
f
u
lly
f
o
r
m
alize
d
p
r
o
ce
d
u
r
e,
b
u
t
d
ep
en
d
s
o
n
t
h
e
ex
p
e
r
ien
ce
a
n
d
u
n
d
er
s
tan
d
in
g
o
f
t
h
e
s
y
s
tem
d
esig
n
e
r
an
d
th
e
s
p
ec
if
ic
tech
n
o
lo
g
ical
co
n
tr
o
l
p
r
o
b
le
m
.
T
h
e
m
ain
f
ea
tu
r
e
o
f
th
e
ADACO
m
eth
o
d
is
th
e
u
n
if
o
r
m
ch
o
ice
o
f
en
er
g
y
in
v
ar
ian
ts
in
th
e
f
o
r
m
o
f
th
e
en
er
g
y
o
f
th
e
s
y
n
th
esized
s
y
s
tem
o
r
its
f
ir
s
t
in
teg
r
als
o
f
m
o
tio
n
.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
th
e
ch
o
ice
o
f
en
e
r
g
y
as
an
i
n
v
ar
ian
t
m
an
if
o
l
d
all
o
ws
s
o
lv
in
g
a
wid
e
class
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l p
r
o
b
lem
s
.
T
h
e
f
ea
tu
r
es
o
f
th
e
ADACO
m
eth
o
d
,
w
h
ich
s
h
o
u
ld
b
e
p
ar
t
icu
lar
ly
n
o
te
d
,
ar
e
th
e
r
esu
lt
o
f
th
e
s
tu
d
y
o
f
a
n
ew
ap
p
r
o
ac
h
to
th
e
s
y
n
t
h
esis
o
f
co
n
tr
o
l sy
s
tem
s
f
o
r
n
o
n
lin
ea
r
o
s
cillatio
n
s
in
v
ar
io
u
s
o
b
jects o
n
th
e
b
asis
o
f
th
e
s
y
n
e
r
g
etic
ap
p
r
o
ac
h
.
T
h
e
ess
en
tial d
if
f
er
en
ce
s
o
f
th
e
ADACO m
eth
o
d
ar
e:
First,
th
e
u
s
e
o
f
m
ac
r
o
v
ar
ia
b
l
es
o
f
th
e
f
o
r
m
1
=
,
wh
er
e
is
r
ep
r
esen
ts
en
er
g
y
,
an
d
o
f
th
e
f
o
r
m
2
=
,
wh
er
e
is
r
ep
r
esen
ts
th
e
f
ir
s
t in
teg
r
al
o
f
th
e
m
o
tio
n
o
f
th
e
s
y
n
th
esis
ed
v
ib
r
atio
n
al
s
y
s
tem
.
Seco
n
d
,
th
e
u
s
e
o
f
b
asic in
v
ar
i
an
t r
elatio
n
s
o
f
th
e
f
o
llo
win
g
f
o
r
m
:
1
̇
1
(
)
+
1
2
=
0
,
2
̇
2
(
)
+
2
=
0
.
Fo
r
m
ec
h
a
n
ical
s
y
s
tem
s
th
e
v
ar
iab
le
is
u
s
u
ally
r
ep
r
esen
ts
th
e
v
elo
city
,
an
d
f
o
r
o
th
er
s
y
s
tem
s
th
e
v
ar
iab
le
is
a
ce
r
tain
p
o
s
itiv
e
f
u
n
ctio
n
o
f
th
e
s
tate
co
o
r
d
in
ates.
Ob
v
io
u
s
ly
,
th
ese
in
v
a
r
ian
t
r
elatio
n
s
ar
e
asy
m
p
to
tically
s
tab
le
ac
co
r
d
i
n
g
to
t
h
e
L
y
a
p
u
n
o
v
cr
iter
i
o
n
with
r
esp
ec
t
to
th
e
s
tates
1
=
0
an
d
2
=
0
at
1
>
0
,
2
>
0
.
T
h
is
m
ea
n
s
th
at
th
e
im
a
g
e
p
o
in
t
o
f
th
e
s
y
n
th
esis
ed
o
s
cillato
r
y
s
y
s
tem
in
ev
itab
l
y
r
ea
c
h
es
th
e
d
esire
d
in
v
a
r
ian
t
m
a
n
if
o
ld
s
1
=
0
o
r
2
=
0
ar
e
th
e
o
s
cillato
r
y
attr
ac
to
r
s
o
f
t
h
e
s
y
s
tem
.
T
o
p
r
o
v
e
th
is
,
th
e
f
o
llo
win
g
L
y
ap
u
n
o
v
f
u
n
ctio
n
s
ar
e
u
s
ed
:
1
=
0
,
5
1
2
,
th
en
̇
1
(
)
=
1
̇
1
(
)
=
−
1
2
1
2
<
0
,
an
d
2
=
0
,
5
2
2
,
the
n
̇
2
(
)
=
2
̇
2
(
)
=
−
2
2
2
<
0
.
T
h
u
s
,
it
is
clea
r
f
r
o
m
th
e
ab
o
v
e
th
at
t
h
e
ab
o
v
e
co
n
d
itio
n
s
o
f
asy
m
p
to
tic
L
y
a
p
u
n
o
v
s
tab
i
lity
with
r
esp
ec
t
to
in
v
ar
ian
t m
an
i
f
o
ld
s
1
=
0
an
d
2
=
0
ar
e
o
b
v
io
u
s
f
o
r
s
y
n
th
esi
z
ed
o
s
cillatin
g
s
y
s
tem
s
.
T
h
e
o
b
v
i
o
u
s
co
n
s
id
er
atio
n
s
o
n
th
e
s
tab
ilit
y
o
f
s
y
n
th
esized
n
o
n
lin
ea
r
o
s
cillatin
g
s
y
s
tem
s
p
r
esen
ted
h
er
e
co
n
tain
s
o
m
e
h
id
d
en
f
e
atu
r
es.
Fo
r
e
x
am
p
le,
th
e
eq
u
atio
n
1
=
0
is
th
e
eq
u
atio
n
o
f
a
d
ec
o
m
p
o
s
ed
co
n
s
er
v
ativ
e
s
y
s
tem
,
wh
ich
is
k
n
o
wn
n
o
t
to
p
o
s
s
ess
th
e
p
r
o
p
er
ty
o
f
asy
m
p
t
o
tic
L
y
ap
u
n
o
v
s
tab
ilit
y
.
Ho
wev
er
,
th
e
o
r
ig
i
n
al
s
y
s
tem
1
̇
1
(
)
+
1
2
=
0
is
a
d
is
s
ip
ativ
e
s
y
s
tem
.
T
h
is
m
ea
n
s
th
a
t
wh
en
th
e
im
ag
in
g
p
o
in
t
o
f
th
e
s
y
s
tem
leav
es
th
e
s
tate
1
=
0
,
th
e
d
is
s
ip
ativ
e
p
r
o
p
er
ty
co
m
es
i
n
to
ef
f
ec
t,
wh
ic
h
will
r
etu
r
n
t
h
e
s
y
s
tem
to
th
e
s
tate
1
=
0
in
th
e
tim
e
d
ef
in
ed
b
y
th
e
p
ar
am
eter
1
>
0
.
Simil
ar
p
r
o
ce
s
s
es
o
cc
u
r
in
th
e
s
y
s
tem
2
̇
2
(
)
+
2
=
0
.
I
n
g
en
er
al,
th
is
m
ea
n
s
th
at
as
a
r
esu
lt
o
f
th
e
in
ter
ac
tio
n
o
f
d
is
s
ip
ativ
ity
an
d
en
er
g
y
co
n
s
er
v
atio
n
in
th
e
f
ir
s
t sy
s
tem
.
T
h
e
f
u
n
ctio
n
1
=
0
is
an
attr
ac
tin
g
in
v
ar
ian
t m
an
if
o
ld
o
n
wh
ich
s
tab
le
o
s
cillato
r
y
p
r
o
ce
s
s
es
with
g
iv
en
p
r
o
p
er
ties
ar
is
e.
T
h
e
m
ec
h
a
n
is
m
o
f
d
is
s
ip
ativ
e
-
co
n
s
er
v
ativ
e
in
ter
ac
tio
n
r
e
v
ea
led
in
th
e
ADACO
m
eth
o
d
is
n
ew
in
t
h
e
th
eo
r
y
o
f
s
y
n
th
esis
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l sy
s
tem
s
.
T
h
ir
d
,
th
e
ADACO
m
eth
o
d
h
as
a
clea
r
p
h
y
s
ical
b
asis
in
th
e
p
r
o
b
lem
s
o
f
o
p
tim
al
co
n
tr
o
l
o
f
th
e
g
en
er
atio
n
o
f
r
eg
u
lar
o
s
cillatio
n
s
in
n
o
n
lin
ea
r
s
y
s
tem
s
,
wh
i
ch
ar
e
b
ased
o
n
th
e
to
tal
en
er
g
y
.
T
h
e
r
e
ar
e
s
o
m
e
p
ec
u
liar
ities
in
th
e
p
r
o
ce
d
u
r
e
o
f
a
p
p
ly
in
g
th
e
ADACO
m
eth
o
d
f
o
r
s
y
n
th
esis
o
f
n
o
n
lin
ea
r
o
s
cillatin
g
s
y
s
tem
s
.
I
n
th
is
m
eth
o
d
,
th
e
ac
h
iev
e
m
en
t
o
f
s
tab
le
n
o
n
lin
ea
r
o
s
cillatio
n
s
is
ca
r
r
ied
o
u
t
b
y
in
t
r
o
d
u
cin
g
“in
ter
n
al
”
co
n
tr
o
ls
in
to
th
e
n
o
n
lin
ea
r
o
b
j
ec
t.
T
h
ese
co
n
tr
o
ls
ch
an
g
e
t
h
e
eq
u
atio
n
s
o
f
th
e
o
b
ject
m
o
d
el
in
s
u
ch
a
way
th
at
th
e
d
esire
d
co
o
r
d
in
ate,
r
ef
lect
in
g
th
e
tech
n
o
l
o
g
ical
p
r
o
c
ess
in
th
e
s
y
s
tem
,
in
ev
itab
ly
m
o
v
es
to
th
e
m
o
d
e
o
f
s
tab
le
o
s
cillatio
n
s
with
s
p
ec
if
ied
p
r
o
p
er
ties
.
T
h
e
d
ep
en
d
en
c
e
o
f
th
e
s
p
ec
if
ie
d
co
o
r
d
i
n
ate
o
n
th
e
r
e
q
u
ir
em
en
ts
to
th
e
tec
h
n
o
lo
g
ical
p
r
o
ce
s
s
an
d
th
e
s
tr
u
ctu
r
e
o
f
th
e
o
b
ject
m
o
d
el
ca
n
b
e
eith
er
an
i
n
ter
m
ed
iate
o
r
an
o
u
tp
u
t
co
o
r
d
in
ate
o
f
th
e
o
b
ject.
So
,
b
y
in
tr
o
d
u
cin
g
ap
p
r
o
p
r
iate
in
ter
n
al
co
n
tr
o
ls
th
at
tr
an
s
f
o
r
m
th
e
o
b
ject
m
o
d
el,
s
tab
le
n
o
n
lin
ea
r
o
s
cillatio
n
s
ar
is
e
in
th
e
s
y
s
tem
“o
b
ject
-
o
s
cillatio
n
co
n
tr
o
ller
”.
T
h
e
ap
p
l
icatio
n
o
f
th
is
ty
p
e
o
f
n
o
n
lin
ea
r
tr
a
n
s
f
o
r
m
atio
n
s
th
r
o
u
g
h
th
e
in
tr
o
d
u
ctio
n
o
f
ap
p
r
o
p
r
iate
in
ter
n
al
co
n
t
r
o
l
s
d
is
tin
g
u
is
h
es
th
e
ADACO m
eth
o
d
f
r
o
m
o
th
er
m
eth
o
d
s
o
f
s
y
n
th
esis
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l
s
y
s
tem
s
.
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
Op
tima
l c
o
n
tr
o
l o
f th
e
d
y
n
a
mi
cs o
f n
o
n
lin
ea
r
o
s
cilla
tin
g
s
ystems
u
s
in
g
…
(
S
id
d
iko
v
I
s
o
mid
d
in
X
a
kimo
vich
)
6277
5.
CO
NCLU
SI
O
N
I
n
co
n
clu
s
io
n
,
th
e
an
al
y
tical
d
esig
n
m
eth
o
d
o
f
ag
g
r
eg
ate
d
v
ib
r
atio
n
co
n
tr
o
ller
a
n
aly
tic
r
ep
r
esen
ts
a
s
ig
n
if
ican
t step
f
o
r
war
d
in
th
e
f
ield
o
f
co
n
tr
o
l th
eo
r
y
o
f
n
o
n
li
n
ea
r
o
s
cillatin
g
s
y
s
tem
s
.
B
ase
d
o
n
th
e
p
r
in
cip
les
o
f
s
y
n
er
g
etic
co
n
t
r
o
l
th
e
o
r
y
,
th
e
ADACO
m
eth
o
d
e
f
f
e
ctiv
ely
co
m
b
i
n
es
s
elf
-
o
r
g
a
n
izatio
n
an
d
co
n
tr
o
l
p
r
o
ce
s
s
es to
p
r
o
d
u
ce
en
er
g
y
-
e
f
f
icien
t c
o
n
tr
o
l sy
s
tem
s
f
o
r
a
wid
e
r
an
g
e
o
f
n
o
n
lin
ea
r
o
s
cillatin
g
s
y
s
tem
s
.
Usi
n
g
en
er
g
y
i
n
v
ar
ian
ts
an
d
f
ir
s
t
i
n
teg
r
als
o
f
m
o
tio
n
,
th
e
ADACO
m
eth
o
d
o
f
f
e
r
s
a
m
o
r
e
co
m
p
r
eh
e
n
s
iv
e
ap
p
r
o
ac
h
to
t
h
e
s
y
n
th
esis
o
f
co
n
tr
o
l
laws,
wh
ich
p
r
o
v
id
es
h
ig
h
e
f
f
icien
cy
an
d
r
o
b
u
s
tn
ess
in
ap
p
licatio
n
s
r
an
g
in
g
f
r
o
m
ae
r
o
s
p
ac
e
s
y
s
tem
s
to
co
m
p
lex
o
b
jects
with
ch
ao
tic
d
y
n
am
ics.
T
h
e
ad
v
an
ta
g
es
o
f
th
e
ADACO
m
eth
o
d
o
v
er
tr
ad
itio
n
al
m
eth
o
d
s
lie
in
its
an
aly
tical
n
atu
r
e,
wh
ich
allo
ws
ac
cu
r
ate
an
d
ef
f
icien
t
s
y
n
th
esis
o
f
co
n
tr
o
l la
ws ev
en
f
o
r
u
n
s
tab
le
n
o
n
lin
ea
r
o
b
jects.
I
n
th
e
co
u
r
s
e
o
f
t
h
e
s
tu
d
y
th
e
th
eo
r
etica
l
b
asis
o
f
th
e
ADACO
m
eth
o
d
,
its
m
ain
s
tag
es
an
d
p
r
o
ce
d
u
r
es
f
o
r
s
y
n
th
esizin
g
c
o
n
tr
o
l
ac
tio
n
s
wer
e
d
is
cu
s
s
ed
in
d
etail.
T
h
e
h
i
g
h
ef
f
icien
c
y
o
f
th
e
m
eth
o
d
is
d
em
o
n
s
tr
ated
th
r
o
u
g
h
an
aly
s
e
s
an
d
p
r
ac
tical
ex
am
p
les
o
f
a
p
p
licatio
n
.
I
t
is
s
h
o
wn
th
at
th
e
ADACO
m
eth
o
d
n
o
t
o
n
ly
g
en
er
alize
s
th
e
k
n
o
w
n
r
esu
lts
o
f
th
e
class
ical
th
eo
r
y
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
s
,
b
u
t
also
d
e
v
elo
p
s
n
ew
m
eth
o
d
s
o
f
en
er
g
y
-
ef
f
icien
t
c
o
n
tr
o
l
o
f
co
m
p
lex
d
y
n
am
ic
o
b
jects.
T
h
u
s
,
th
e
ADACO
m
eth
o
d
is
a
p
r
o
m
is
in
g
to
o
l f
o
r
s
o
lv
in
g
ac
tu
al
p
r
o
b
le
m
s
o
f
n
o
n
lin
ea
r
o
s
cillatio
n
co
n
tr
o
l,
o
f
f
e
r
in
g
a
u
n
if
ied
ap
p
r
o
ac
h
to
th
e
cr
ea
tio
n
o
f
s
tab
le
o
s
cillatio
n
s
an
d
s
u
p
p
r
e
s
s
io
n
o
f
u
n
wan
ted
p
er
tu
r
b
ati
o
n
s
.
Fu
r
th
er
d
ev
elo
p
m
en
t
an
d
ap
p
licatio
n
o
f
th
e
ADACO
m
eth
o
d
ca
n
s
ig
n
i
f
ican
tly
ad
v
a
n
ce
th
e
m
o
d
er
n
co
n
t
r
o
l
th
eo
r
y
a
n
d
th
e
p
r
ac
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