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I
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Vo
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,
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Octo
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20
25
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5
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4
I
SS
N:
2088
-
8
7
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,
DOI
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4542
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CC B
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C
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Vietn
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m
ail: tr
u
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csk
td
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tn
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t.e
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.
v
n
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
e
ce
n
t d
ec
ad
es,
u
n
m
a
n
n
ed
ae
r
ial
v
eh
icles
(
UAVs)
h
av
e
b
ee
n
in
cr
ea
s
in
g
ly
u
s
ed
to
p
e
r
f
o
r
m
v
a
r
io
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s
task
s
,
s
u
ch
as
s
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r
v
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m
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air
tr
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co
n
tr
o
l,
ag
r
icu
ltu
r
e
m
an
a
g
em
en
t
[
1
]
–
[
3
]
.
T
o
p
er
f
o
r
m
tas
k
ef
f
ec
tiv
ely
,
it
is
o
f
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m
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I
n
p
r
ac
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a
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p
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,
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two
co
n
tr
o
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r
eq
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ir
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ar
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ec
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p
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o
f
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with
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d
tr
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s
la
tio
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s
u
b
-
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y
s
tem
s
[
1
]
–
[
7
]
.
I
n
s
tu
d
y
[
6
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,
th
e
co
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t
r
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s
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NNs)
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ased
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m
an
ce
(
AT
PP
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tech
n
iq
u
e
[
5
]
.
I
n
[
2
]
,
a
n
ad
ap
tiv
e
tr
ajec
to
r
y
tr
ac
k
in
g
c
o
n
tr
o
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was
p
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s
ed
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o
r
UAV
ex
p
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s
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tem
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ter
esti
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atin
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les
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ased
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i
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Mo
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
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p
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n
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I
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N:
2088
-
8
7
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Dis
co
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cto
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-
b
a
s
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d
a
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men
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(
N
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Tr
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Da
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4543
f
o
r
g
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al
r
o
b
o
tics
co
n
tr
o
l
d
esig
n
s
tu
d
ied
in
[
8
]
,
o
u
tp
u
t
f
e
ed
b
ac
k
law
with
s
tate
o
b
s
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v
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h
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o
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s
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y
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ac
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o
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ilter
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g
tech
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iq
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e
[
2
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.
B
u
t
as
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ar
as
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n
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wn
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it c
a
n
b
e
f
o
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n
d
th
a
t th
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e
is
litt
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tio
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o
n
th
e
o
p
tim
al
co
n
tr
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l U
AV
s
y
s
tem
s
.
W
ith
th
e
co
m
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lex
ity
o
f
UAV
m
o
d
el
an
d
th
e
d
iv
er
s
i
fi
ca
tio
n
o
f
p
r
ac
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task
s
,
it
is
d
if
f
icu
lt
to
o
b
tain
th
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co
n
tr
o
l
o
b
jectiv
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co
m
p
lex
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r
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s
es
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n
l
y
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ely
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o
n
a
s
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le
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Hen
ce
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UAV
r
esear
ch
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u
t
f
o
r
war
d
th
e
c
o
n
ce
p
t
o
f
m
u
lti
-
ag
en
t
s
y
s
tem
s
(
MA
Ss
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,
wh
ich
in
v
o
lv
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two
r
esear
ch
h
o
ts
p
o
ts
o
f
co
n
s
en
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s
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f
o
r
m
atio
n
c
o
n
tr
o
l
p
r
o
b
lem
s
[
1
]
,
[
3
]
,
[
7
]
,
[
9
]
–
[
1
2
]
.
I
n
[
9
]
,
a
c
o
n
s
en
s
u
s
co
n
tr
o
l
law
was
d
ev
elo
p
ed
f
o
r
m
u
ltip
le
UAV
s
y
s
tem
s
with
tim
e
d
el
ay
an
d
ca
s
ca
d
e
m
o
d
el.
Ho
wev
er
,
th
e
Kr
o
n
ec
k
er
p
r
o
d
u
ct
an
d
L
in
ea
r
Ma
tr
i
x
I
n
eq
u
alities
(
L
MI
s
)
we
r
e
im
p
lem
en
ted
i
n
[
9
]
d
u
e
t
o
th
e
s
im
p
lific
atio
n
o
f
UAV
m
o
d
el.
T
h
e
r
esear
c
h
co
n
d
u
cte
d
b
y
[
1
3
]
is
co
n
ce
r
n
ed
with
th
e
co
n
s
en
s
u
s
co
n
tr
o
ller
with
th
e
s
ig
n
f
u
n
ctio
n
.
Hen
ce
,
th
e
s
tab
ilit
y
co
n
s
id
er
atio
n
r
eq
u
ir
es
th
e
Fil
lip
o
v
th
eo
r
y
em
p
lo
y
m
e
n
t.
Ad
d
itio
n
ally
,
th
e
b
ea
r
in
g
p
e
r
s
is
ten
ce
o
f
ex
citatio
n
(
PE)
b
ased
lead
er
-
f
o
llo
wer
f
o
r
m
atio
n
co
n
tr
o
l
s
tr
ateg
y
was
p
r
o
p
o
s
ed
f
o
r
m
u
ltip
le
d
o
u
b
le
-
in
teg
r
ato
r
s
in
th
r
ee
d
im
en
s
io
n
al
(
3
D)
s
p
ac
e
u
s
in
g
th
e
p
r
o
jectio
n
o
f
v
ec
to
r
o
n
t
h
e
p
lan
e
o
r
t
h
o
g
o
n
al
to
2
-
s
p
h
e
r
e
[
1
4
]
.
W
h
en
ea
ch
ag
en
t
was
co
n
s
id
er
ed
m
o
r
e
co
m
p
licated
with
E
u
ler
-
L
ag
r
a
n
g
e
s
y
s
tem
s
,
th
e
s
tate
r
ep
r
esen
tatio
n
ca
n
b
e
u
s
ed
t
o
o
b
tain
th
e
ev
en
t
-
t
r
ig
g
er
e
d
b
ased
co
n
s
en
s
u
s
co
n
t
r
o
ller
w
ith
Kr
o
n
ec
k
er
p
r
o
d
u
ct
[
1
5
]
.
T
h
e
f
au
lt
-
to
ler
an
t
co
n
s
en
s
u
s
co
n
tr
o
l
p
r
o
b
lem
f
o
r
n
o
n
s
tr
ict
-
f
ee
d
b
ac
k
n
o
n
lin
e
ar
MA
Ss
with
in
ter
m
itten
t
a
ctu
ato
r
f
a
u
lts
was
in
v
esti
g
ated
s
tate
o
b
s
er
v
er
a
n
d
b
ac
k
s
tep
p
in
g
tech
n
iq
u
e
[
1
6
]
.
M
o
r
eo
v
er
,
th
e
f
o
r
m
atio
n
co
n
tr
o
l
o
f
m
u
ltip
l
e
UAVs
wa
s
also
co
n
s
id
er
ed
b
y
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
MPC
)
with
th
e
af
f
in
e
tr
ac
k
in
g
er
r
o
r
m
o
d
el
[
1
7
]
–
[
1
9
]
.
Desp
ite
th
is
,
s
tu
d
ies
[
1
7
]
–
[
1
9
]
d
id
n
o
t
e
x
am
in
e
th
e
s
tab
ilit
y
p
r
o
p
er
ties
o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
wh
en
o
p
e
r
atin
g
u
n
d
er
MPC
f
r
am
ewo
r
k
.
Fo
r
th
e
f
o
r
m
atio
n
tr
ac
k
in
g
c
o
n
tr
o
l
p
r
o
b
lem
,
ad
d
r
ess
in
g
th
e
tim
e
-
v
ar
y
in
g
f
o
r
m
atio
n
(
T
VF)
is
also
ex
tr
em
ely
cr
u
cial
f
o
r
m
ee
tin
g
ap
p
licatio
n
r
eq
u
ir
em
en
t
[
1
]
,
[
7
]
,
[
1
0
]
,
[
1
1
]
.
Acc
o
r
d
in
g
to
lin
ea
r
UAV
m
o
d
el,
t
h
e
T
VF
tr
ac
k
in
g
c
o
n
tr
o
l
was
i
n
v
esti
g
ated
b
y
Kr
o
n
ec
k
er
p
r
o
d
u
ct
co
n
s
id
er
atio
n
an
d
L
MI
s
tec
h
n
iq
u
e
[
7
]
.
Alth
o
u
g
h
th
e
co
s
t
f
u
n
ctio
n
was
m
en
tio
n
e
d
i
n
[
7
]
b
u
t
th
e
o
p
tim
al
co
n
tr
o
l
law
h
as
n
o
t
b
ee
n
s
tu
d
ied
in
th
is
wo
r
k
.
On
th
e
o
th
er
h
an
d
,
ex
ten
d
e
d
o
b
s
er
v
er
(
E
SO)
b
ased
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
was
p
r
o
p
o
s
ed
in
th
e
s
ec
o
n
d
-
o
r
d
er
attitu
d
e
s
u
b
-
s
y
s
tem
[
1
]
.
Fu
r
th
er
m
o
r
e,
th
e
esti
m
atio
n
o
f
y
aw
an
g
le
i
n
v
ir
tu
al
lead
e
r
was
ca
r
r
ied
o
u
t
with
t
h
e
co
n
n
ec
tio
n
to
th
e
tim
e
-
v
ar
y
in
g
co
m
m
u
n
icatio
n
to
p
o
lo
g
y
as
well
as
th
e
d
is
tr
ib
u
ted
f
o
r
m
atio
n
tr
ac
k
in
g
co
n
t
r
o
l
was
ad
d
r
ess
ed
in
th
e
p
o
s
itio
n
s
u
b
-
s
y
s
tem
[
1
]
.
B
ased
o
n
th
e
lin
ea
r
m
o
d
el
o
f
f
ix
ed
-
s
win
g
U
AVs,
th
e
T
VF
tr
ac
k
in
g
co
n
tr
o
l
was
d
is
cu
s
s
ed
b
y
em
p
lo
y
in
g
th
e
s
o
lu
tio
n
o
f
R
icca
ti
eq
u
atio
n
[
1
0
]
.
No
tab
ly
,
[
1
1
]
tack
le
d
th
e
T
VF
tr
ac
k
in
g
co
n
tr
o
l
f
o
r
m
u
ltip
le
lin
ea
r
s
y
s
tem
s
b
y
ex
ten
d
in
g
E
v
en
t
-
T
r
ig
g
er
ed
m
ec
h
an
is
m
.
Alth
o
u
g
h
th
er
e
h
as
b
ee
n
s
o
m
e
r
esear
ch
o
n
th
e
d
is
tr
ib
u
ted
co
n
tr
o
l
s
ch
em
es
f
o
r
MA
Ss
esp
ec
ially
th
e
co
n
s
en
s
u
s
an
d
f
o
r
m
atio
n
s
y
s
tem
s
,
m
o
s
t
o
f
th
e
r
ec
en
t
r
ef
er
en
ce
s
h
av
e
f
o
cu
s
ed
o
n
s
im
p
le
UAV
m
o
d
el
an
d
r
ar
ely
co
n
s
id
er
ed
th
e
ca
s
ca
d
e
UAV
s
tr
u
ctu
r
e
as
well
as
o
p
tim
izatio
n
-
b
ased
c
o
n
tr
o
l
f
o
r
m
u
latio
n
.
I
m
p
l
em
en
ti
n
g
t
h
e
o
p
ti
m
a
l c
o
n
t
r
o
l la
w
i
n
r
ea
l
-
wo
r
l
d
s
y
s
te
m
s
r
eq
u
i
r
es
t
h
e
u
s
e
o
f
ite
r
a
ti
v
e
al
g
o
r
it
h
m
s
t
o
co
m
p
u
te
s
o
l
u
t
io
n
s
t
o
th
e
Ha
m
i
lto
n
-
J
a
co
b
i
-
B
el
lm
an
(
HJB
)
e
q
u
at
io
n
s
f
o
r
n
o
n
li
n
e
ar
s
y
s
te
m
s
o
r
R
ic
ca
ti e
q
u
ati
o
n
s
f
o
r
li
n
ea
r
s
y
s
t
em
s
,
s
i
n
c
e
a
n
al
y
ti
ca
l
s
o
l
u
ti
o
n
s
a
r
e
t
y
p
ic
all
y
n
o
t
f
ea
s
i
b
l
e.
T
o
ad
v
a
n
ce
t
h
e
im
p
le
m
e
n
t
ati
o
n
o
f
o
p
ti
m
al
co
n
t
r
o
l
i
n
r
o
b
o
t
ic
s
y
s
tem
s
,
it
is
ess
e
n
t
ial
to
in
c
o
r
p
o
r
ate
r
e
in
f
o
r
ce
m
e
n
t
lea
r
n
i
n
g
c
o
n
t
r
o
l
(
R
L
C
)
in
co
n
j
u
n
ct
io
n
w
it
h
m
et
h
o
d
s
f
r
o
m
a
p
p
r
o
x
i
m
at
e
a
n
d
a
d
a
p
t
iv
e
d
y
n
am
ic
p
r
o
g
r
a
m
m
i
n
g
(
ADP
)
,
as
h
i
g
h
li
g
h
te
d
i
n
s
tu
d
ies
[
1
2
]
,
[
2
0
]
–
[
2
7
]
.
I
n
[
1
2
]
,
[
2
0
]
–
[
2
2
]
,
th
e
ac
to
r
/
cr
iti
c
s
tr
u
ct
u
r
e
w
as
r
e
ali
ze
d
v
ia
n
e
u
r
al
n
etw
o
r
k
(
N
N)
ap
p
r
o
x
i
m
a
ti
o
n
m
et
h
o
d
s
,
wit
h
le
ar
n
i
n
g
al
g
o
r
i
th
m
s
f
o
r
we
i
g
h
t
ad
a
p
tat
i
o
n
p
r
o
p
o
s
ed
a
lo
n
g
s
i
d
e
o
p
t
im
i
za
ti
o
n
s
tr
a
te
g
ies
,
e
n
a
b
l
in
g
t
h
e
cl
o
s
e
d
-
l
o
o
p
s
y
s
te
m
t
o
s
at
is
f
y
b
o
th
t
r
ac
k
i
n
g
p
e
r
f
o
r
m
a
n
c
e
a
n
d
o
p
ti
m
al
it
y
r
e
q
u
i
r
e
m
e
n
ts
.
Ho
w
ev
er
,
i
t
is
n
ec
ess
a
r
y
t
o
el
im
i
n
a
te
e
x
t
e
r
n
al
d
is
t
u
r
b
a
n
ce
a
n
d
d
y
n
a
m
ic
u
n
c
er
tai
n
t
ies
i
n
t
h
e
p
r
ac
tic
al
m
o
d
el,
wh
i
ch
ar
e
h
an
d
l
e
b
y
t
r
a
d
it
io
n
a
l r
o
b
u
s
t
c
o
n
t
r
o
l d
esi
g
n
[
1
2
]
,
[
2
0
]
–
[
2
2
]
.
A
d
i
f
f
e
r
e
n
t
a
p
p
r
o
ac
h
o
f
h
a
n
d
li
n
g
d
ir
ec
t
ly
th
e
e
x
t
e
r
n
al
d
is
t
u
r
b
a
n
ce
a
n
d
d
y
n
a
m
ic
u
n
ce
r
ta
in
ties
i
n
o
p
t
im
al
co
n
t
r
o
l
la
w
ca
n
b
e
k
n
o
wn
i
n
ze
r
o
an
d
n
o
n
-
ze
r
o
s
u
m
g
am
e
m
e
th
o
d
s
[
2
8
]
–
[
3
0
]
.
On
t
h
e
o
th
er
h
a
n
d
,
it
is
d
i
f
f
er
en
t
f
r
o
m
t
h
e
s
i
m
u
lta
n
e
o
u
s
lea
r
n
i
n
g
i
n
ac
t
o
r
/
cr
i
tic
f
r
am
ew
o
r
k
i
n
[
1
2
]
,
[
2
0
]
–
[
2
2
]
,
a
u
t
h
o
r
s
i
n
[
3
1
]
,
[
3
2
]
d
e
v
el
o
p
e
d
t
h
e
s
eq
u
en
tia
l
le
ar
n
i
n
g
v
alu
e
it
er
ati
o
n
(
VI
)
alg
o
r
it
h
m
t
o
o
b
tai
n
t
h
e
B
ell
m
an
f
u
n
cti
o
n
a
n
d
o
p
ti
m
al
co
n
t
r
o
l
l
aw
.
So
m
e
r
esea
r
ch
er
s
f
o
c
u
s
e
d
o
n
u
s
in
g
d
a
ta
-
d
r
iv
e
n
R
L
t
o
o
b
t
ai
n
th
e
o
p
ti
m
al
c
o
n
t
r
o
l
s
t
r
ate
g
i
es
f
o
r
u
n
ce
r
tai
n
s
y
s
te
m
s
[
6
]
,
[
2
2
]
,
[
2
8
]
,
[
3
0
]
,
[
3
3
]
–
[
3
7
]
.
Acc
o
r
d
in
g
t
o
th
e
d
ata
co
lle
cti
o
n
i
n
ti
m
e
i
n
t
e
r
v
al
,
th
e
a
p
p
r
o
x
im
a
te
o
p
t
im
al
f
u
n
c
ti
o
n
c
a
n
b
e
co
m
p
u
te
d
f
r
o
m
t
h
e
ap
p
r
o
x
i
m
a
te
o
p
t
im
al
c
o
n
tr
o
l
i
n
p
u
t
wi
th
o
u
t
t
h
e
k
n
o
w
le
d
g
e
o
f
m
o
d
e
l.
H
o
we
v
er
,
to
h
an
d
l
e
t
h
e
co
m
p
le
te
u
n
ce
r
t
ai
n
t
y
i
n
t
h
e
i
n
v
e
r
s
e
d
i
r
e
cti
o
n
,
t
h
e
a
d
d
iti
o
n
o
f
o
f
f
-
p
o
lic
y
te
c
h
n
iq
u
e
o
r
Q
-
l
ea
r
n
in
g
is
n
ec
ess
ar
y
t
o
co
n
s
i
d
e
r
[
2
]
,
[
3
6
]
,
[
3
7
]
.
A
d
a
ta
-
d
r
i
v
e
n
r
ei
n
f
o
r
ce
m
e
n
t
le
ar
n
i
n
g
c
o
n
tr
o
l
s
t
r
at
eg
y
was
r
ec
e
n
tl
y
i
n
tr
o
d
u
ce
d
f
o
r
q
u
a
d
r
o
t
o
r
s
,
d
e
m
o
n
s
tr
ati
n
g
t
h
e
c
a
p
a
b
il
it
y
t
o
a
ch
ie
v
e
o
p
ti
m
al
c
o
n
tr
o
l
w
h
ile
e
n
s
u
r
in
g
t
r
aje
ct
o
r
y
t
r
a
c
k
i
n
g
,
wh
ic
h
is
c
lo
s
el
y
r
el
ate
d
t
o
t
h
e
f
o
c
u
s
o
f
t
h
is
a
r
ti
cle
[
3
7
]
.
H
o
we
v
er
,
t
h
e
d
ata
-
d
r
i
v
e
n
R
L
a
p
p
r
o
a
ch
i
n
[
3
7
]
w
as
a
p
p
lie
d
s
o
le
ly
t
o
t
h
e
attit
u
d
e
s
u
b
s
y
s
t
em
o
f
a
UAV
,
a
n
d
t
h
e
ass
o
c
iat
ed
c
o
s
t
f
u
n
cti
o
n
d
id
n
o
t
i
n
c
o
r
p
o
r
at
e
a
d
is
co
u
n
t
f
ac
t
o
r
.
On
ac
c
o
u
n
t
o
f
t
h
e
a
b
o
v
e
r
esu
lts
,
we
wil
l
f
u
r
t
h
e
r
e
x
p
l
o
r
er
th
e
c
a
s
ca
d
e
UA
V
c
o
n
t
r
o
l
s
tr
u
ct
u
r
e
,
wh
i
ch
in
v
o
l
v
es
tw
o
d
at
a
-
d
r
i
v
e
n
R
L
wit
h
a
d
is
c
o
u
n
t
f
ac
to
r
-
b
ase
d
p
er
f
o
r
m
an
ce
i
n
d
ex
,
a
n
d
t
h
is
is
a
n
o
th
e
r
i
n
t
er
est
o
f
t
h
is
s
t
u
d
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
.
5
,
Octo
b
e
r
20
25
:
4
5
4
2
-
4
5
5
4
4544
T
h
is
s
tu
d
y
i
n
v
esti
g
ates
a
ca
s
ca
d
e
co
n
tr
o
l
ar
c
h
itectu
r
e
f
o
r
a
f
u
lly
u
n
ce
r
tain
q
u
ad
r
o
to
r
UAV
b
y
em
p
lo
y
in
g
two
d
ata
-
d
r
iv
en
R
L
alg
o
r
ith
m
s
b
ased
o
n
a
p
er
f
o
r
m
an
ce
in
d
e
x
with
a
d
is
co
u
n
t
f
ac
to
r
.
T
h
r
o
u
g
h
co
n
s
tr
u
ctin
g
a
d
ata
s
et
tailo
r
e
d
to
t
h
is
g
en
er
al
class
o
f
a
f
f
i
n
e
co
n
ti
n
u
o
u
s
-
tim
e
s
y
s
tem
s
an
d
in
teg
r
atin
g
a
R
L
s
tr
ateg
y
u
s
in
g
an
o
f
f
-
p
o
licy
al
g
o
r
ith
m
,
a
co
n
tr
o
l f
r
am
ewo
r
k
is
f
o
r
m
u
lated
f
o
r
UAVs w
ith
u
n
k
n
o
wn
d
y
n
am
ics.
T
h
e
s
u
m
m
ar
y
co
n
tr
i
b
u
tio
n
s
o
f
th
is
s
tu
d
y
ar
e
g
iv
e
n
in
th
e
f
o
ll
o
win
g
:
a.
B
ased
o
n
th
e
o
p
tim
al
co
n
tr
o
l
s
ch
em
e
with
a
d
is
co
u
n
t
f
ac
to
r
-
b
ased
p
er
f
o
r
m
an
ce
in
d
ex
,
we
f
u
r
th
er
in
tr
o
d
u
ce
a
R
L
alg
o
r
ith
m
f
o
r
an
af
f
in
e
co
n
tin
u
o
u
s
-
tim
e
s
y
s
tem
to
g
u
ar
an
tee
th
e
f
in
ite
v
alu
e
o
f
t
h
e
in
teg
r
al
co
s
t f
u
n
ctio
n
with
i
n
f
in
ity
ter
m
in
al.
b.
W
e
p
r
o
p
o
s
e
a
n
o
v
el
d
ata
-
d
r
iv
en
R
L
b
ased
ca
s
ca
d
e
c
o
n
tr
o
l
s
tr
u
ctu
r
e
in
b
o
th
two
s
u
b
-
s
y
s
tem
s
f
o
r
co
m
p
letely
u
n
ce
r
tain
UAVs
b
y
o
f
f
-
p
o
licy
m
eth
o
d
.
C
o
m
p
ar
ed
with
th
e
cu
r
r
en
t
r
e
s
u
lts
[
3
7
]
,
o
n
l
y
co
n
s
id
er
in
g
t
h
e
R
L
alg
o
r
ith
m
f
o
r
th
e
attitu
d
e
s
u
b
-
s
y
s
tem
with
o
u
t
d
is
co
u
n
t
f
ac
to
r
,
a
d
ata
-
d
r
iv
en
R
L
b
ased
ca
s
ca
d
e
co
n
tr
o
l
s
tr
u
ctu
r
e
is
f
ir
s
t
p
r
o
p
o
s
ed
f
o
r
co
m
p
letely
u
n
ce
r
tain
UAVs
with
a
d
is
co
u
n
t
f
ac
to
r
-
b
ase
d
p
er
f
o
r
m
an
ce
in
d
e
x
.
Fin
ally
,
s
im
u
latio
n
r
esu
lts
ar
e
p
r
esen
ted
to
v
alid
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el
-
f
r
ee
,
d
ata
-
d
r
iv
en
R
L
al
g
o
r
ith
m
.
2.
CO
NT
RO
L
L
E
R
M
E
T
H
O
D
O
L
O
DY
F
O
R
Q
UADR
O
T
O
R
As s
h
o
wn
in
Fig
u
r
e
1
,
th
e
E
ar
t
h
-
f
ix
ed
f
r
am
e
an
d
th
e
b
o
d
y
-
f
i
x
ed
f
r
am
e
ar
e
estab
lis
h
ed
to
d
escr
ib
e
th
e
d
y
n
am
ic
m
o
d
el
o
f
th
e
q
u
a
d
r
o
t
o
r
.
T
h
e
m
o
v
em
en
ts
o
f
th
is
Qu
ad
r
o
to
r
as
s
h
o
wn
in
Fig
u
r
e
1
ca
n
b
e
estab
lis
h
ed
b
y
c
h
an
g
es
o
n
f
o
u
r
lift
f
o
r
ce
s
,
wh
ich
ar
e
g
en
er
ated
b
y
ad
ju
s
tin
g
th
e
an
g
le
v
el
o
cities
o
f
f
o
u
r
r
o
to
r
s
.
I
t
ca
n
b
e
s
ee
n
th
at
a
v
e
r
ti
ca
l
m
o
v
em
en
t
ca
n
b
e
o
b
ta
in
e
d
b
y
t
h
e
v
a
r
ia
ti
o
n
o
f
t
h
e
s
u
m
o
f
f
o
u
r
li
f
t
f
o
r
c
es
o
n
t
h
e
f
o
u
r
r
o
t
o
r
s
.
Du
e
t
o
t
h
e
d
i
f
f
e
r
e
n
c
e
b
e
twe
e
n
t
h
e
c
o
u
n
te
r
-
t
o
r
q
u
es
a
c
h
ie
v
e
d
b
y
t
h
e
g
r
o
u
p
o
f
r
o
to
r
s
(
R
o
t
o
r
1
a
n
d
R
o
t
o
r
3
)
an
d
th
e
g
r
o
u
p
o
f
r
o
t
o
r
s
(
R
o
t
o
r
2
a
n
d
R
o
t
o
r
4
)
,
th
e
y
aw
m
o
v
e
m
e
n
t
is
estab
lis
h
ed
.
A
d
d
itio
n
ally
,
th
e
p
itch
an
d
r
o
ll
m
o
v
em
en
ts
ca
n
b
e
g
en
e
r
ated
b
y
ch
a
n
g
in
g
th
e
lift
f
o
r
ce
s
o
f
ea
ch
p
air
,
wh
ich
r
esu
lt
in
th
e
l
o
n
g
itu
d
i
n
al
m
o
tio
n
an
d
th
e
later
al
m
o
tio
n
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
p
o
s
itio
n
o
f
th
e
UAV
q
u
ad
r
o
to
r
a
n
d
th
e
q
u
ad
r
o
t
o
r
attitu
d
e
ar
e
g
iv
en
as
=
[
,
,
]
∈
ℝ
3
an
d
=
[
,
,
]
∈
ℝ
3
,
r
esp
ec
tiv
ely
.
I
t
is
wo
r
th
n
o
tin
g
th
at
E
u
le
r
an
g
les
R
o
ll
-
Pit
ch
-
Yaw
ar
e
s
atis
f
ied
th
e
b
o
u
n
d
co
n
d
itio
n
as
−
/
2
<
<
/
2
,
−
/
2
<
<
/
2
an
d
−
<
<
.
Mo
r
eo
v
er
,
th
e
UAV
q
u
a
d
r
o
to
r
p
ar
am
eter
s
ar
e
e
x
p
r
ess
ed
in
T
ab
le
1
.
Fig
u
r
e
1
.
Qu
a
d
r
o
to
r
m
o
d
el
in
No
r
th
-
E
ast
-
Do
wn
(
NE
D)
c
o
o
r
d
in
ate
T
ab
le
1
.
UAV
p
ar
am
eter
s
an
d
v
ar
iab
les
U
A
V
p
a
r
a
m
e
t
e
r
s
v
a
r
i
a
b
l
e
s
W
e
i
g
h
t
o
f
t
h
e
q
u
a
d
r
o
t
o
r
A
c
c
e
l
e
r
a
t
i
o
n
o
f
t
h
e
g
r
a
v
i
t
y
1
,
2
,
3
,
4
A
n
g
l
e
v
e
l
o
c
i
t
y
o
f
e
a
c
h
r
o
t
o
r
Th
e
a
r
m
l
e
n
g
t
h
=
{
,
,
}
∈
ℝ
3
×
3
Th
e
i
n
e
r
t
i
a
ma
t
r
i
x
i
s s
y
mm
e
t
r
i
c
a
n
d
p
o
si
t
i
v
e
d
e
f
i
n
i
t
e
,
,
P
o
si
t
i
v
e
p
a
r
a
me
t
e
r
s
T
h
e
r
o
tatio
n
m
atr
ix
∈
(
3
)
r
ep
r
esen
tin
g
th
e
tr
a
n
s
f
o
r
m
atio
n
f
r
o
m
th
e
E
ar
th
-
f
ix
ed
f
r
am
e
t
o
th
e
body
-
f
ix
ed
co
o
r
d
in
ate
s
y
s
tem
is
g
iv
en
as
(
1
)
:
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
Dis
co
u
n
t fa
cto
r
-
b
a
s
ed
d
a
ta
-
d
r
iven
r
ein
fo
r
ce
men
t le
a
r
n
in
g
ca
s
ca
d
e
co
n
tr
o
l
…
(
N
g
o
c
Tr
u
n
g
Da
n
g
)
4545
=
[
−
−
+
+
−
]
(
1
)
wh
er
e
(
•
)
=
(
•
)
,
(
•
)
=
(
•
)
.
I
n
th
e
v
iew
o
f
[
1
]
,
th
e
co
m
p
let
e
q
u
ad
r
o
to
r
d
y
n
a
m
ic
m
o
d
el
ca
n
b
e
r
e
p
r
esen
ted
as
(
2
)
:
̈
=
̈
=
(
,
̇
)
̇
+
(
2
)
wh
er
e
th
e
p
a
r
am
eter
s
ar
e
g
iv
en
in
T
a
b
le
1
a
n
d
t
h
e
C
o
r
io
lis
m
atr
ix
(
,
̇
)
∈
ℝ
3
×
3
is
d
escr
ib
ed
in
[
2
]
.
Ad
d
itio
n
ally
,
th
e
f
o
r
ce
∈
ℝ
3
×
1
is
r
elativ
e
to
th
e
b
o
d
y
f
ix
ed
f
r
am
e
o
f
th
e
q
u
ad
r
o
to
r
ca
n
b
e
o
b
tain
e
d
as
(
3
)
:
=
[
0
0
]
−
[
0
0
]
(
3
)
wh
er
e
th
e
liftin
g
f
o
r
ce
∈
ℝ
an
d
t
h
e
to
r
q
u
e
=
[
]
∈
ℝ
3
ar
e
g
iv
e
n
as
(
4
)
,
(
5
)
:
=
(
1
2
+
2
2
+
3
2
+
4
2
)
(
4
)
=
(
2
2
−
4
2
)
,
=
(
1
2
−
3
2
)
,
=
(
1
2
−
2
2
+
3
2
−
4
2
)
(
5
)
I
n
wh
er
e,
t
h
e
co
n
tr
o
l sig
n
als o
f
th
e
q
u
a
d
r
o
t
o
r
(
2
)
ar
e
d
ef
in
ed
as
(
6
)
:
=
1
2
+
2
2
+
3
2
+
4
2
,
=
2
2
−
4
2
,
=
1
2
−
3
2
=
1
2
−
2
2
+
3
2
−
4
2
.
(
6
)
T
h
e
co
n
tr
o
l
o
b
jectiv
e
o
f
th
is
p
ap
er
is
to
d
ev
elo
p
a
d
ata
-
d
r
i
v
en
R
L
alg
o
r
ith
m
b
ased
o
n
t
h
e
o
p
tim
al
co
n
tr
o
l
s
ch
em
e
to
ac
h
iev
e
a
n
o
p
tim
ized
tr
ac
k
in
g
co
n
tr
o
l
law
f
o
r
a
q
u
ad
r
o
to
r
,
en
ab
li
n
g
th
e
q
u
ad
r
o
to
r
to
ef
f
ec
tiv
ely
tr
ac
k
th
e
d
esire
d
tr
ajec
to
r
y
with
h
ig
h
ac
cu
r
ac
y
.
T
h
e
o
p
tim
al
c
o
n
tr
o
l
s
ig
n
al
en
s
u
r
es
tr
ajec
to
r
y
tr
ac
k
in
g
wh
ile
s
im
u
ltan
eo
u
s
ly
ac
h
iev
in
g
ap
p
r
o
x
im
ate
o
p
t
im
ality
b
y
m
in
im
izin
g
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
Ad
d
itio
n
ally
,
th
e
d
ata
-
d
r
iv
e
n
R
L
-
b
ased
o
p
tim
al
co
n
tr
o
l
law
is
d
ev
elo
p
ed
f
o
r
n
o
t o
n
ly
th
e
p
o
s
itio
n
s
u
b
-
s
y
s
tem
b
u
t a
ls
o
th
e
attitu
d
e
s
u
b
-
s
y
s
tem
with
o
u
t th
e
k
n
o
wled
g
e
o
f
t
h
e
UAV
m
o
d
el.
1
.
Un
lik
e
th
e
co
n
v
e
n
tio
n
al
tr
ajec
to
r
y
tr
ac
k
in
g
co
n
tr
o
l
p
u
r
p
o
s
e
in
UAV
co
n
tr
o
l
s
y
s
tem
s
[
1
]
,
[
3
]
,
[
6
]
,
[
7
]
,
[
1
1
]
,
th
e
c
o
n
tr
o
l
o
b
jecti
v
e
in
th
is
p
ap
er
co
n
s
id
er
s
b
o
th
th
e
tr
ajec
to
r
y
tr
ac
k
in
g
p
er
f
o
r
m
a
n
ce
an
d
th
e
o
p
tim
al
co
n
tr
o
l
p
r
o
b
lem
.
I
n
a
d
d
itio
n
,
b
o
th
s
u
b
s
y
s
tem
s
as
s
h
o
wn
in
Fig
u
r
e
2
ac
h
iev
e
a
u
n
if
ied
f
r
am
ewo
r
k
o
f
o
p
tim
al
co
n
tr
o
l
an
d
s
tab
ilit
y
,
wh
ich
is
ty
p
ically
d
if
f
icu
lt
to
attain
d
u
e
to
th
e
tim
e
-
v
ar
y
in
g
d
y
n
am
ics
o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
s
.
Fig
u
r
e
2
.
T
h
e
q
u
ad
r
o
t
o
r
co
n
tr
o
l sch
em
atic
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
.
5
,
Octo
b
e
r
20
25
:
4
5
4
2
-
4
5
5
4
4546
I
n
th
is
s
ec
tio
n
,
a
d
ata
-
d
r
i
v
en
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
a
p
p
r
o
a
ch
is
in
tr
o
d
u
ce
d
t
o
ad
d
r
ess
th
e
tr
ad
e
-
o
f
f
b
etwe
en
tr
ac
k
i
n
g
p
er
f
o
r
m
an
c
e
an
d
o
p
tim
ality
with
in
t
h
e
q
u
ad
r
o
to
r
c
o
n
tr
o
l
s
y
s
tem
.
T
h
e
co
n
tr
o
l
ar
ch
itectu
r
e
illu
s
tr
ated
in
Fig
u
r
e
2
in
teg
r
ates
b
o
th
p
o
s
itio
n
an
d
attitu
d
e
co
n
tr
o
l
s
tr
ateg
ies
u
n
d
er
th
e
ap
p
licatio
n
o
f
a
d
is
co
u
n
t
f
ac
to
r
.
T
h
ese
c
o
n
tr
o
ller
s
ar
e
u
p
d
ated
co
n
cu
r
r
en
tly
u
s
in
g
th
e
c
o
llected
d
ata
to
h
an
d
le
s
y
s
tem
u
n
ce
r
tain
ties
ef
f
ec
tiv
ely
.
2
.
1
.
Dis
co
un
t
f
a
ct
o
r
-
ba
s
ed
RL
co
ntr
o
l desig
n f
o
r
a
ug
m
e
nte
d qua
dro
t
o
r
s
y
s
t
em
First o
f
all,
we
co
n
s
id
er
a
n
o
n
l
in
ea
r
af
f
in
e
s
y
s
tem
as
(
7
)
:
(
)
=
(
(
)
)
+
(
(
)
)
(
)
.
(
7
)
an
d
th
e
ass
o
ciate
d
co
s
t f
u
n
ctio
n
is
d
ef
in
ed
b
y
(
8
)
:
(
(
)
,
(
)
)
=
∫
[
(
)
(
)
+
(
)
(
)
]
∞
.
(
8
)
wh
er
e
∈
ℝ
×
>
0
,
∈
ℝ
×
>
0
ar
e
b
o
th
s
y
m
m
etr
ic
p
o
s
itiv
e
d
ef
in
ite
m
atr
ices.
T
h
e
tr
ac
k
in
g
er
r
o
r
m
o
d
el
o
f
n
o
n
lin
ea
r
af
f
i
n
e
s
y
s
tem
s
(
7
)
with
th
e
d
esire
d
tr
ajec
to
r
y
(
)
,
wh
ich
is
estab
lis
h
ed
b
y
a
co
m
m
an
d
g
en
er
ato
r
m
o
d
el
(
)
=
ℎ
(
(
)
)
,
ℎ
(
0
)
=
0
,
ca
n
b
e
f
o
r
m
u
lated
as
(
9
)
:
(
)
=
(
(
)
)
−
ℎ
(
(
)
)
+
(
(
)
)
(
)
.
(
9
)
wh
er
e
(
)
=
(
)
−
(
)
,
ℎ
(
(
)
)
is
th
e
u
n
k
n
o
wn
f
u
n
cti
o
n
.
Hen
ce
,
ac
c
o
r
d
in
g
to
tr
ac
k
in
g
er
r
o
r
m
o
d
el
(
9
)
an
d
th
e
c
o
m
m
an
d
g
en
e
r
ato
r
m
o
d
el
ℎ
(
(
)
)
,
we
ac
h
iev
e
th
e
f
o
llo
win
g
au
g
m
e
n
ted
s
y
s
tem
:
(
)
=
(
(
)
)
+
(
(
)
)
(
)
.
(
1
0
)
wh
er
e
(
)
=
[
(
)
(
)
]
,
(
(
)
)
=
[
(
(
)
+
(
)
)
−
ℎ
(
(
)
)
ℎ
(
(
)
)
]
,
(
(
)
)
=
[
(
(
)
+
(
)
)
0
]
(
1
1
)
T
h
e
o
p
tim
al
c
o
n
tr
o
l
law
∗
(
)
is
d
esig
n
ed
to
m
in
im
ize
th
e
d
is
co
u
n
ted
c
o
s
t
f
u
n
ctio
n
ass
o
ciate
d
with
th
e
au
g
m
en
ted
s
y
s
tem
(
1
0
)
.
(
(
)
,
(
)
)
=
∫
−
(
−
)
∞
(
(
)
,
(
)
)
,
(
1
2
)
wh
er
e
>
0
is
a
d
is
co
u
n
t
f
ac
to
r
,
(
(
)
,
(
)
)
≜
(
)
(
)
+
(
(
)
)
(
)
,
=
[
0
0
0
]
an
d
=
.
T
h
e
ad
d
itio
n
o
f
th
e
d
is
co
u
n
t
f
ac
to
r
in
th
e
co
s
t
f
u
n
ctio
n
(
1
2
)
is
ab
le
to
g
u
ar
an
tee
th
at
it
w
ill
b
e
f
in
ite
v
alu
e
alth
o
u
g
h
th
e
in
teg
r
al
ter
m
in
a
l
is
in
f
in
ity
.
T
h
er
e
f
o
r
e,
it
is
u
n
n
ec
ess
ar
y
to
ex
p
licitly
d
ef
in
e
th
e
ad
m
is
s
ib
le
co
n
tr
o
l
s
et,
as
d
is
cu
s
s
ed
in
[
2
]
.
T
h
e
s
et
ϒ
(
)
is
d
ef
in
ed
as
th
e
c
o
n
s
tr
ain
t
s
et
o
f
co
n
tr
o
l
in
p
u
t
(
)
s
u
ch
th
at
th
e
co
s
t
f
u
n
ctio
n
(
1
2
)
is
f
in
ite
.
B
ased
o
n
th
e
d
y
n
am
ic
p
r
o
g
r
am
m
in
g
p
r
i
n
cip
le,
th
e
tr
ac
k
i
n
g
B
ellm
an
f
u
n
ctio
n
f
o
r
th
e
a
u
g
m
e
n
ted
s
y
s
tem
(
1
0
)
ca
n
b
e
e
x
p
r
ess
ed
as th
e
f
o
llo
win
g
s
tatic
f
u
n
ctio
n
:
∗
(
(
)
)
=
(
(
)
)
∈
(
)
(
(
)
,
(
(
)
)
)
(
1
3
)
B
ased
o
n
two
ap
p
r
o
ac
h
es
f
o
r
co
m
p
u
tin
g
th
e
tim
e
d
er
iv
ativ
e
o
f
th
e
B
ellm
an
f
u
n
ctio
n
∗
(
(
)
)
in
(
1
3
)
,
th
e
ass
o
ciate
d
Ham
ilto
n
ian
f
u
n
cti
o
n
u
n
d
er
a
d
is
co
u
n
t
f
ac
to
r
>
0
is
f
o
r
m
u
lated
.
T
h
e
f
ir
s
t
ap
p
r
o
a
ch
in
v
o
lv
es
a
d
ir
ec
t c
o
m
p
u
tatio
n
,
as d
etailed
:
∗
(
(
)
)
=
∗
=
∗
(
(
(
)
)
+
(
)
∗
(
)
)
.
(
1
4
)
wh
er
e
∗
(
)
d
en
o
tes
th
e
o
p
tim
al
c
o
n
tr
o
l
in
p
u
t.
Acc
o
r
d
in
g
to
th
e
B
ellm
an
p
r
in
cip
le,
a
s
ec
o
n
d
ap
p
r
o
ac
h
f
o
r
co
m
p
u
tin
g
th
e
tim
e
d
er
i
v
ativ
e
o
f
t
h
e
B
ellm
an
f
u
n
ctio
n
∗
(
(
)
)
is
f
o
r
m
u
lated
b
y
u
tili
zin
g
th
e
s
tatic
B
ellm
an
f
u
n
ctio
n
i
n
(
1
3
)
:
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
Dis
co
u
n
t fa
cto
r
-
b
a
s
ed
d
a
ta
-
d
r
iven
r
ein
fo
r
ce
men
t le
a
r
n
in
g
ca
s
ca
d
e
co
n
tr
o
l
…
(
N
g
o
c
Tr
u
n
g
Da
n
g
)
4547
∗
(
(
)
)
=
∫
−
(
−
)
+
(
(
)
,
∗
(
)
)
+
−
∫
−
(
−
(
+
)
)
∞
+
(
(
)
,
∗
(
)
)
=
∫
−
(
−
)
+
(
(
)
,
∗
(
)
)
+
−
∗
(
(
+
)
)
(
1
5
)
T
h
e
r
ep
r
esen
tatio
n
(
1
5
)
o
b
tain
s
th
at:
∗
(
(
)
)
−
∗
(
(
(
+
)
)
=
1
∫
−
(
−
)
+
(
(
)
,
∗
(
)
)
+
(
−
−
1
)
∗
(
(
+
)
)
.
(
1
6
)
I
n
th
e
v
iew
o
f
(
1
6
)
an
d
(
1
4
)
a
s
→
0
,
we
ac
h
ie
v
e
th
at
th
e
s
tatic
B
ellm
an
f
u
n
ctio
n
∗
(
(
)
)
ca
n
b
e
s
o
v
ed
b
y
th
e
o
p
tim
al
co
n
tr
o
l sig
n
al
∗
(
)
u
s
in
g
th
e
f
o
llo
win
g
p
ar
tial d
er
iv
a
tiv
e
eq
u
atio
n
as
(
1
7
)
(
(
)
,
∗
(
)
)
−
∗
(
(
(
)
)
+
∗
(
(
(
)
)
+
(
)
∗
(
)
)
=
0
.
(
1
7
)
C
o
n
v
er
s
ely
,
to
d
eter
m
in
e
th
e
o
p
tim
al
co
n
tr
o
l
in
p
u
t
∗
(
)
u
s
in
g
th
e
s
tatic
B
ellm
an
f
u
n
ctio
n
∗
(
(
(
)
)
an
d
b
ased
o
n
th
e
B
ellm
an
p
r
in
cip
l
e,
th
e
co
r
r
esp
o
n
d
i
n
g
o
p
tim
izatio
n
p
r
o
b
lem
ca
n
b
e
f
o
r
m
u
late
d
as
(
1
8
)
:
∗
(
(
)
)
=
(
)
∈
(
)
(
∫
(
(
)
,
(
)
)
+
+
−
∗
(
(
(
+
)
)
)
(
1
8
)
Sin
ce
→
0
+
,
(
1
8
)
lead
s
to
th
e
c
o
r
r
es
p
o
n
d
in
g
o
p
tim
izatio
n
p
r
o
b
lem
as
(
1
9
)
:
(
)
(
)
∈
(
)
[
(
(
)
,
(
)
)
−
∗
(
(
)
)
+
∗
(
(
(
)
)
+
(
(
)
)
(
)
)
]
=
0
.
(
1
9
)
Def
in
in
g
th
e
m
o
d
if
ied
Ham
ilto
n
ian
f
u
n
ctio
n
i
n
th
e
p
r
esen
ce
o
f
a
d
is
co
u
n
t f
ac
to
r
>
0
as
(
1
9
)
,
(
,
(
)
,
,
)
=
(
(
)
)
(
)
+
(
(
)
)
(
)
−
(
(
)
)
+
(
(
)
)
(
(
(
)
)
+
(
(
)
)
(
)
)
(
2
0
)
wh
er
e
(
)
≜
(
)
,
it f
o
llo
ws th
at
th
e
o
p
ti
m
al
co
n
tr
o
l so
lu
tio
n
is
th
en
o
b
tain
ed
b
y
(
1
9
)
as
(
2
0
)
,
∗
(
(
)
)
=
ar
g
m
in
∈
(
)
[
(
,
(
)
,
∗
(
(
)
)
)
]
=
−
1
2
−
1
(
(
)
)
∗
(
(
)
)
(
2
1
)
Ad
d
itio
n
ally
,
s
u
b
s
titu
tin
g
th
e
o
p
tim
al
co
n
tr
o
l
law
∗
(
(
)
)
(
2
1
)
in
to
(
1
9
)
,
it
im
p
lies
th
e
p
ar
tial
d
er
iv
ativ
e
eq
u
atio
n
(
PDE)
is
ex
p
r
ess
ed
a
s
(
2
2
)
:
∗
(
(
)
,
∗
(
)
,
∗
,
∗
(
)
)
=
(
)
(
)
−
1
4
∗
(
(
)
)
(
(
)
)
−
1
(
(
)
)
∗
(
(
)
)
−
∗
(
(
)
)
+
∗
(
(
)
)
(
(
)
)
=
0
.
(
2
2
)
2
.
I
n
clu
d
i
n
g
a
p
o
s
itiv
e
d
is
co
u
n
t
f
ac
to
r
>
0
en
s
u
r
es
th
at
th
e
c
o
s
t
f
u
n
ctio
n
in
(
8
)
r
em
ai
n
s
f
in
it
e,
ev
en
wh
en
th
e
s
tate
v
ar
iab
le
(
)
d
o
es
n
o
t
co
n
v
e
r
g
e
to
ze
r
o
as
→
∞
.
T
h
is
co
n
s
id
er
atio
n
lead
s
to
th
e
ap
p
ea
r
an
ce
o
f
th
e
ter
m
"
∗
(
)
"
in
(
1
9
)
r
esu
ltin
g
in
n
ec
ess
ar
y
ad
j
u
s
tm
en
ts
with
in
th
e
d
is
co
u
n
t
f
ac
to
r
-
b
ased
R
L
co
n
tr
o
l f
r
am
ew
o
r
k
d
escr
ib
ed
in
s
ec
tio
n
s
2
.
2
an
d
2
.
3
.
2
.
2
.
Da
t
a
-
driv
en
pro
po
rt
io
n
a
l
-
inte
g
ra
l
po
s
it
io
n c
o
ntr
o
lle
r
I
n
th
is
s
ec
tio
n
,
a
ca
s
ca
d
e
c
o
n
tr
o
l
f
r
am
ewo
r
k
f
o
r
a
q
u
a
d
r
o
to
r
UAV
as
s
h
o
wn
in
F
ig
u
r
e
2
is
f
o
r
m
u
lated
f
o
llo
win
g
th
e
m
o
d
el
s
ep
ar
atio
n
in
(
2
)
,
w
h
er
e
ea
ch
s
u
b
s
y
s
tem
ap
p
lies
a
d
is
co
u
n
t
f
ac
to
r
-
b
ase
d
o
p
tim
al
co
n
tr
o
l
a
p
p
r
o
ac
h
.
H
o
wev
er
,
d
u
e
to
th
e
in
h
e
r
en
t
u
n
ce
r
tain
ties
an
d
n
o
n
lin
ea
r
iti
es
p
r
esen
t
in
(
2
2
)
,
o
b
tain
in
g
a
d
ir
ec
t
an
aly
tical
s
o
lu
tio
n
is
in
f
ea
s
ib
le.
As
a
r
esu
lt,
a
d
ata
-
d
r
iv
e
n
R
L
alg
o
r
ith
m
is
em
p
lo
y
ed
to
esti
m
ate
th
e
s
tatic
B
ellm
an
f
u
n
ctio
n
∗
(
)
co
r
r
esp
o
n
d
in
g
to
t
h
e
o
p
tim
al
c
o
n
tr
o
l
p
o
lic
y
∗
(
)
f
o
r
ea
ch
s
u
b
s
y
s
tem
.
T
h
e
d
y
n
am
ic
m
o
d
el
o
f
t
h
e
p
o
s
itio
n
s
u
b
-
s
y
s
tem
(
2
)
c
an
b
e
m
o
d
if
ied
as
(
2
3
)
:
̈
=
1
[
0
0
1
]
−
[
0
0
1
]
=
1
(
2
3
)
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
.
5
,
Octo
b
e
r
20
25
:
4
5
4
2
-
4
5
5
4
4548
wh
er
e
=
[
0
0
1
]
−
[
0
0
1
]
.
Fo
r
d
ev
el
o
p
in
g
th
e
co
n
tr
o
l
d
esig
n
o
f
t
h
e
p
o
s
itio
n
s
u
b
-
s
y
s
tem
(
2
3
)
,
th
e
tr
ac
k
i
n
g
er
r
o
r
m
o
d
el
is
n
ec
ess
ar
y
to
m
ad
e
with
th
e
tim
e
in
v
ar
ian
t
m
o
d
el
as
s
h
o
w
n
in
(
7
)
.
T
h
er
ef
o
r
e,
th
e
s
tate
v
ar
iab
les
v
ec
to
r
=
(
,
̇
,
,
̇
,
,
̇
)
∈
ℝ
6
is
a
p
p
lied
to
r
ed
u
ce
th
e
o
r
d
er
o
f
(
2
3
)
.
He
n
ce
,
th
e
m
o
d
el
(
2
3
)
ca
n
b
e
tr
a
n
s
f
o
r
m
e
d
in
to
th
e
f
ir
s
t o
r
d
er
s
y
s
tem
as
(
2
4
)
:
̇
=
+
(
2
4
)
wh
er
e
=
(
,
,
)
∈
ℝ
6
×
6
,
=
[
0
1
0
0
]
an
d
=
[
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
]
.
Mo
r
eo
v
er
,
d
u
e
to
th
e
tim
e
v
a
r
y
in
g
o
f
th
e
d
esire
d
tr
ajec
to
r
y
(
)
=
[
(
)
,
(
)
,
(
)
]
∈
ℝ
3
,
to
tr
an
s
f
o
r
m
th
e
tr
ac
k
in
g
er
r
o
r
m
o
d
el
o
f
th
e
p
o
s
itio
n
s
u
b
-
s
y
s
tem
(
2
4
)
in
to
th
e
tim
e
in
v
a
r
ian
t
m
o
d
el
(
7
)
,
it
is
n
ec
ess
ar
y
to
u
tili
ze
th
e
f
o
llo
wi
n
g
ass
u
m
p
tio
n
s
:
1
.
T
h
e
d
esire
d
tr
ajec
to
r
y
(
)
=
[
(
)
,
(
)
,
(
)
]
∈
ℝ
3
is
b
o
u
n
d
e
d
an
d
its
tim
e
d
er
iv
ativ
e
(
)
is
th
e
L
ip
s
ch
itz
f
u
n
ctio
n
.
2
.
T
h
e
r
ef
er
en
ce
v
ec
to
r
=
[
,
̇
,
,
̇
,
,
̇
]
∈
ℝ
6
ca
n
b
e
co
m
p
letely
ex
p
r
ess
ed
as
(
2
5
)
,
(
)
=
(
)
(
2
5
)
T
h
er
ef
o
r
e,
in
th
e
v
iew
o
f
(
2
4
)
an
d
(
2
5
)
,
it
o
b
tain
s
th
e
tim
e
in
v
ar
ian
t m
o
d
el
(
7
)
as:
=
[
̇
̇
]
=
[
−
0
6
,
6
]
+
[
0
6
,
3
]
wh
er
e
=
−
,
=
[
]
(
2
6
)
T
h
e
tr
ac
k
in
g
co
s
t f
u
n
ctio
n
is
m
o
d
if
ied
as
(
2
7
)
:
(
(
)
)
=
∫
−
(
−
)
∞
×
[
(
)
(
)
+
(
)
(
)
]
(
2
7
)
wh
er
e
=
[
0
6
,
6
0
6
,
6
0
6
,
6
]
an
d
∈
ℝ
6
×
6
,
∈
ℝ
3
×
3
ar
e
s
y
m
m
etr
ic
m
atr
ices w
ith
p
o
s
itiv
e
d
ef
in
iten
ess
.
No
t
e
th
at,
th
e
ter
m
−
(
−
)
is
ad
d
ed
to
(
2
7
)
f
o
r
e
n
s
u
r
in
g
th
e
f
in
ite
c
o
s
t
f
u
n
ctio
n
wh
ile
=
[
]
d
o
es
n
o
t
co
n
v
er
g
e
to
ze
r
o
as
tim
e
ap
p
r
o
ac
h
es
in
f
in
ity
.
Acc
o
r
d
in
g
t
o
(
1
7
)
-
(
2
1
)
an
d
th
e
o
f
f
-
p
o
licy
tech
n
iq
u
e
[
3
]
,
th
e
d
ata
-
d
r
iv
e
n
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
to
d
ev
elo
p
th
e
p
o
s
itio
n
co
n
tr
o
ller
as f
o
llo
ws:
Alg
o
r
ith
m
1
.
Data
-
d
r
iv
e
n
alg
o
r
ith
m
f
o
r
p
o
s
itio
n
c
o
n
tr
o
ller
1
.
I
n
itializatio
n
:
E
m
p
lo
y
i
n
g
th
e
s
tab
ilizin
g
p
o
licy
0
(
)
an
d
th
e
ad
d
itio
n
al
n
o
is
e
(
)
to
s
ati
s
f
y
PE
co
n
d
itio
n
.
C
o
llectin
g
th
e
in
p
u
t
-
o
u
tp
u
t
d
ata
in
th
e
q
u
ad
r
o
to
r
s
y
s
tem
an
d
estab
lis
h
in
g
th
e
th
r
esh
o
ld
2
.
Po
licy
ev
alu
atio
n
:
B
ased
o
n
th
e
co
n
tr
o
l
in
p
u
t
(
)
=
̂
(
)
+
an
d
th
e
co
n
tr
o
l
p
o
licy
̂
(
)
,
we
s
o
lv
e
th
e
(
2
8
)
to
f
in
d
s
im
u
ltan
eo
u
s
ly
+
1
(
)
an
d
+
1
(
)
:
+
1
(
(
+
)
)
−
+
1
(
(
)
)
=
−
∫
−
(
−
−
)
(
(
)
(
)
+
(
̂
)
̂
+
+
2
̂
)
;
̂
(
)
=
(
)
+
(
)
(
2
8
)
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
Dis
co
u
n
t fa
cto
r
-
b
a
s
ed
d
a
ta
-
d
r
iven
r
ein
fo
r
ce
men
t le
a
r
n
in
g
ca
s
ca
d
e
co
n
tr
o
l
…
(
N
g
o
c
Tr
u
n
g
Da
n
g
)
4549
3
.
Po
licy
im
p
r
o
v
em
en
t
:
Ob
ta
in
th
e
co
n
tr
o
l
p
o
licy
(
)
=
+
1
(
)
,
→
(
+
1
)
an
d
g
o
to
s
tep
2
u
n
til
‖
+
1
−
‖
<
.
I
n
th
e
Alg
o
r
ith
m
1
,
th
e
s
o
lu
tio
n
o
f
B
ellm
an
eq
u
atio
n
(
2
4
)
is
im
p
r
o
v
ed
b
y
d
ata
co
llectio
n
b
y
th
e
f
o
llo
win
g
m
o
d
if
icatio
n
:
+
1
(
(
+
)
)
−
+
1
(
(
)
)
=
−
∫
(
(
)
(
)
+
(
)
(
(
)
)
(
(
)
)
)
+
+
∫
+
+
1
(
(
)
)
+
2
∫
(
+
1
(
(
)
)
)
+
(
(
)
)
(
2
9
)
Af
ter
ac
h
iev
i
n
g
t
h
e
p
o
s
itio
n
co
n
tr
o
l
s
ig
n
al
in
th
e
q
u
a
d
r
o
to
r
co
n
tr
o
l
s
tr
u
ctu
r
e
as
s
h
o
wn
i
n
Fig
u
r
e
2
,
we
p
r
o
ce
ed
t
o
co
m
p
u
te
th
e
r
e
f
er
en
ce
o
f
attitu
d
e
co
n
tr
o
l
s
ch
em
e
[
]
as
f
o
llo
ws.
Acc
o
r
d
in
g
t
o
=
[
0
0
1
]
−
[
0
0
1
]
,
it f
o
llo
ws th
at:
+
[
0
0
1
]
=
[
(
)
(
)
+
(
)
(
)
(
)
(
)
(
)
(
)
−
(
)
(
)
(
)
(
)
]
(
3
0
)
B
y
s
ettin
g
th
e
y
aw
an
g
le
r
ef
er
en
ce
(
)
as a
co
n
s
tan
t n
u
m
b
er
to
s
y
n
ch
r
o
n
ize
i
n
p
r
ac
tical
ap
p
licatio
n
s
,
b
ased
o
n
(
3
0
)
,
we
ca
n
ac
h
iev
e
th
e
d
e
s
ir
ed
,
,
as
(
3
1
)
:
=
(
+
)
(
)
(
)
=
(
−
)
,
=
(
+
)
.
(
3
1
)
2
.
3
.
Da
t
a
-
driv
en
RL
ba
s
ed
a
t
t
it
ud
e
co
ntr
o
ller
I
n
th
is
p
ar
t,
a
d
ata
-
d
r
iv
en
R
L
-
b
ased
attitu
d
e
co
n
tr
o
l
law
is
s
im
ilar
ly
d
esig
n
ed
as
ab
o
v
e
to
o
b
tain
th
e
in
p
u
t
s
ig
n
als
f
o
r
s
atis
f
y
in
g
o
p
tim
al
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
with
th
e
d
esire
d
tr
ajec
to
r
y
(
3
1
)
.
T
h
e
attitu
d
e
d
y
n
am
ic
m
o
d
el
(
2
)
ca
n
b
e
r
ew
r
itten
b
y
(
3
2
)
:
̈
=
−
1
−
−
1
(
,
̇
)
̇
(
3
2
)
B
y
co
n
s
id
er
in
g
th
e
attitu
d
e
s
tate
v
ec
to
r
=
[
,
̇
,
,
̇
,
,
̇
]
an
d
r
ef
er
r
i
n
g
to
th
e
attitu
d
e
co
n
t
r
o
l
s
tr
u
ctu
r
e
illu
s
tr
ated
in
Fig
u
r
e
2
,
th
e
d
esig
n
ap
p
r
o
ac
h
m
ir
r
o
r
s
th
e
p
o
s
itio
n
co
n
tr
o
l
s
tr
ateg
y
d
escr
ib
ed
in
s
u
b
s
ec
tio
n
2
.
3
.
B
ased
o
n
(
3
2
)
,
th
e
au
g
m
en
te
d
attitu
d
e
d
y
n
am
ics ca
n
b
e
r
e
f
o
r
m
u
lated
as
(
3
3
)
:
=
[
̇
̇
]
=
[
−
0
6
,
6
]
+
[
0
6
,
3
]
(
3
3
)
Acc
o
r
d
in
g
ly
,
th
e
attitu
d
e
c
o
n
tr
o
l stra
teg
y
is
s
u
m
m
ar
ized
in
t
h
e
A
lg
o
r
ith
m
2
:
Alg
o
r
ith
m
2
.
Data
-
d
r
iv
e
n
R
L
b
ased
attitu
d
e
co
n
tr
o
l sch
em
e
1
.
I
n
itializatio
n
:
E
m
p
lo
y
in
g
th
e
s
tab
ilizin
g
p
o
licy
0
(
)
an
d
t
h
e
ad
d
itio
n
al
n
o
is
e
(
)
to
s
atis
f
y
PE
co
n
d
itio
n
.
C
o
llectin
g
th
e
in
p
u
t
-
o
u
tp
u
t
d
ata
o
f
th
e
q
u
ad
r
o
t
o
r
s
y
s
tem
.
2
.
Po
licy
ev
al
u
atio
n
:
B
ased
o
n
th
e
co
n
tr
o
l
s
ig
n
al
(
)
=
̂
(
)
+
an
d
th
e
co
n
tr
o
l
p
o
licy
(
)
,
we
s
o
lv
e
th
e
(
3
4
)
to
f
in
d
s
im
u
ltan
eo
u
s
ly
+
1
(
)
an
d
+
1
(
)
:
+
1
(
(
+
)
)
−
+
1
(
(
)
)
=
−
∫
(
(
)
(
)
+
(
)
(
(
)
)
(
(
)
)
)
+
+
∫
+
+
1
(
(
)
)
+
2
∫
(
+
1
(
(
)
)
)
+
(
(
)
)
(
3
4
)
3
.
Po
licy
im
p
r
o
v
e
m
en
t
:
Ob
tain
th
e
co
n
tr
o
l
p
o
licy
(
)
=
+
1
(
)
,
→
(
+
1
)
an
d
g
o
to
s
tep
2
u
n
til
‖
+
1
−
‖
<
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
.
5
,
Octo
b
e
r
20
25
:
4
5
4
2
-
4
5
5
4
4550
3
.
T
wo
d
ata
-
d
r
iv
en
R
L
alg
o
r
ith
m
s
in
co
r
p
o
r
atin
g
a
d
is
co
u
n
t
f
ac
to
r
ar
e
p
r
o
p
o
s
ed
f
o
r
th
e
q
u
ad
r
o
to
r
,
ad
d
r
ess
in
g
b
o
th
t
h
e
attitu
d
e
a
n
d
p
o
s
itio
n
s
u
b
s
y
s
tem
s
.
T
h
is
wo
r
k
ex
ten
d
s
th
e
s
tu
d
y
i
n
[
3
7
]
,
wh
ich
f
o
cu
s
e
d
s
o
lely
o
n
R
L
co
n
tr
o
l f
o
r
th
e
at
titu
d
e
s
u
b
s
y
s
tem
with
o
u
t c
o
n
s
id
er
in
g
a
d
is
co
u
n
t f
ac
to
r
.
3.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
I
n
th
is
s
ec
tio
n
,
we
u
s
e
th
e
ex
am
p
le
o
f
q
u
ad
r
o
to
r
to
illu
s
tr
ate
th
e
p
r
o
p
o
s
ed
d
ata
R
L
alg
o
r
ith
m
with
th
e
f
o
llo
win
g
p
ar
am
eter
as f
o
l
lo
ws:
=
2
.
0
(
)
,
=
1
(
2
)
,
=
1
(
2
)
,
=
9
.
8
(
2
)
,
=
0
.
2
(
)
,
=
1
0
−
3
(
5
.
1
,
5
.
1
,
5
.
2
)
(
.
2
)
.
T
h
e
d
esire
d
tr
ajec
to
r
y
o
f
th
e
p
o
s
itio
n
co
n
tr
o
ller
is
ch
o
s
en
as:
(
)
=
[
0
.
5
,
0
.
5
,
1
.
5
+
]
,
it
ca
n
b
e
o
b
tain
ed
th
at
t
h
e
(
2
5
)
is
g
u
a
r
a
n
teed
with
m
atr
ix
=
[
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
]
Mo
r
eo
v
er
,
th
e
co
s
t
f
u
n
ctio
n
u
tili
ze
s
th
e
weig
h
t
m
atr
ice
s
=
100
6
,
=
3
,
=
100
6
,
=
3
,
=
0
.
01
,
=
0
.
01
,
an
d
a
d
is
co
u
n
t
f
ac
t
o
r
o
f
=
0
.
01
.
Du
r
in
g
th
e
in
itial
d
ata
co
llectio
n
p
h
ase
[
1
7
]
,
two
p
r
o
p
o
r
tio
n
al
-
d
e
r
iv
at
iv
e
(
PD
)
co
n
tr
o
ller
s
ar
e
ap
p
lied
to
th
e
p
o
s
itio
n
a
n
d
attitu
d
e
l
o
o
p
s
to
g
ath
er
d
ata
f
o
r
t
h
e
lear
n
in
g
p
r
o
ce
s
s
.
T
o
en
s
u
r
e
th
e
p
er
s
is
ten
ce
o
f
e
x
citatio
n
(
PE)
co
n
d
itio
n
s
r
eq
u
ir
e
d
f
o
r
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
,
n
o
is
e
s
ig
n
als
d
ef
in
ed
as
=
∑
0
100
=
1
.
01
(
)
an
d
=
∑
0
500
=
1
.
002
(
)
,
wh
er
e
ea
ch
is
r
an
d
o
m
l
y
s
elec
ted
with
in
[
−1
0
0
,
1
0
0
]
,
a
r
e
in
jecte
d
in
to
th
e
p
o
s
itio
n
a
n
d
attitu
d
e
co
n
tr
o
l
in
p
u
ts
,
r
esp
ec
tiv
ely
.
Fo
r
th
e
c
r
itic
an
d
ac
to
r
n
e
u
r
al
n
etwo
r
k
s
,
s
e
co
n
d
-
o
r
d
er
an
d
f
ir
s
t
-
o
r
d
er
p
o
ly
n
o
m
ial
ac
tiv
atio
n
f
u
n
ctio
n
s
ar
e
em
p
l
o
y
ed
,
r
esp
e
ctiv
ely
.
I
t
is
wo
r
t
h
n
o
tin
g
t
h
at
th
e
tr
ac
k
i
n
g
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
d
ata
-
d
r
iv
en
R
L
-
b
ased
p
o
s
itio
n
a
n
d
attitu
d
e
co
n
tr
o
ller
s
is
ill
u
s
tr
ated
in
Fig
u
r
es
3
to
7
,
d
em
o
n
s
tr
atin
g
f
ast
co
n
v
er
g
en
ce
with
o
n
ly
f
o
u
r
it
er
atio
n
s
r
eq
u
ir
ed
f
o
r
th
e
alg
o
r
ith
m
weig
h
ts
to
s
tab
ilize.
Mo
r
eo
v
er
,
th
e
p
o
s
itio
n
tr
ac
k
in
g
er
r
o
r
s
co
n
v
er
g
e
t
o
ze
r
o
with
in
4
s
ec
o
n
d
s
,
w
h
ile
th
e
attitu
d
e
tr
ac
k
in
g
er
r
o
r
s
r
ea
ch
ze
r
o
in
ap
p
r
o
x
im
ately
0
.
5
s
ec
o
n
d
s
,
as
illu
s
tr
ated
in
F
ig
u
r
es
3
an
d
5
,
r
esp
ec
tiv
el
y
.
Fu
r
t
h
er
m
o
r
e
,
Fig
u
r
e
7
d
em
o
n
s
tr
ates
th
e
q
u
ad
r
o
to
r
’
s
t
r
ajec
to
r
y
tr
ac
k
in
g
p
er
f
o
r
m
a
n
c
e
r
elativ
e
to
a
p
r
ed
ef
i
n
ed
r
ef
er
en
ce
p
ath
,
s
h
o
win
g
th
at
th
e
q
u
ad
r
o
to
r
’
s
p
o
s
itio
n
clo
s
ely
f
o
llo
ws
th
e
r
ef
er
en
ce
tr
ajec
to
r
y
with
h
ig
h
ac
cu
r
ac
y
.
Fu
r
th
e
r
m
o
r
e,
to
ev
alu
ate
th
e
e
f
f
ec
tiv
en
ess
o
f
th
e
tr
ac
k
in
g
p
e
r
f
o
r
m
an
ce
,
n
u
m
er
o
u
s
p
er
f
o
r
m
a
n
ce
in
d
ices,
in
clu
d
in
g
t
h
e
in
teg
r
al
o
f
ab
s
o
lu
te
er
r
o
r
(
I
AE
)
an
d
t
h
e
in
teg
r
al
o
f
ab
s
o
lu
te
tim
e
-
weig
h
ted
er
r
o
r
(
I
AT
E
)
,
ar
e
p
r
esen
ted
as
s
h
o
wn
in
T
ab
le
2
.
Fig
u
r
e
3
.
T
h
e
p
o
s
itio
n
t
r
ac
k
in
g
er
r
o
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
-
8
7
0
8
Dis
co
u
n
t fa
cto
r
-
b
a
s
ed
d
a
ta
-
d
r
iven
r
ein
fo
r
ce
men
t le
a
r
n
in
g
ca
s
ca
d
e
co
n
tr
o
l
…
(
N
g
o
c
Tr
u
n
g
Da
n
g
)
4551
Fig
u
r
e
4
.
T
h
e
co
n
v
er
g
e
n
ce
o
f
tr
ain
in
g
weig
h
ts
in
p
o
s
itio
n
co
n
tr
o
ller
Fig
u
r
e
5
.
T
h
e
tr
ac
k
in
g
o
f
o
r
ie
n
tatio
n
an
g
les
Fig
u
r
e
6
.
T
h
e
co
n
v
er
g
e
n
ce
o
f
tr
ain
in
g
weig
h
ts
in
attitu
d
e
c
o
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.