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T
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[
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5
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u
r
bo
-
alter
n
ato
r
s
is
th
a
t
th
e
o
p
er
atin
g
n
et
h
ea
d
m
u
s
t
s
atis
f
y
th
e
r
eq
u
ir
e
m
e
n
ts
f
o
r
ac
ce
p
tab
le
en
er
g
y
co
n
v
er
s
i
o
n
b
y
th
e
t
u
r
b
in
e
.
T
h
er
ef
o
r
e,
th
e
o
p
ti
m
al
co
n
tr
o
l
p
r
o
b
lem
s
o
lv
ed
i
n
t
h
is
w
o
r
k
i
s
th
e
d
eter
m
i
n
atio
n
o
f
th
e
b
e
s
t
co
n
tr
o
l
v
ec
to
r
a
n
d
r
esu
lti
n
g
s
tate
tr
a
j
ec
to
r
ies
w
h
i
ch
m
in
i
m
ize
s
ce
r
tai
n
p
er
f
o
r
m
an
ce
i
n
d
ex
,
s
u
b
j
ec
t
to
s
y
s
te
m
co
n
s
tr
ain
ts
.
I
n
th
i
s
ca
s
e,
th
e
o
p
ti
m
al
co
n
tr
o
l
p
r
o
b
le
m
r
esu
lts
,
w
h
er
eb
y
a
co
n
t
r
o
l
s
ig
n
a
l
is
d
esire
d
th
at
w
i
ll
f
o
r
ce
th
e
r
eser
v
o
ir
h
ea
d
at
J
HE
P
S
to
m
o
v
e
f
r
o
m
an
i
n
itia
l
p
o
in
t
to
th
e
d
esi
r
ed
p
o
in
t
i
n
a
f
i
n
ite
t
i
m
e
an
d
s
u
b
j
ec
t
to
co
n
s
tr
ain
t
s
i
m
p
o
s
ed
b
y
th
e
s
y
s
te
m
d
y
n
a
m
ics.
U
n
f
o
r
tu
n
a
t
ely
,
m
an
y
p
r
o
b
l
em
s
th
a
t
a
r
e
r
o
o
t
e
d
in
n
o
n
li
n
ea
r
o
p
t
im
a
l
c
o
n
t
r
o
l
th
e
o
r
y
d
o
n
o
t
h
av
e
c
o
m
p
u
t
a
b
l
e
s
o
lu
ti
o
n
s
o
r
th
ey
h
av
e
s
o
lu
t
i
o
n
s
th
a
t
m
ay
b
e
o
b
t
a
i
n
e
d
o
n
ly
w
i
th
a
g
r
e
at
d
e
a
l
o
f
c
o
m
p
u
ti
n
g
e
f
f
o
r
t
[
1
2
,
1
3
]
.
T
h
e
s
o
l
u
ti
o
n
v
ia
a
n
a
ly
ti
c
al
m
ea
n
s
a
ls
o
s
e
em
s
n
o
t
f
e
as
i
b
l
e
ex
c
e
p
t
b
y
n
u
m
e
r
i
ca
l
m
ea
n
s
.
Nu
m
e
r
ic
a
l
s
o
lu
t
i
o
n
s
t
o
o
p
t
im
a
l
c
o
n
t
r
o
l
p
r
o
b
l
em
s
a
r
e
e
ith
e
r
th
r
o
u
g
h
d
ir
e
c
t
o
r
i
n
d
i
r
e
c
t
m
eth
o
d
s
.
I
n
th
e
d
i
r
e
ct
m
e
th
o
d
s
,
t
h
e
in
f
in
i
t
ely
d
im
en
s
i
o
n
a
l
s
t
a
te
a
n
d
c
o
n
t
r
o
ls
a
r
e
d
i
s
c
r
et
i
z
e
d
.
T
h
e
in
d
i
r
e
c
t
m
et
h
o
d
a
p
p
li
e
s
c
a
l
cu
lu
s
o
f
v
a
r
i
a
ti
o
n
t
o
s
e
t
u
p
n
e
c
e
s
s
a
r
y
c
o
n
d
it
i
o
n
s
th
a
t
m
u
s
t
b
e
s
at
i
s
f
i
e
d
b
y
t
h
e
o
p
tim
al
c
o
n
t
r
o
l
.
C
a
l
cu
lu
s
o
f
v
a
r
ia
t
i
o
n
,
t
o
g
e
th
e
r
w
ith
Po
n
t
r
y
ag
i
n
’
s
m
in
im
u
m
p
r
i
n
c
ip
l
e
s
a
r
e
u
s
e
d
t
o
s
e
tu
p
o
p
t
im
a
l
i
ty
c
o
n
d
i
ti
o
n
s
.
T
h
es
e
c
o
n
d
i
tio
n
s
p
r
o
d
u
c
e
o
p
t
im
al
c
o
n
t
r
o
l
ca
n
o
n
ic
a
l
e
q
u
a
ti
o
n
s
s
u
ch
th
a
t
th
e
i
r
s
o
lu
t
i
o
n
en
s
u
r
es
th
at
a
n
o
p
tim
u
m
p
o
in
t
h
a
s
b
e
en
r
ea
c
h
e
d
[
1
4
,
15]
.
T
h
e
in
d
ir
ec
t
ap
p
r
o
ac
h
lead
s
to
a
n
o
n
lin
ea
r
t
w
o
-
p
o
in
t
b
o
u
n
d
a
r
y
-
v
al
u
e
p
r
o
b
lem
.
T
h
e
co
n
tr
o
l
task
t
h
en
r
e
d
u
c
es
t
o
th
e
s
o
lu
t
i
o
n
o
f
a
b
o
u
n
d
a
r
y
v
a
lu
e
p
r
o
b
l
em
.
T
h
e
r
e
ar
e
d
i
f
f
e
r
en
t
a
p
p
r
o
a
ch
e
s
w
i
th
a
s
s
o
c
i
a
te
d
a
d
v
a
n
t
ag
e
s
a
n
d
d
i
s
a
d
v
an
ta
g
e
s
.
I
n
a
l
l
th
e
s
o
l
u
ti
o
n
te
ch
n
i
q
u
es
,
an
in
i
ti
a
l
g
u
es
s
is
u
s
e
d
t
o
o
b
t
a
in
a
s
o
lu
tio
n
in
w
h
i
ch
o
n
e
o
r
m
o
r
e
o
f
th
e
n
e
ce
s
s
a
r
y
o
p
t
im
al
ity
c
o
n
d
i
t
i
o
n
s
a
r
e
n
o
t
s
a
t
is
f
i
e
d
.
T
h
e
s
o
lu
ti
o
n
is
th
en
u
s
e
d
t
o
a
d
ju
s
t
th
e
in
it
i
a
l
g
u
e
s
s
t
o
m
ak
e
th
e
n
ex
t
s
o
lu
ti
o
n
c
o
m
e
c
l
o
s
e
r
t
o
s
at
is
f
y
in
g
a
l
l
th
e
n
e
c
e
s
s
a
r
y
c
o
n
d
i
t
i
o
n
s
.
I
f
th
e
s
t
ep
s
a
r
e
r
e
p
e
a
te
d
an
d
t
h
e
i
t
e
r
at
iv
e
p
r
o
c
e
d
u
r
e
c
o
n
v
e
r
g
e
s
,
th
e
n
e
c
ess
a
r
y
c
o
n
d
it
i
o
n
s
w
il
l
ev
en
tu
a
lly
b
e
r
ea
ch
e
d
[
1
6
-
1
8
]
.
Ma
n
y
au
t
h
o
r
s
h
ad
p
r
o
p
o
s
ed
m
eth
o
d
s
o
f
s
o
lv
in
g
a
n
o
p
ti
m
a
l c
o
n
tr
o
l p
r
o
b
lem
,
t
h
ese
m
e
th
o
d
s
ca
n
b
e
i
n
th
e
f
o
r
m
o
f
n
o
n
li
n
ea
r
p
r
o
g
r
am
m
in
g
,
s
h
o
o
tin
g
m
et
h
o
d
,
f
o
r
w
ar
d
b
ac
k
w
ar
d
s
w
ee
p
,
s
teep
est
d
escen
t,
co
n
j
u
g
ate
g
r
ad
ien
t,
d
y
n
a
m
ic
p
r
o
g
r
a
m
m
i
n
g
,
t
h
e
v
ar
iatio
n
o
f
ex
t
er
n
als,
q
u
asi
-
li
n
ea
r
izatio
n
,
g
r
ad
ien
t
p
r
o
j
ec
tio
n
,
co
llo
ca
tio
n
,
etc
[
1
9
,
20]
.
T
h
er
e
h
a
s
b
ee
n
n
o
p
er
f
ec
t
m
et
h
o
d
as
ea
c
h
h
as
i
ts
o
w
n
ad
v
a
n
ta
g
es
an
d
d
is
ad
v
an
ta
g
es.
Fo
r
ex
a
m
p
le,
t
h
e
f
o
r
w
ar
d
-
b
ac
k
w
ar
d
s
w
ee
p
(
FB
S)
w
o
r
k
s
o
n
l
y
i
f
t
h
e
L
ip
s
c
h
itz
co
n
s
ta
n
ts
f
o
r
th
e
s
tate,
co
s
tate
an
d
co
n
tr
o
l
v
ar
iab
les
ar
e
s
m
all
en
o
u
g
h
o
r
th
e
tim
e
in
ter
v
al
is
v
er
y
s
m
a
ll.
L
i
k
e
w
i
s
e,
th
e
c
o
v
er
g
e
n
ce
o
f
th
e
s
h
o
o
tin
g
m
et
h
o
d
d
ep
en
d
s
o
n
th
e
n
u
m
er
ical
p
r
o
ce
d
u
r
e
an
d
th
e
in
itia
l
d
ata
s
et,
else
th
er
e
w
il
l b
e
n
o
s
o
lu
tio
n
[
2
1
]
.
T
h
e
m
u
l
tip
le
s
h
o
o
tin
g
a
n
d
p
ar
allel
s
h
o
o
tin
g
tec
h
n
iq
u
es
w
er
e
ea
r
lier
ex
p
lo
r
ed
in
[
2
2
-
27]
b
y
r
esetti
n
g
th
e
p
r
o
b
le
m
an
d
i
n
cr
ea
s
i
n
g
th
e
s
in
g
le
i
n
itia
l v
a
l
u
e
p
r
o
b
le
m
t
o
a
f
a
m
i
l
y
o
f
in
itial
v
al
u
e
p
r
o
b
le
m
s
co
n
f
ig
u
r
ed
s
o
as
to
li
m
it
t
h
e
e
f
f
ec
t
o
f
th
e
g
r
o
w
t
h
o
f
co
m
p
u
tatio
n
a
l
er
r
o
r
s
.
T
h
e
o
u
tco
m
e
r
esu
lted
i
n
a
m
eth
o
d
th
at
i
n
cr
ea
s
ed
th
e
n
u
m
b
er
o
f
g
u
es
s
es
w
h
ic
h
w
er
e
m
u
ch
f
e
w
er
th
a
n
th
e
m
et
h
o
d
s
th
at
d
ep
en
d
ed
o
n
v
ar
i
atio
n
al
an
d
o
th
er
ap
p
r
o
x
im
a
tio
n
m
et
h
o
d
s
t
h
at
f
o
r
th
e
s
a
m
e
ac
c
u
r
ac
y
m
a
y
i
n
v
o
l
v
e
t
h
e
s
o
lu
tio
n
o
f
lar
g
e
lin
ea
r
o
r
n
o
n
li
n
ea
r
eq
u
atio
n
s
t
h
at
h
a
v
e
d
i
m
e
n
s
io
n
alit
y
s
e
v
er
al
o
r
d
er
s
o
f
m
ag
n
it
u
d
e
w
h
en
co
m
p
ar
ed
w
ith
th
e
co
r
r
esp
o
n
d
in
g
s
h
o
o
tin
g
m
eth
o
d
.
T
h
e
m
et
h
o
d
w
as
ap
p
lied
s
u
cc
es
s
f
u
l
l
y
i
n
t
h
e
m
o
d
elin
g
o
f
d
is
tr
ib
u
ted
p
ar
a
m
eter
s
y
s
te
m
s
a
n
d
p
r
o
v
ed
to
b
e
v
er
y
ef
f
icie
n
t,
ac
cu
r
ate
an
d
f
ast.
T
h
e
p
r
o
g
r
ess
iv
e
d
o
m
ai
n
ex
p
a
n
s
io
n
m
et
h
o
d
(
P
DE
M)
p
r
o
p
o
s
ed
in
t
h
i
s
p
ap
er
is
a
n
o
th
er
m
o
d
if
icatio
n
s
h
o
o
tin
g
m
et
h
o
d
.
I
t
is
le
s
s
co
m
p
u
ta
tio
n
al
a
n
d
f
ea
s
ib
le
i
n
s
o
l
v
i
n
g
th
e
o
p
ti
m
al
co
n
tr
o
l p
r
o
b
lem
at
J
HE
P
S.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
s
o
lu
tio
n
to
an
o
p
tim
a
l
co
n
tr
o
l
p
r
o
b
lem
r
eq
u
ir
es
a
p
r
o
p
er
m
o
d
el
o
f
th
e
s
y
s
te
m
d
y
n
a
m
ics
i
n
th
e
f
o
r
m
o
f
a
d
i
f
f
er
en
t
ial
eq
u
atio
n
o
r
d
if
f
er
en
ce
eq
u
atio
n
.
A
s
u
itab
le
p
er
f
o
r
m
a
n
ce
in
d
e
x
w
ith
it
s
as
s
o
ciate
d
co
n
s
tr
ain
ts
m
u
s
t
b
e
d
ev
elo
p
e
d
;
th
er
e
s
h
o
u
ld
also
b
e
a
n
u
m
er
ical
tech
n
iq
u
e
f
o
r
s
o
lv
i
n
g
th
e
m
o
d
el
eq
u
atio
n
an
d
a
p
r
o
ce
d
u
r
e
f
o
r
s
o
lv
in
g
th
e
r
esu
lti
n
g
b
o
u
n
d
ar
y
v
al
u
e
p
r
o
b
lem
.
T
h
e
s
y
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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3
-
6930
T
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Evaluation Warning : The document was created with Spire.PDF for Python.
T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
18
,
No
.
4
,
A
u
g
u
s
t 2
0
2
0
:
2
0
6
3
-
2
0
6
9
2066
2
.
1
.
Co
m
p
uta
t
io
n o
f
t
he
o
pti
m
a
l c
o
ntr
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l by
a
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a
in e
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pa
n
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et
ho
d
(
P
DE
M
)
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(
2
1
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d
(
2
2
)
p
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asis
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e
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tate
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ied
at
th
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itia
l
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m
e.
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h
e
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t
b
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ar
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v
al
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(
T
PB
VP
)
h
as
attr
ac
ted
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n
s
id
er
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le
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t
h
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.
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m
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f
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u
n
d
in
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lties
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s
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g
tech
n
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t
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g
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ial
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n
ed
b
y
o
n
e
o
f
s
e
v
er
al
p
o
s
s
ib
ilit
ies,
th
e
n
at
u
r
e
o
f
th
e
co
-
s
tate
eq
u
atio
n
s
lead
to
a
r
ap
id
g
r
o
w
th
o
f
t
h
e
in
itial
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al
u
e
p
r
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b
lem
t
h
at
t
h
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co
m
p
u
ted
v
al
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es
s
o
o
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lo
s
e
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elatio
n
s
h
ip
w
it
h
th
e
p
r
o
b
lem
s
in
ce
er
r
o
r
s
in
co
m
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u
tat
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n
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ex
p
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m
p
li
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y
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e
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y
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te
m
.
T
h
e
P
DE
M
is
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o
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h
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m
o
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if
ic
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n
p
r
o
p
o
s
ed
an
d
p
r
e
-
test
ed
b
y
[
2
6
]
,
w
h
er
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y
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n
s
tead
o
f
p
ar
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o
n
i
n
g
th
e
d
o
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ai
n
[
0
,
T
]
,
th
e
f
in
al
d
o
m
a
in
b
o
u
n
d
ar
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i
s
ad
j
u
s
ted
i
n
s
u
ch
a
m
a
n
n
er
th
a
t
th
e
in
i
ti
al
g
u
ess
r
e
s
u
l
ts
s
till
r
etain
a
s
e
m
b
lan
ce
w
i
th
t
h
e
o
r
ig
in
a
l
p
r
o
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lem
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n
d
th
e
g
r
o
w
i
n
g
eq
u
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n
s
ar
e
b
o
u
n
d
s
o
th
a
t
th
e
co
r
r
ec
t
in
itial
va
lu
e
p
r
o
b
le
m
is
s
o
lv
ed
ass
u
m
i
n
g
t
h
e
p
s
eu
d
o
-
d
o
m
ai
n
[
0
,
]
w
h
er
e
is
d
eter
m
i
n
ed
o
n
th
e
f
l
y
.
I
n
th
e
n
e
x
t
iter
atio
n
,
th
e
in
i
tial
g
u
e
s
s
f
o
r
th
e
m
is
s
i
n
g
b
o
u
n
d
ar
y
co
n
d
i
tio
n
as
s
u
m
es
th
e
v
al
u
e
t
h
at
w
o
u
ld
h
a
v
e
s
o
l
v
ed
th
e
p
r
o
b
lem
f
o
r
th
e
p
s
eu
d
o
-
d
o
m
a
in
.
Me
an
w
h
i
le,
th
e
p
r
o
b
l
e
m
is
s
o
lv
ed
b
e
y
o
n
d
ag
ain
u
n
t
il
th
e
g
r
o
w
t
h
b
eg
in
s
to
ca
u
s
e
co
n
ce
r
n
.
T
h
e
n
e
w
+
1
is
th
u
s
d
ef
i
n
ed
an
d
a
n
e
w
co
r
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ec
tio
n
m
ad
e
s
o
th
at
t
h
e
co
r
r
esp
o
n
d
in
g
p
r
o
b
lem
is
s
o
lv
ed
.
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
=
in
w
h
ich
ca
s
e
t
h
e
v
al
u
e
o
f
th
e
i
n
itial
g
u
e
s
s
co
n
v
er
g
e
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to
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e
co
r
r
ec
t in
itia
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g
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e
s
s
f
o
r
th
e
p
r
o
b
lem
.
T
h
e
p
r
o
ce
d
u
r
e
is
p
r
esen
ted
in
t
h
e
f
lo
w
c
h
ar
t o
f
Fi
g
u
r
e
2
.
Fig
u
r
e
2
.
Flo
w
c
h
ar
t f
o
r
th
e
s
o
lu
tio
n
o
f
o
p
ti
m
al
co
n
tr
o
l c
an
o
n
ical
eq
u
atio
n
s
b
y
a
P
DE
M
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
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o
m
p
u
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l
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o
n
tr
o
l
A
p
r
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g
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o
ma
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ex
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o
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l p
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(
Ola
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g
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n
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iyi
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2067
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
I
t
is
b
etter
to
d
ef
i
n
e
a
p
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ese
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t
atio
n
f
o
r
m
at
t
h
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lects
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m
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o
r
tan
t
f
ea
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u
r
es
o
f
t
h
e
tr
aj
ec
to
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y
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m
a
n
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f
w
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ic
h
ar
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ed
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ce
d
b
u
t
n
o
t
d
ef
i
n
iti
v
e
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y
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h
e
m
s
el
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es
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n
a
s
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ess
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ec
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h
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m
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atter
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ti
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u
r
p
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h
e
n
o
tati
o
n
s
f
o
r
s
p
ec
if
y
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n
g
o
p
er
atin
g
co
n
d
itio
n
s
w
er
e
f
o
r
m
u
lated
as
f
o
llo
w
s
:
(
n
u
m
b
er
o
f
o
p
er
atin
g
m
ac
h
i
n
es
,
s
tar
ti
n
g
h
ea
d
(
m
)
,
d
u
r
atio
n
(
h
r
)
,
co
n
s
tr
ain
t
s
o
n
m
a
x
i
m
u
m
in
f
lo
w
)
.
T
h
is
n
o
tatio
n
w
o
u
ld
b
e
u
s
ed
in
t
h
e
p
r
esen
ta
tio
n
o
f
r
e
s
u
lt
s
.
3
.
1
.
Ca
s
e
1
:
(
5
,
2
5
.
8
,
2
4
,
u
(
T
)
un
co
ns
t
ra
ined)
Fig
u
r
e
3
p
r
ese
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ts
th
e
r
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u
lt
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o
r
a
n
i
n
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ir
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ti
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al
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o
l
w
ith
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h
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itio
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s
o
f
th
e
m
ac
h
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n
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an
d
th
e
in
it
ial
v
alu
e
o
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t
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e
h
ea
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at
J
HE
P
S
s
p
ec
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ied
as
(
5
,
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.
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,
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,
(
)
)
.
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h
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o
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atin
g
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n
d
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m
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li
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v
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tu
r
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ile
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atin
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5
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8
m
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esire
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atin
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d
in
cr
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t
o
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o
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al
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e
26
.
1
in
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ℎ
(
86400
)
.
T
h
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n
tr
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lem
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h
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eter
m
i
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o
f
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h
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i
n
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r
eq
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ir
ed
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i
s
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tated
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jectiv
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T
h
e
o
p
ti
m
a
l
co
n
tr
o
l s
y
s
te
m
g
e
n
er
ated
a
co
n
tr
o
l la
w
o
f
(
23)
;
(
)
=
−
1
×
10
−
11
3
+
2
×
10
−
6
2
−
0
.
1182
+
4715
.
9
(
23)
T
h
e
co
n
tr
o
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s
tar
ted
f
r
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m
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v
alu
e
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n
d
4
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m
3
/s
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t
0
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d
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ad
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at
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ec
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e
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m
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i
m
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m
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n
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tr
ain
ed
,
th
e
tr
aj
ec
to
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y
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f
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atin
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o
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ch
t
h
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ter
m
i
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al
v
alu
e
ℎ
(
)
=
26
.
1
,
as
ℎ
(
)
=
25
.
94m
.
T
h
e
o
p
e
r
atin
g
h
ea
d
also
r
o
s
e
to
a
p
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v
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e
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d
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ec
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s
es
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Hen
ce
th
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es
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lt is
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o
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s
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a
cto
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y
,
t
h
e
alg
o
r
it
h
m
h
a
s
to
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e
m
o
d
i
f
ied
.
3
.
2
.
Ca
s
e
2
:
(
3
,
2
5
.
8
,
2
4
,
u
(
T
)
u
nco
ns
t
ra
ined)
C
ase
2
co
n
s
id
er
ed
a
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itu
atio
n
w
h
er
e
t
h
e
n
u
m
b
er
o
f
u
n
it
s
in
o
p
er
atio
n
r
ed
u
ce
s
to
3
m
ac
h
in
e
s
an
d
th
e
o
p
er
atin
g
h
ea
d
2
5
.
8
m
.
A
s
i
m
ilar
r
esu
lt
to
t
h
at
o
f
F
ig
u
r
e
3
w
as
o
b
s
er
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ed
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d
p
r
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te
d
in
Fig
u
r
e
4
.
I
t
ca
n
b
e
co
n
clu
d
ed
th
a
t
to
u
s
e
P
D
E
M,
a
co
n
s
tr
ai
n
t
i
n
t
h
e
f
o
r
m
o
f
p
en
al
t
y
o
n
t
h
e
ter
m
i
n
al
c
o
n
tr
o
l
(
)
ca
n
b
e
in
co
r
p
o
r
ated
in
to
th
e
alg
o
r
ith
m
.
(
)
=
−
9
×
10
−
12
3
+
2
×
10
−
6
2
−
0
.
1165
+
4143
.
5
(
24)
Fig
u
r
e
3
.
Op
ti
m
u
m
r
esp
o
n
s
e
(
5
,
25
.
8
,
1
,
(
)
)
Fig
u
r
e
4
.
Op
ti
m
u
m
r
esp
o
n
s
e
(
3
,
25
.
8
,
1
,
u
(
T
)
Unpe
n
a
l
ize
d
)
3.
3
.
Ca
s
e
3
:
(
5
,
2
5
.
8
,
1
,
u
(
T
)
=
1
8
0
0
m
3
⁄s)
C
ase
3
p
r
esen
t
s
a
s
i
m
i
lar
co
n
d
itio
n
to
th
at
o
f
ca
s
e
1
b
u
t
w
i
th
a
co
n
s
tr
ain
t
o
n
t
h
e
f
in
al
co
n
tr
o
l.
T
h
is
i
m
p
lies
t
h
at
t
h
e
f
in
al
co
n
tr
o
l
ca
n
n
o
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d
ec
r
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s
e
to
ze
r
o
,
b
u
t
a
f
in
ite
v
alu
e
s
p
ec
if
ied
as
(
)
.
T
h
e
p
r
o
ce
d
u
r
e
f
o
r
th
e
s
elec
tio
n
o
f
s
u
itab
le
v
al
u
e
f
o
r
(
)
ca
n
b
e
f
o
u
n
d
i
n
[
5
]
.
Fig
u
r
e
5
s
h
o
w
s
a
b
etter
r
esu
l
t
o
f
w
h
ic
h
th
e
h
ea
d
m
o
v
e
s
f
r
o
m
an
in
it
ial
v
al
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e
ℎ
(
0
)
=
25
.
8
,
to
a
f
in
al
v
alu
e
ℎ
(
)
=
26
.
1
w
it
h
o
u
t
an
o
v
er
s
h
o
o
t,
as
ex
p
er
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ce
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in
t
h
e
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ir
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t
o
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tim
al
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n
tr
o
l.
T
h
e
o
p
ti
m
al
co
n
t
r
o
l
d
ef
in
ed
as
(
2
5
)
s
tar
ts
ar
o
u
n
d
4327
.
4
3
/
an
d
en
d
s
at
1800
3
/
.
(
)
=
5
×
10
−
07
2
−
0
.
0702
+
4327
.
4
(
25)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
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t E
l
C
o
n
tr
o
l
,
Vo
l.
18
,
No
.
4
,
A
u
g
u
s
t 2
0
2
0
:
2
0
6
3
-
2
0
6
9
2068
3.
4
.
C
a
s
e
4
:
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5
,
2
5
.
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,
2
,
u
(
T
)
=
1
8
0
0
m
3
⁄s)
A
s
it
u
atio
n
ca
n
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e
co
n
s
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er
ed
w
h
er
e
t
h
e
ti
m
e
li
m
it
f
o
r
w
h
ich
o
p
ti
m
al
co
n
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l
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s
r
eq
u
ir
ed
in
cr
ea
s
es
to
t
w
o
d
a
y
s
(
4
8
h
r
.
)
.
I
t
ca
n
b
e
o
b
s
er
v
ed
f
r
o
m
Fi
g
u
r
e
6
th
at
th
e
P
DE
M
co
u
ld
d
eter
m
i
n
e
t
h
e
s
o
l
u
tio
n
a
s
w
ell
ex
ce
p
t.
I
n
ca
s
e
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8
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[9
]
T
.
O.
A
le,
K.
E.
A
lo
w
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d
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,
J.
O.
Ba
b
a
to
la,
a
n
d
B
.
J.
Ol
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a
,
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o
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stin
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Da
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Us
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M
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Arc
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0
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O.
D.
Jim
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,
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1
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h
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m
a
s,
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Og
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M
.
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n
d
J.
B.
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a
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b
a
,
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2
]
O.
V
o
n
S
try
k
,
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m
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rica
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S
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ti
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-
Ca
lc.
V
a
r.
Op
ti
m.
Co
n
tro
l
T
h
e
o
ry
Nu
me
r.
M
e
th
o
d
s,
In
t
.
S
e
r.
N
u
me
r.
M
a
th
m
a
t
ics
,
v
o
l.
1
1
1
,
p
p
.
1
2
9
-
1
4
3
,
1
9
9
3
.
[1
3
]
F
.
Biral,
E
.
Be
rto
laz
z
i,
a
n
d
P
.
Bo
se
tt
i,
“
No
tes
o
n
n
u
m
e
ric
a
l
m
e
th
o
d
s
f
o
r
so
lv
in
g
o
p
ti
m
a
l
c
o
n
tro
l
p
r
o
b
lem
s,”
IEE
J
J
.
In
d
.
Ap
p
l.
,
v
o
l.
5
,
n
o
.
2
,
p
p
.
1
5
4
-
1
6
6
,
2
0
1
6
.
[
1
4
]
J
.
T
.
B
e
t
t
s
,
“
A
D
i
r
e
c
t
A
p
p
r
o
a
c
h
t
o
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o
l
v
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n
g
O
p
t
i
m
a
l
C
o
n
t
r
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l
P
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o
b
l
e
m
s
,
”
C
o
m
p
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t
.
S
c
i
.
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n
g
.
,
v
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l
.
1
,
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o
.
3
,
p
p
.
7
3
-
7
5
,
1
9
9
9
.
[1
5
]
H.
S
.
Ro
d
rig
u
e
s,
M
.
T
.
T
.
M
o
n
teir
o
,
a
n
d
D.
F
.
M
.
T
o
rre
s,
“
Op
ti
m
a
l
Co
n
tro
l
a
n
d
Nu
m
e
rica
l
S
o
f
t
wa
re
:
A
n
Ov
e
r
v
ie
w
,
”
S
y
st.
T
h
e
o
ry
Per
sp
e
c
t.
Ap
p
l.
De
v
.
,
p
p
.
9
3
-
1
1
0
,
2
0
1
4
.
[1
6
]
R.
Ju
n
a
n
d
C.
S
h
o
u
-
l
u
n
,
“
Op
ti
m
a
l
Re
g
u
latio
n
Co
n
tro
l
S
y
st
e
m
f
o
r
Ca
sc
a
d
e
H
y
d
ro
p
o
w
e
r
S
tatio
n
s
,”
2
0
0
9
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
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e
o
n
S
u
st
a
in
a
b
le P
o
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r Ge
n
e
ra
ti
o
n
a
n
d
S
u
p
p
ly
,
2
0
0
9
.
[1
7
]
V
.
M
.
Be
c
e
rra
,
“
Op
ti
m
a
l
c
o
n
tro
l,
”
S
c
h
o
l
a
rp
e
d
i
a
,
2
0
1
8
.
[1
8
]
A
.
V
R
a
o
,
“
A
s
u
r
v
e
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o
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n
u
m
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r
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c
a
l
m
e
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o
d
s
f
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o
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t
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m
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l
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l
,
”
A
d
v
.
A
s
t
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n
a
u
t
.
S
c
i
.
,
v
o
l
.
1
3
5
,
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o
.
1
,
p
p
.
4
9
7
-
5
2
8
,
2
0
0
9
.
[1
9
]
M
.
Ke
y
a
n
p
o
u
r
a
n
d
M
.
A
z
izs
e
f
a
t,
“
Nu
m
e
ric
a
l
so
lu
ti
o
n
o
f
o
p
ti
m
a
l
c
o
n
tro
l
p
ro
b
lem
s
b
y
a
n
,
”
AM
O
-
Ad
v
.
M
o
d
e
l.
Op
ti
m.
,
v
o
l
.
1
3
,
n
o
.
1
,
p
p
.
1
1
-
1
4
,
2
0
1
1
.
[2
0
]
D.
P
.
Be
rtse
k
a
s,
"
D
y
n
a
m
ic
P
ro
g
ra
m
m
in
g
a
n
d
Op
ti
m
a
l
Co
n
tro
l,
"
Ed
it
io
n
:
2
n
d
,
Vo
ls.
I
a
n
d
II
P
u
b
li
sh
e
r:
At
h
e
n
a
S
c
ien
ti
fi
c
ol
,
2
0
0
5
.
[2
1
]
G
.
R.
Ro
se
,
“
Nu
m
e
ri
c
a
l
M
e
th
o
d
s f
o
r
S
o
lv
in
g
Op
ti
m
a
l
Co
n
tro
l
P
ro
b
lem
s,”
T
h
is
T
h
e
sis
is
b
ro
u
g
h
t
to
y
o
u
f
o
r
f
re
e
a
n
d
o
p
e
n
a
c
c
e
ss
b
y
th
e
G
r
a
d
u
a
te
S
c
h
o
o
l
a
t
T
ra
c
e
:
T
e
n
n
e
ss
e
e
Re
s
e
a
rc
h
a
n
d
Cre
a
ti
v
e
Ex
c
h
a
n
g
e
a
t
Un
iv
e
rsit
y
o
f
T
e
n
n
e
ss
e
e
,
Kn
o
x
v
il
le
,
2
0
1
5
.
[2
2
]
B.
J.
Olu
f
e
a
g
b
a
a
n
d
R.
H.
F
lak
e
,
“
P
a
ra
ll
e
l
S
h
o
o
ti
n
g
M
o
d
e
ls
f
o
r
Co
n
tr
o
l
o
f
P
h
o
sp
h
o
ru
s
i
n
Est
u
a
ries
,
”
IFA
C
Pro
c
.
,
v
o
l.
1
0
,
n
o
.
7
,
p
p
.
3
5
7
-
3
6
4
,
1
9
7
7
.
[2
3
]
A
.
Ca
p
o
lei
a
n
d
J.
B.
Jo
rg
e
n
se
n
,
“
S
o
l
u
ti
o
n
o
f
c
o
n
stra
in
e
d
o
p
t
im
a
l
c
o
n
tro
l
p
ro
b
lem
s
u
sin
g
m
u
lt
ip
le
sh
o
o
ti
n
g
a
n
d
ES
DIRK
m
e
th
o
d
s,”
Pro
c
.
A
m.
Co
n
tr
o
l
C
o
n
f
.
,
p
p
.
2
9
5
-
3
0
0
,
2
0
1
2
.
[2
4
]
B.
J.
Olu
f
e
a
b
g
a
,
R.
H.
F
lak
e
,
a
n
d
A
.
N.
E.
,
“
A
Bo
u
n
d
a
ry
V
a
lu
e
A
p
p
ro
a
c
h
F
o
r
Est
u
a
rin
e
W
a
ter
Q
u
a
li
ty
M
o
d
e
ll
in
g
W
it
h
Re
su
lt
s F
o
r
Ja
m
a
i
c
a
Ba
y
,
N
e
w
Yo
rk
,
”
Eco
l.
M
o
d
e
ll
.
,
v
o
l
.
1
,
p
p
.
1
-
3
0
,
1
9
7
5
.
[2
5
]
B.
Olu
f
e
a
g
b
a
,
R.
F
lak
e
,
a
n
d
K.
Alm
q
u
ist,
“
Op
ti
m
a
l
c
o
n
tro
l
o
f
th
e
p
h
o
s
p
h
o
ru
s d
istri
b
u
ti
o
n
i
n
a
n
e
stu
a
r
y
,
”
EE
E
Co
n
f.
De
c
is.
Co
n
tro
l
In
c
l.
1
5
th
S
y
mp
.
A
d
a
p
t.
Pr
o
c
e
ss
.
,
p
p
.
1
0
5
8
-
1
0
6
4
,
1
9
7
6
.
[2
6
]
B.
J.
Olu
f
e
a
g
b
a
,
R.
H.
F
lak
e
,
a
n
d
K.
J.
A
l
m
q
u
ist,
“
M
u
lt
ip
le
S
h
o
o
ti
n
g
a
n
d
S
w
e
e
p
A
l
g
o
rit
h
m
f
o
r
Op
ti
m
a
l
P
o
i
n
t
Co
n
tr
o
ll
e
d
Distr
ib
u
ted
P
a
ra
m
e
ter
S
y
st
e
m
s.,
”
IFA
C
Pro
c
.
Vo
l.
,
v
o
l
.
9
,
n
o
.
3
,
p
p
.
1
5
5
-
1
6
6
,
1
9
8
0
.
[2
7
]
B.
J.
Olu
f
e
a
g
b
a
a
n
d
R.
H.
F
lak
e
,
“
M
o
d
e
ll
i
n
g
a
n
d
c
o
n
tr
o
l
o
f
d
isso
l
v
e
d
o
x
y
g
e
n
in
a
n
e
stu
a
ry
,
”
Eco
l.
M
o
d
e
ll
.
,
v
o
l.
1
4
,
n
o
.
1
-
2
,
p
p
.
7
9
-
9
4
,
1
9
8
1
.
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