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o
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(
I
J
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)
Vo
l.
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,
No
.
3
,
Sep
tem
b
er
201
7
,
p
p
.
20
7
~
21
5
I
SS
N:
2089
-
4856
,
DOI
: 1
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C
o
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A
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:
A
lire
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R
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Un
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m
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m
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r
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t.a
c.
ir
1.
I
NT
RO
D
UCT
I
O
N
Mo
d
el
P
r
ed
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e
C
o
n
tr
o
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s
(
MP
C
)
ar
e
w
id
el
y
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o
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in
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d
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s
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o
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s
,
1
9
9
9
;
Nag
y
et
al,
2
0
0
5
)
.
T
h
e
m
ain
id
ea
o
f
MP
C
lies
in
o
n
lin
e
co
n
s
tr
u
c
tio
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o
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th
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s
y
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m
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ati
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t
h
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r
eq
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ir
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co
n
tr
o
l
ac
tio
n
s
b
y
r
ep
etitiv
e
s
o
l
u
tio
n
o
f
an
o
p
ti
m
al
co
n
tr
o
l
p
r
o
b
lem
.
I
s
s
u
e
s
m
a
y
ar
is
e
f
o
r
g
u
ar
a
n
teei
n
g
clo
s
ed
-
lo
o
p
s
tab
ilit
y
,
m
o
d
el
u
n
ce
r
t
ain
t
y
h
a
n
d
li
n
g
an
d
r
ed
u
cin
g
th
e
o
n
-
li
n
e
co
m
p
u
tat
io
n
s
.
T
h
er
e
ar
e
th
r
ee
k
in
d
s
o
f
MP
C
co
n
tr
o
ller
s
ch
e
m
es
th
at
u
s
e
d
if
f
er
en
t
m
et
h
o
d
s
f
o
r
s
y
s
te
m
m
o
d
elin
g
b
u
t
ar
e
s
i
m
il
ar
to
ea
ch
o
th
er
i
n
co
n
t
r
o
l p
r
o
ce
s
s
(
L
ik
ar
et
al,
2
0
0
7
)
:
1.
MA
C
: u
s
e
s
i
m
p
u
ls
e
r
esp
o
n
s
e
f
o
r
s
y
s
te
m
m
o
d
elin
g
.
2.
GP
C
: u
s
e
s
tr
an
s
f
er
f
u
n
ctio
n
f
o
r
s
y
s
te
m
m
o
d
eli
n
g
.
3.
DM
C
: u
s
e
s
s
tep
r
esp
o
n
s
e
f
o
r
s
y
s
te
m
m
o
d
eli
n
g
.
T
h
ese
co
n
tr
o
ller
s
o
p
ti
m
ize
a
co
s
t
f
u
n
ctio
n
th
at
d
ep
en
d
s
o
n
t
h
e
co
n
tr
o
l
la
w
(
Ha
u
g
e
et
al,
2
0
0
2
)
.
A
lth
o
u
g
h
DM
C
is
p
r
i
m
ar
il
y
d
ev
e
lo
p
ed
f
o
r
co
n
tr
o
l
o
f
ch
e
m
ical
p
r
o
ce
s
s
es
(
C
a
m
ac
h
o
an
d
B
o
r
d
o
n
s
,
1
9
9
9
;
Gar
cia
et
al.
,
1
9
8
9
;
L
i
m
o
n
e
t
al,
2
0
0
5
)
,
it
h
as
b
ee
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ed
s
u
cc
e
s
s
f
u
ll
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th
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licatio
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s
s
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a
s
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f
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s
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s
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s
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m
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s
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ete
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s
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;
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et
al,
2
0
0
2
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.
Ho
w
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v
er
i
m
p
le
m
e
n
tatio
n
o
f
th
i
s
co
n
tr
o
l
s
ch
e
m
e
in
r
o
b
o
tics
h
a
s
b
ee
n
less
r
ep
o
r
ted
an
d
s
ee
m
s
to
b
e
in
s
till
i
n
its
i
n
f
an
c
y
(
L
i
m
o
n
et
al,
2
0
0
5
;
Ko
u
v
ar
itak
is
et
a
l,
2
0
0
6
)
.
I
n
th
is
w
o
r
k
w
e
co
n
ce
n
tr
ate
o
n
ap
p
licatio
n
o
f
MP
C
/D
MC
co
n
tr
o
ller
s
i
n
p
o
s
itio
n
co
n
tr
o
l o
f
r
o
b
o
tic
s
y
s
t
e
m
s
.
T
h
e
r
est
o
f
th
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
T
h
e
n
ex
t
s
e
ct
io
n
p
r
esen
ts
t
h
e
id
ea
o
f
MP
C
co
n
tr
o
ller
,
s
ec
tio
n
3
d
escr
ib
es
P
2
A
T
r
o
b
o
t,
s
ec
tio
n
4
d
i
s
cu
s
s
e
s
t
h
e
e
f
f
ec
t
o
f
v
ar
iatio
n
o
f
DM
C
p
ar
a
m
eter
s
o
n
s
p
ee
d
er
r
o
r
,
s
ec
tio
n
5
d
is
cu
s
s
es
r
es
u
lts
o
f
th
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e
x
p
er
i
m
e
n
tal
i
m
p
l
e
m
en
tatio
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o
f
MP
C
/DM
C
o
n
a
r
ea
l
r
o
b
o
t,
an
d
f
i
n
all
y
th
e
la
s
t sectio
n
co
n
tai
n
s
th
e
co
n
cl
u
s
io
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
20
1
7
:
20
7
–
21
5
208
2.
M
O
DE
L
P
RE
DIC
T
I
V
E
CO
NT
RO
L
L
E
R
T
h
e
m
a
in
s
tr
ateg
y
o
f
a
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
ller
is
ill
u
s
tr
ated
i
n
Fi
g
u
r
e
1
.
I
n
a
t
y
p
ical
MP
C
alg
o
r
ith
m
th
e
s
y
s
te
m
o
u
tp
u
t
s
ar
e
p
r
ed
icted
f
o
r
a
ce
r
tain
in
t
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f
ti
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e
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r
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r
izo
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m
a
k
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s
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p
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r
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m
m
o
d
el
w
h
i
ch
is
co
n
s
tr
u
cted
b
ased
o
n
th
e
in
f
o
r
m
atio
n
(
i
n
p
u
t
s
an
d
o
u
tp
u
ts
)
g
a
th
er
ed
f
r
o
m
th
e
s
y
s
te
m
p
as
t
as
w
el
l
as
f
u
t
u
r
e
co
n
tr
o
l
s
ig
n
a
ls
th
a
t
h
av
e
t
o
b
e
d
eter
m
i
n
ed
p
r
o
p
er
ly
.
A
s
s
h
o
w
n
i
n
th
e
f
ig
u
r
e
th
e
co
n
tr
o
l
s
i
g
n
al
i
s
a
s
eq
u
e
n
ce
o
f
s
tep
f
u
n
ctio
n
s
w
it
h
v
ar
iab
le
am
p
li
tu
d
e.
Am
p
li
tu
d
es
o
f
th
ese
i
n
p
u
t
s
ar
e
o
b
tain
ed
b
y
s
o
lv
i
n
g
an
o
p
ti
m
izatio
n
p
r
o
b
lem
t
h
at
tr
ie
s
to
k
ee
p
th
e
s
y
s
te
m
o
u
tp
u
t
clo
s
e
to
th
e
r
ef
er
en
ce
s
e
t
p
o
in
t.
Ob
j
ec
tiv
e
f
u
n
ctio
n
o
f
th
is
p
r
o
b
le
m
i
s
u
s
u
all
y
a
q
u
ad
r
a
tic
f
u
n
ctio
n
o
f
t
h
e
d
i
f
f
er
en
ce
b
et
w
ee
n
t
h
e
p
r
ed
icted
o
u
tp
u
t sig
n
als a
n
d
th
e
r
ef
er
en
ce
tr
aj
ec
to
r
y
.
A
ll
t
h
e
MP
C
alg
o
r
ith
m
s
u
s
in
g
a
lin
ea
r
m
o
d
el
h
a
v
e
s
i
m
ila
r
b
eh
av
io
r
.
Her
e
w
e
d
e
m
o
n
s
tr
ate
h
o
w
DM
C
w
o
r
k
s
(
1
)
.
Y=
A
∆u
+Y
0
(
1
)
W
h
er
e
A
in
cl
u
d
es
th
e
s
tep
r
e
s
p
o
n
s
e,
Y
is
th
e
p
r
ed
icted
o
u
tp
u
t,
Y0
is
p
ast
o
u
tp
u
t,
an
d
u
is
th
e
co
n
tr
o
l
la
w
(
A
ze
v
ed
o
et
al,
2
0
0
2
,
Sh
r
id
h
ar
an
d
C
o
o
p
er
,
1
9
9
7
)
.
Fig
u
r
es
ar
e
p
r
esen
ted
ce
n
ter
,
as
s
h
o
wn
b
elo
w
a
n
d
cited
in
th
e
m
a
n
u
s
cr
ip
t.
Fig
u
r
e
1
.
Me
th
o
d
o
lo
g
y
o
f
MP
C
Du
e
to
u
n
ce
r
tai
n
itie
s
o
f
t
h
e
m
o
d
el
i
t
is
v
er
y
h
ar
d
to
ac
h
i
ev
e
th
e
e
x
ac
t
v
al
u
e
o
f
A
to
s
atis
f
y
th
e
d
es
ir
ed
b
ah
av
io
r
.
T
o
c
o
m
p
an
s
ate
f
o
r
th
is
p
r
o
b
le
m
an
er
r
o
r
ter
m
is
a
d
d
ed
to
th
e
s
y
s
te
m
o
u
tp
u
t
(2
-
3)
:
(
2
)
(
3
)
W
h
er
e
th
e
co
r
r
ec
tio
n
ter
m
r
e
p
r
esen
ts
th
e
d
if
f
er
en
ce
b
et
w
e
en
t
h
e
c
u
r
r
en
t
p
lan
t
ac
t
u
al
o
u
tp
u
t
a
n
d
t
h
e
o
u
tp
u
t
ex
tr
ac
ted
f
r
o
m
t
h
e
m
o
d
el.
T
h
e
er
r
o
r
v
ec
to
r
o
v
er
p
r
ed
ictio
n
h
o
r
izo
n
is
th
e
n
w
r
itte
n
as
(
4
)
(
4
)
Usi
n
g
t
h
e
ab
o
v
e
ex
p
r
ess
io
n
a
q
u
ad
r
atic
co
s
t
f
u
n
ct
io
n
,
J
,
c
an
b
e
d
ef
in
ed
w
h
ic
h
is
m
in
i
m
ized
to
o
b
tain
th
e
o
p
tim
a
l
co
n
tr
o
ller
(
5
)
(
5
)
w
h
er
e
W
1
an
d
W
2
ar
e
co
n
s
tan
ts
.
T
h
e
m
o
d
if
ied
co
n
tr
o
l la
w
is
o
b
tain
ed
as
(
6
)
:
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
C
o
n
tr
o
llin
g
o
f Mo
b
ile
R
o
b
o
t b
y
Usi
n
g
o
f P
r
ed
ictive
C
o
n
tr
o
ller
(
A
lir
e
z
a
R
eza
ee
)
209
Fig
u
r
e
2
s
h
o
w
s
t
h
e
s
tr
u
ct
u
r
e
o
f
a
m
o
d
el
p
r
ed
icti
v
e
co
n
tr
o
ller
.
I
n
th
i
s
co
n
f
i
g
u
r
atio
n
t
h
e
b
lo
ck
lab
eled
as "
Mo
d
el
"
co
n
tain
s
t
h
e
m
o
d
el
o
f
th
e
r
o
b
o
t
th
at
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ed
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t
h
e
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io
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f
t
h
e
r
o
b
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t o
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er
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tain
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m
e
h
o
r
izo
n
.
T
h
e
Fu
tu
r
e
I
n
p
u
ts
(
u
(
t+
k
|
t)
)
ar
e
ca
lcu
lated
u
n
d
er
co
n
s
tr
ain
s
an
d
b
y
o
p
ti
m
izi
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co
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t
f
u
n
ctio
n
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h
is
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r
o
ce
s
s
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n
tin
u
es
u
n
t
il
th
e
en
d
o
f
th
e
tr
aj
ec
t
o
r
y
.
Fig
u
r
es
ar
e
p
r
esen
ted
ce
n
ter
,
as
s
h
o
w
n
b
elo
w
an
d
cited
in
th
e
m
an
u
s
cr
ip
t.
Fig
u
r
e
2
.
T
h
e
s
tr
u
ctu
r
e
o
f
a
M
P
C
2
.
2
.
T
he
A
lg
o
r
ith
m
o
f
a
DM
C
co
ntr
o
ller
T
h
e
alg
o
r
ith
m
o
f
a
DM
C
co
n
t
r
o
ller
is
as f
o
llo
w
s
:
a.
Ob
tain
m
o
d
el
o
f
t
h
e
r
o
b
o
t to
b
e
co
n
tr
o
lled
.
b.
Use th
e
m
o
d
el
to
p
r
ed
ict
b
eh
a
v
io
r
o
f
th
e
r
o
b
o
t o
v
er
a
ce
r
tain
ti
m
e
h
o
r
izo
n
.
c.
C
alcu
lated
th
e
E
f
r
o
m
eq
u
atio
n
(
4
)
.
d.
Dete
r
m
i
n
e
t
h
e
co
n
tr
o
l a
ctio
n
b
y
o
p
ti
m
iz
in
g
a
p
er
f
o
r
m
a
n
ce
i
n
d
ex
,
w
h
ic
h
t
y
p
icall
y
is
t
h
e
er
r
o
r
b
etw
ee
n
t
h
e
o
u
tp
u
ts
p
r
ed
icted
f
r
o
m
t
h
e
m
o
d
el
an
d
th
e
d
esire
d
o
u
tp
u
t o
v
e
r
th
e
ti
m
e
h
o
r
izo
n
.
e.
A
p
p
l
y
t
h
e
o
p
ti
m
al
co
n
tr
o
l
ac
t
io
n
s
a
n
d
th
e
n
m
ea
s
u
r
e
r
o
b
o
t
o
u
tp
u
ts
o
v
er
th
e
t
i
m
e
h
o
r
izo
n
.
T
h
e
m
ea
s
u
r
ed
v
alu
e
s
at
t
h
e
f
i
n
al
s
tag
e
w
il
l b
e
u
s
ed
as i
n
itial c
o
n
d
itio
n
s
o
f
t
h
e
m
o
d
el
in
t
h
e
n
ex
t i
ter
atio
n
.
f.
R
ep
ea
t step
s
2
to
5
u
n
til t
h
e
e
n
d
o
f
th
e
tr
aj
ec
to
r
y
.
3.
RO
B
O
T
CO
NT
RO
L
Fo
r
r
o
b
o
t
co
n
tr
o
l
w
it
h
MP
C
c
o
n
tr
o
ller
w
e
n
ee
d
to
h
av
e
t
h
e
m
o
d
el
eq
u
atio
n
o
f
t
h
e
r
o
b
o
t
as
s
h
o
w
n
i
n
Fig
u
r
e
3
.
T
h
e
r
o
b
o
t u
n
d
er
co
n
s
id
er
atio
n
in
th
i
s
s
t
u
d
y
i
s
a
f
o
u
r
w
h
ee
l P
2
A
T
r
o
b
o
t in
w
h
ic
h
w
h
ee
ls
o
f
t
h
e
r
o
b
o
t
ar
e
co
n
tr
o
lled
in
d
ep
en
d
en
t
l
y
.
Fig
u
r
es a
r
e
p
r
esen
ted
ce
n
ter
,
a
s
s
h
o
w
n
b
elo
w
a
n
d
cited
in
t
h
e
m
an
u
s
cr
ip
t.
Fig
u
r
e
3
.
P
2
A
T
r
o
b
o
t
I
n
o
r
d
er
to
o
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tain
th
e
s
y
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te
m
m
o
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el
a
n
d
d
esi
g
n
th
e
p
r
o
p
er
co
n
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o
ller
f
o
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it,
a
s
o
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n
d
ap
p
r
ec
iatio
n
o
f
d
y
n
a
m
ic
b
eh
a
v
io
r
o
f
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e
s
y
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te
m
is
n
ee
d
ed
.
T
o
d
o
th
at
a
s
im
p
le
s
k
etch
o
f
th
e
r
o
b
o
t
is
s
h
o
w
n
if
F
ig
u
r
e
.
4
,
it
is
ass
u
m
ed
t
h
at
th
e
d
is
ta
n
ce
b
et
w
ee
n
ea
c
h
w
h
ee
l
i
s
co
n
s
ta
n
t
an
d
f
o
u
r
w
h
ee
ls
h
a
v
e
t
h
e
s
a
m
e
r
ad
iu
s
.
Ki
n
e
m
a
tic
m
o
d
el
o
f
th
e
r
o
b
o
t is d
escr
ib
ed
b
y
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
20
1
7
:
20
7
–
21
5
210
(
7
)
W
h
er
e
u
(
k
)
=
[
ϑ(
k
)
,
α
(
k
)
]
T
i
s
th
e
co
n
tr
o
l
v
ec
to
r
f
o
r
m
o
tio
n
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ac
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t
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m
p
le
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d
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p
ee
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o
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le
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t
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h
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d
t
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et
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s
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d
w
.
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r
eo
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er
,
a
is
th
e
d
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s
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ce
b
et
w
ee
n
r
ef
er
e
n
ce
p
o
in
t
o
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th
e
r
o
b
o
t
an
d
th
e
w
h
ee
l
s
.
A
d
d
itio
n
all
y
,
th
e
p
o
s
itio
n
o
f
t
h
e
r
o
b
o
t
in
g
lo
b
al
r
ef
er
en
ce
f
r
a
m
e
is
s
p
ec
i
f
ied
b
y
co
o
r
d
in
ates
X
a
n
d
Y.
T
h
e
an
g
u
lar
d
i
f
f
er
en
ce
b
et
w
ee
n
th
e
g
lo
b
al
an
d
lo
ca
l r
ef
er
en
ce
f
r
a
m
e
s
is
g
iv
e
n
b
y
θ.
Su
c
h
a
n
o
n
-
l
in
ea
r
s
y
s
te
m
i
s
o
p
en
lo
o
p
co
n
tr
o
llab
le,
w
h
ich
ca
n
b
e
l
in
ea
r
i
s
ed
in
o
r
d
er
to
u
s
e
tr
ad
itio
n
al
li
n
ea
r
f
ee
d
b
ac
k
co
n
tr
o
l to
r
eg
u
late
t
h
e
r
o
b
o
t.
B
u
t i
f
t
h
e
r
o
b
o
t o
p
er
ates o
v
er
a
lar
g
e
r
an
g
e
i
n
it
s
s
ta
te
s
p
ac
e,
esp
ec
iall
y
w
h
e
n
th
e
r
o
b
o
t
tu
r
n
s
ar
o
u
n
d
co
r
n
er
s
,
th
e
lin
ea
r
izatio
n
o
f
t
h
e
k
i
n
e
m
atics
w
il
l
lead
to
th
e
lo
s
s
o
f
co
n
tr
o
llab
ilit
y
.
S
in
ce
th
e
MP
C
’
s
m
o
d
els
ar
e
b
ased
o
n
l
in
ea
r
r
eg
r
e
s
s
io
n
s
.
F
ig
u
r
es
ar
e
p
r
esen
ted
ce
n
ter
,
as
s
h
o
w
n
b
elo
w
a
n
d
cited
in
th
e
m
an
u
s
cr
ip
t.
Fig
u
r
e
4
.
Sch
e
m
atic
o
f
t
h
e
P
2
A
T
r
o
b
o
t
4.
T
H
E
E
F
F
E
C
T
O
F
DM
C
P
A
RAM
E
T
E
RS O
N
CO
N
T
RO
L
L
E
R
P
E
RF
O
RM
ANCE
Du
e
to
th
e
s
i
m
p
le
n
at
u
r
e
o
f
th
e
li
n
ea
r
m
at
h
e
m
atica
l
m
o
d
els
(
Ma
y
n
e
et
al,
2
0
0
0
;
A
x
e
h
ill,
2
0
0
4
;
Ax
e
h
ila,
2
0
0
4
)
m
o
s
t
o
f
th
e
MP
C
s
in
cl
u
d
in
g
i
m
p
u
l
s
e
an
d
s
tep
r
esp
o
n
s
e
m
o
d
e
ls
an
d
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
m
o
d
el
ar
e
b
ased
o
n
th
is
t
y
p
e
o
f
m
o
d
el
d
escr
ip
tio
n
(
Do
u
g
h
er
t
y
an
d
co
o
p
er
,
2
0
0
4
;
Gilb
er
t
an
d
T
an
.
,
1
9
9
1
)
.
T
h
u
s
,
th
e
f
ir
s
t
s
tep
in
co
n
tr
o
ll
er
d
esig
n
is
to
lin
ea
r
ize
t
h
e
m
o
d
el
eq
u
atio
n
s
an
d
th
e
n
ca
lcu
l
ate
th
e
co
n
tr
o
l
la
w
s
.
Fig
u
r
e
5
s
h
o
w
s
t
h
e
s
c
h
e
m
atic
o
f
th
e
MP
C
co
n
tr
o
ller
th
a
t is c
o
n
n
ec
ted
to
th
e
s
y
s
te
m
(
r
o
b
o
t)
.
R
est o
f
t
h
is
p
ap
er
is
d
ev
o
ted
to
s
tu
d
y
e
f
f
ec
t
o
f
d
if
f
er
e
n
t
p
ar
a
m
eter
s
o
f
t
h
e
m
o
d
el
o
n
th
e
co
n
tr
o
ller
p
er
f
o
r
m
an
ce
.
T
o
d
o
th
at
a
s
er
ies
o
f
ex
p
er
i
m
e
n
t
s
w
er
e
co
n
d
u
cted
o
n
a
s
i
m
p
le
s
tr
ai
g
h
t
p
ath
an
d
s
p
ee
d
o
f
r
o
b
o
t
w
a
s
m
e
asu
r
ed
f
o
r
d
if
f
er
e
n
t
in
s
ta
n
ce
s
(
F
ig
u
r
es.
6
-
1
3
)
.
Fig
u
r
es a
r
e
p
r
esen
ted
ce
n
ter
,
as sh
o
w
n
b
elo
w
a
n
d
cited
in
th
e
m
a
n
u
s
cr
ip
t.
MP
C
co
n
tr
o
ller
is
to
o
p
tim
ize
a
co
s
t in
d
ex
J
(
x
(
k
)
,
u
(
k
)
)
u
n
d
er
th
e
co
n
s
tr
ai
n
t
s
o
f
f
o
r
m
u
la
7
(
8
)
:
Min
u
(
k
)
J
(
x
(
k
)
,
u
(
k
)
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(
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T
h
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cu
r
r
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t
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l
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ch
o
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en
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n
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u
tu
r
e
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at
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h
e
p
ath
tr
ac
k
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o
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th
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r
o
b
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t
is
s
m
o
o
th
aa
n
d
s
tab
le.
T
h
er
f
o
r
e,
th
e
co
s
t
in
d
ex
ca
n
b
e
ex
p
r
ess
ed
as
(
9
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(
9
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
C
o
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llin
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211
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u
r
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5
.
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n
MP
C
co
n
tr
o
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th
e
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y
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te
m
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r
o
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o
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4
.
1
.
E
f
f
ec
t
o
f
M
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co
ntr
o
l ho
r
izo
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Fig
u
r
es
6
,
7
s
h
o
w
t
h
e
ef
f
ec
t
o
f
co
n
tr
o
l
h
o
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izo
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ar
a
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eter
,
M,
o
n
th
e
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n
tr
o
l
o
u
tp
u
t
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d
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n
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o
l
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r
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ec
tiv
el
y
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t
is
o
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s
er
v
ed
t
h
at
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y
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n
cr
ea
s
in
g
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al
u
e
o
f
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e
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ettli
n
g
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m
e
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r
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ed
a
n
d
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e
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n
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o
l
e
f
f
o
r
t
is
in
cr
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s
ed
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h
is
also
in
cr
ea
s
es
th
e
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m
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u
tatio
n
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m
p
l
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it
y
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cc
o
r
d
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g
to
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e
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p
er
i
m
en
tal
r
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lt
s
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e
o
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tim
a
l v
al
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e
o
f
m
s
elec
ted
as
2
.
Fig
u
r
es a
r
e
p
r
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ted
ce
n
te
r
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as sh
o
w
n
b
elo
w
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d
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th
e
m
a
n
u
s
cr
ip
t.
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1
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N=
2
0
,
P
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,
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.
5
,
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2
=
0
.
(
a)
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2
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2
0
,
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.
5
,
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2
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0
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)
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4
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2
0
,
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,
α
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.
5
,
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2
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(
c)
Fig
u
r
e
6
.
O
u
tp
u
t
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1
,
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2
0
,
P
=5
,
α
=0
.
5
,
W
2
=0
.
(
a)
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2
,
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2
0
,
P
=5
,
α
=0
.
5
,
W
2
=0
.
(
b
)
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4
,
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2
0
,
P
=5
,
α
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.
5
,
W
2
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.
(
c)
Fig
u
r
e
7
.
C
o
n
tr
o
l la
w
4
.
1
.
E
f
f
ec
t
o
f
P
(
predict
io
n ho
rizo
n)
Fig
u
r
es
8
,
9
s
h
o
w
th
e
s
y
s
te
m
o
u
tp
u
t
an
d
co
n
tr
o
l
la
w
f
o
r
t
w
o
d
if
f
er
en
t
v
al
u
es
o
f
p
a
r
a
m
eter
P
r
esp
ec
tiv
el
y
.
I
t c
a
n
b
e
s
ee
n
t
h
at
b
y
in
cr
ea
s
in
g
v
alu
e
o
f
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e
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ettli
n
g
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m
e
is
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r
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s
ed
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d
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e
co
n
tr
o
l e
f
f
o
r
t i
s
in
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ea
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ed
a
n
d
t
h
e
co
m
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m
p
lex
it
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ed
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m
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lta
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l
y
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g
u
r
es
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ce
n
ter
,
a
s
s
h
o
w
n
b
elo
w
a
n
d
cited
in
th
e
m
an
u
s
cr
ip
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
20
1
7
:
20
7
–
21
5
212
M=
2
,
N=
2
0
,
P
=3
,
α
=0
.
5
,
W
2
=0
.
(
a)
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2
,
N=
2
0
,
P
=1
0
,
α
=0
.
5
,
W
2
=0
.
(
b
)
Fig
u
r
e
8
.
Ou
tp
u
t
M=
2
,
N=
2
0
,
P
=3
,
α
=0
.
5
,
W
2
=0
.
(
a)
M=
2
,
N=
2
0
,
P
=1
0
,
α
=0
.
5
,
W
2
=0
.
(
b
)
Fig
u
r
e
9
.
C
o
n
tr
o
l
la
w
4
.
3
.
E
f
f
ec
t
o
f
W2
Fig
u
r
es
1
0
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1
1
s
h
o
w
th
e
e
f
f
ec
t
o
f
ch
an
g
in
g
w
ei
g
h
t
f
ac
to
r
W
2
(
See
E
q
.
5
)
o
n
th
e
s
y
s
te
m
o
u
tp
u
t
an
d
th
e
co
n
tr
o
l
la
w
.
I
t
is
s
ee
n
th
a
t
b
y
i
n
cr
ea
s
i
n
g
t
h
e
v
al
u
e
o
f
W
2
in
cr
ea
s
es
th
e
s
ettli
n
g
ti
m
e
w
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ile
th
e
co
n
tr
o
l
ef
f
o
r
t
i
s
d
ec
r
ea
s
ed
an
d
co
m
p
u
tatio
n
a
l
co
m
p
le
x
it
y
is
n
o
t
c
h
an
g
ed
.
Fi
g
u
r
e
s
ar
e
p
r
esen
te
d
ce
n
ter
,
as
s
h
o
wn
b
elo
w
an
d
cited
in
t
h
e
m
an
u
s
c
r
ip
t.
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2
,
N=
2
0
,
P
=5
,
α
=0
.
5
,
W
2
=0
.
1
.
(
a)
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2
,
N=
2
0
,
P
=5
,
α
=0
.
5
,
W
2
=1
.
(
b
)
Fig
u
r
e
1
0
.
O
u
tp
u
t
M=
2
,
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2
0
,
P
=5
,
α
=0
.
5
,
W
2
=0
.
1
.
(
a)
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2
,
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2
0
,
P
=5
,
α
=0
.
5
,
W
2
=1
.
(
b
)
Fig
u
r
e
1
1
.
C
o
n
tr
o
l la
w
4
.
4
.
E
f
f
ec
t
o
f
α
Fig
u
r
es
1
2
a
n
d
1
3
s
h
o
w
th
e
e
f
f
ec
t
o
f
v
ar
iatio
n
o
f
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u
s
ed
i
n
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e
in
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u
t
s
ig
n
al
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il
ter
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an
d
a
n
d
ap
p
lied
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n
t
h
e
co
n
tr
o
l
o
u
tp
u
t
an
d
co
n
tr
o
l
la
w
r
e
s
p
ec
tiv
el
y
.
Acc
o
r
d
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g
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h
ese
f
i
g
u
r
e
i
n
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s
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n
g
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h
e
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alu
e
o
f
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es
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h
e
s
ettl
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g
ti
m
e
an
d
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ec
r
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es
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e
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n
tr
o
l
ef
f
o
r
t.
Ho
w
ev
er
th
e
co
m
p
u
tatio
n
al
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m
p
le
x
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y
i
s
n
o
t
ch
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g
ed
.
Fig
u
r
es a
r
e
p
r
esen
te
d
ce
n
ter
,
as sh
o
w
n
b
elo
w
a
n
d
cited
in
th
e
m
a
n
u
s
cr
ip
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
C
o
n
tr
o
llin
g
o
f Mo
b
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R
o
b
o
t b
y
Usi
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f P
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ed
ictive
C
o
n
tr
o
ller
(
A
lir
e
z
a
R
eza
ee
)
213
M=
2
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2
0
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=5
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=0
.
7
,
W
2
=0
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(
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2
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2
0
,
P
=5
,
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9
,
W
2
=0
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(
b
)
Fig
u
r
e
1
2
.
Ou
tp
u
t
M=
2
,
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2
0
,
P
=5
,
α
=0
.
7
,
W
2
=0
.
(
a)
M=
2
,
N=
2
0
,
P
=5
,
α
=0
.
9
,
W
2
=0
.
(
b
)
Fig
u
r
e
1
3
. C
o
n
tr
o
l la
w
5.
CO
M
P
ARIS
O
N
O
F
M
P
C
WI
T
H
O
T
H
E
R
CO
N
T
RO
L
M
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DE
L
S
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o
s
h
o
w
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h
e
e
f
f
ec
tiv
e
n
e
s
s
o
f
th
e
MP
C
co
n
tr
o
ller
t
h
r
ee
d
if
f
er
en
t
co
n
tr
o
ller
s
(
MP
C
,
P
I
D
an
d
ad
ap
tiv
e)
ar
e
i
m
p
le
m
e
n
ted
o
n
P
2
A
T
m
o
b
ile
r
o
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t
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d
th
e
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y
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te
m
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te
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ted
in
a
n
e
llip
tic
al
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ath
a
s
s
h
o
w
n
i
n
Fig
u
r
e
1
4
.
PID
co
n
tr
o
l
tu
n
i
n
g
is
d
escr
ib
ed
at
(
Gu
et
al,
1
9
9
7
)
f
ig
u
r
e
s
ar
e
p
r
esen
ted
ce
n
te
r
,
as
s
h
o
w
n
b
elo
w
an
d
cited
in
th
e
m
a
n
u
s
cr
ip
t.
Fig
u
r
e
14.
E
llip
tical
p
ath
Fig
u
r
es
1
5
-
1
7
s
h
o
w
th
e
er
r
o
r
an
d
its
f
ir
s
t
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er
iv
ati
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e
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o
r
d
if
f
er
en
t
co
n
tr
o
ller
s
.
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r
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er
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e
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ath
m
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y
t
h
e
r
o
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t
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e
n
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th
e
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u
b
p
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.
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s
F
i
g
u
r
e
1
7
s
h
o
w
s
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e
MP
C
co
n
tr
o
ller
h
as
a
lo
w
er
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r
o
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m
p
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e
o
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n
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et
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d
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n
tr
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at
h
m
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ig
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r
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e
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o
w
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n
d
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in
th
e
m
an
u
s
cr
ip
t.
Fig
u
r
e
15.
R
o
b
o
t p
ath
w
it
h
P
I
D
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
3
,
Sep
tem
b
er
20
1
7
:
20
7
–
21
5
214
Fig
u
r
e
1
6
.
R
o
b
o
t p
ath
w
it
h
ad
ap
tiv
e
co
n
tr
o
ller
Fig
u
r
e
17.
R
o
b
o
t p
ath
w
it
h
MP
C
co
n
tr
o
ller
6.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
p
r
o
p
o
s
es
a
Mo
d
el
P
r
ed
ictiv
e
C
o
n
tr
o
ller
(
MP
C
)
f
o
r
co
n
tr
o
l
o
f
a
P2
A
T
m
o
b
ile
r
o
b
o
t.
M
P
C
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ef
er
s
to
a
g
r
o
u
p
o
f
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n
tr
o
ller
s
th
at
e
m
p
lo
y
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d
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n
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en
tical
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o
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el
o
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r
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ce
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s
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r
e
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ict
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u
t
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r
e
b
eh
av
io
r
o
v
er
an
ex
te
n
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ed
p
r
ed
ictio
n
h
o
r
izo
n
.
T
h
e
d
esig
n
o
f
a
MP
C
is
f
o
r
m
u
lated
as
an
o
p
ti
m
al
co
n
tr
o
l
p
r
o
b
lem
.
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h
en
t
h
is
p
r
o
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le
m
i
s
co
n
s
id
er
ed
as
li
n
ea
r
q
u
ad
r
atic
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atio
n
(
L
QR
)
a
n
d
is
s
o
lv
ed
b
y
m
a
k
i
n
g
u
s
e
o
f
R
icatti
eq
u
atio
n
.
T
o
s
h
o
w
th
e
ef
f
ec
ti
v
en
e
s
s
o
f
t
h
e
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r
o
p
o
s
ed
m
et
h
o
d
th
i
s
co
n
tr
o
ller
is
i
m
p
le
m
e
n
ted
o
n
a
r
ea
l
r
o
b
o
t.
T
h
e
co
m
p
ar
is
o
n
b
et
w
e
en
a
P
I
D
co
n
tr
o
ller
,
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ap
tiv
e
co
n
tr
o
ller
,
an
d
t
h
e
MP
C
i
llu
s
t
r
ates
ad
v
a
n
tag
e
o
f
th
e
d
esi
g
n
ed
co
n
tr
o
ller
an
d
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ts
ab
ilit
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f
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r
ex
ac
t c
o
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tr
o
l o
f
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r
o
b
o
t
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n
a
s
p
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if
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g
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id
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ath
.
6
.
1
.
E
qu
a
t
io
ns
Nu
m
b
er
eq
u
atio
n
s
co
n
s
ec
u
tiv
el
y
w
it
h
eq
u
atio
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n
u
m
b
er
s
i
n
p
ar
en
th
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s
f
l
u
s
h
w
it
h
t
h
e
r
ig
h
t
m
ar
g
i
n
,
as
in
(
1
)
.
First
u
s
e
th
e
eq
u
atio
n
ed
ito
r
to
c
r
ea
te
th
e
eq
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atio
n
.
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h
en
s
elec
t
th
e
“
E
q
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m
ar
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p
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P
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tab
k
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d
w
r
ite
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P
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L
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CA
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P
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NCIP
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t
w
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co
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ten
t
s
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f
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at
ar
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p
u
b
lis
h
ed
ar
e;
1
)
p
ee
r
r
ev
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w
ed
an
d
2
)
ar
ch
iv
a
l.
T
h
e
T
r
an
s
ac
tio
n
s
p
u
b
lis
h
es
s
c
h
o
la
r
l
y
ar
ticles
o
f
ar
ch
iv
a
l
v
al
u
e
as
w
ell
as
t
u
to
r
ial
ex
p
o
s
itio
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s
an
d
cr
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r
ev
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w
s
o
f
class
ica
l su
b
j
ec
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an
d
to
p
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cu
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r
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ter
est.
Au
t
h
o
r
s
s
h
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ld
co
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s
id
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th
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f
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llo
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p
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in
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s
:
a.
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p
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cite
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b.
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p
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c.
Au
t
h
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s
m
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s
t
co
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v
in
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b
o
th
p
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r
r
ev
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w
er
s
an
d
th
e
ed
ito
r
s
o
f
th
e
s
cien
tific
a
n
d
tec
h
n
i
ca
l
m
er
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o
f
a
p
ap
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; th
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s
tan
d
ar
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s
o
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w
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ex
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ar
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o
r
u
n
ex
p
ec
ted
r
esu
lts
ar
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r
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ted
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
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2089
-
4856
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Usi
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215
d.
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t
h
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latest
t
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n
ica
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ac
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v
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m
e
n
t,
w
h
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s
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itab
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tatio
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a
p
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e
ap
p
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p
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iate
f
o
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p
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b
licatio
n
.
RE
F
E
R
E
NC
E
S
[1
]
G
u
a
n
g
,
L
i.
,
L
e
n
n
o
x
,
B.
,
Zh
e
n
g
tao
,
Din
g
.
,
2
0
0
5
,
In
f
in
it
e
h
o
riz
o
n
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tro
l
f
o
r
trac
k
in
g
p
ro
b
lem
s,
[2
]
Co
n
tr
o
l
a
n
d
A
u
to
m
a
ti
o
n
,
.
ICCA
'
0
5
.
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
,
p
a
g
e
s
516
–
5
2
1
.
[3
]
Ca
m
a
c
h
o
,
E.
F
.
,
Bo
r
d
o
n
s,
C.
,
1
9
9
9
.
M
o
d
e
l
P
re
d
ictiv
e
Co
n
tro
l
,
S
p
ri
n
g
e
r
-
V
e
rlag
2
e
d
it
i
o
n
.
[4
]
Na
g
y
,
Z.
,
F
ra
n
k
e
,
R.
,
M
a
h
n
,
B
.
,
A
ll
g
,
o
we
r,
F
.
,
2
0
0
5
,
Re
a
l
-
ti
m
e
im
p
le
m
e
n
tatio
n
o
f
n
o
n
li
n
e
a
r
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tro
l
o
f
in
it
e
ti
m
e
p
ro
c
e
ss
e
s
in
a
n
in
d
u
strial
,
f
ra
m
e
w
o
r
k
.
In
In
tern
a
ti
o
n
a
l
W
o
rk
sh
o
p
o
n
A
ss
e
ss
m
e
n
t
a
n
d
F
u
tu
re
Dire
c
ti
o
n
s o
f
No
n
li
n
e
a
r
M
o
d
e
l
P
r
e
d
ictiv
e
Co
n
tro
l,
G
e
r
m
a
n
y
,
p
a
g
e
s
4
8
3
-
4
9
0
.
[5
]
L
ik
a
r,
B.
,
Ko
c
ij
a
n
,
J.,
2
0
0
7
,
P
re
d
ictiv
e
c
o
n
tro
l
o
f
a
g
a
s
-
li
q
u
id
se
p
a
ra
ti
on
p
la
n
t
b
a
se
d
o
n
a
G
a
u
ss
ian
p
ro
c
e
ss
m
o
d
e
l.
Co
m
p
u
ters
&
Ch
e
m
ic
a
l
En
g
in
e
e
rin
g
,
3
1
(1
):
1
4
2
–
1
5
2
.
[6
]
Ha
u
g
e
,
T
.
A
.
,
S
lo
ra
,
R.
a
n
d
L
ie,
B.
,
M
o
d
e
l
P
re
d
ictiv
e
Co
n
tr
o
l
o
f
a
No
rsk
e
S
k
o
g
,
P
re
li
m
in
a
ry
S
tu
d
y
,
in
p
ro
c
e
e
d
in
g
s o
f
Co
n
tro
l
S
y
ste
m
s,2
0
0
2
,
Ju
n
e
3
-
5
,
S
to
c
k
h
o
lm
,
S
w
e
d
e
n
,
p
a
g
e
s 7
5
-
7
9
.
[7
]
G
a
r
c
ia,
C.
E.
,
P
re
tt
,
D.M
,
M
o
r
a
ri,
M
.
,
1
9
8
9
.
M
o
d
e
l
P
re
d
ictiv
e
Co
n
tro
l:
T
h
e
o
ry
a
n
d
P
ra
c
ti
c
e
,
A
S
u
rv
e
y
.
A
u
to
m
a
ti
c
a
,
2
5
(3
):
3
3
5
-
3
4
8
.
[8
]
A
li
re
z
a
Re
z
a
e
e
,
"
Ge
n
e
ti
c
s
y
m
b
i
o
sis
a
lg
o
rit
h
m
g
e
n
e
ra
ti
n
g
T
e
st
d
a
ta
f
o
r
c
o
n
stra
in
t
a
u
to
m
a
ta
"
,
A
p
p
li
e
d
a
n
d
Co
m
p
u
tatio
n
a
l
M
a
th
e
m
a
ti
c
s.,
V
OL
.
7
,
NO
.
1
,
A
z
e
rb
a
ij
a
n
,
A
P
RIL
2
0
0
8
p
p
1
2
6
-
1
3
7
.
[9
]
Ko
u
v
a
rit
a
k
is,
B.
,
Ca
n
n
o
n
,
M
.
,
C
o
u
c
h
m
a
n
,
P
.
,
2
0
0
6
,
M
P
C
a
s
a
to
o
l
f
o
r
su
sta
in
a
b
le
d
e
v
e
lo
p
m
e
n
t
in
teg
ra
ted
p
o
li
c
y
a
ss
e
ss
m
e
n
t.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
A
u
to
m
a
ti
c
Co
n
tro
l,
5
1
(1
4
5
–
1
4
9
).
[1
0
]
Be
ll
e
m
a
n
s,
B.
,
S
c
h
u
tt
e
r,
D.,
De
M
o
o
r
,
B.
,
2
0
0
6
,
M
o
d
e
l
p
re
d
ictiv
e
c
o
n
tro
l
f
o
r
ra
m
p
m
e
terin
g
o
f
m
o
t
o
rw
a
y
tra
ff
ic:
A
c
a
se
stu
d
y
,
Co
n
tro
l
E
n
g
in
e
e
rin
g
P
ra
c
ti
c
e
,
1
4
(7
):
7
5
7
-
7
6
7
.
[1
1
]
V
a
n
D
e
n
Bo
o
m
,
T
.
J.J.,
De
S
c
h
u
tt
e
r,
B.
,
2
0
0
6
.
M
P
C
o
f
im
p
li
c
it
s
w
it
c
h
in
g
m
a
x
-
p
lu
s
-
li
n
e
a
r
d
isc
re
te
e
v
e
n
t
s
y
ste
m
s
-
T
i
m
in
g
a
sp
e
c
ts,
P
r
o
c
e
e
d
in
g
s
o
f
th
e
8
th
In
ter
n
a
ti
o
n
a
l
W
o
rk
sh
o
p
o
n
Disc
re
te
Ev
e
n
t
S
y
ste
m
s
(W
OD
ES
'
0
6
),
A
n
n
A
rb
o
r,
M
ich
i
g
a
n
,
p
a
g
e
s 4
5
7
-
4
6
2
.
[1
2
]
A
z
e
v
e
d
o
,
C.
,
P
o
ig
n
e
t,
P
.
,
Esp
iau
,
B.
,
2
0
0
2
.
M
o
v
in
g
h
o
rizo
n
c
o
n
tr
o
l
f
o
r
b
ip
e
d
ro
b
o
ts
w
it
h
o
u
t
re
f
e
re
n
c
e
traje
c
to
r
y
.
In
IEE
E
In
tern
a
t
io
n
a
l
Co
n
f
e
re
n
c
e
o
n
R
o
b
o
ti
c
s an
d
A
u
to
m
a
ti
o
n
,
p
a
g
e
s 2
7
6
2
–
2
7
6
7
.
[1
3
]
S
h
rid
h
a
r,
R.
,
Co
o
p
e
r,
J.,
1
9
9
7
.
A
T
u
n
in
g
S
trate
g
y
f
o
r
Un
c
o
n
stra
in
e
d
S
IS
O
M
o
d
e
l
P
re
d
ic
ti
v
e
Co
n
tro
l.
En
g
lan
d
:
C
h
e
m
.
[1
4
]
A
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