Indonesian Journal of
Electrical
Engineer
ing and
Computer Science
V
o
l. 10
, No
. 3, Jun
e
20
18
, pp
. 10
00
~
1
006
ISSN: 2502-4752,
DOI: 10.115
91/ijeecs
.v10.i
3.pp1000-1006
1
000
Jo
urn
a
l
h
o
me
pa
ge
: http://iaescore.c
om/jo
urnals/index.php/ijeecs
Positive Interval Observer-based
State F
e
edback Cont
roll
er for
Uncertain General Anaesthesia System
Ji
ng
Ji
n
g
Ch
a
n
g
1
, S. Syafiie
2
1
Faculty
of Infor
m
ation and
Co
mmunication
Tech
nolog
y
,
Univ
ersi
ti Tunku
Abdul Rahm
an, Malay
s
ia
2
Faculty
of Engineering
,
S
y
ia
h K
u
ala University
,
Indonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 11, 2018
Rev
i
sed
Mar
20
, 20
18
Accepte
d Apr 5, 2018
The drug deliver
y
process of general
anaes
th
esia
in the hum
an bo
d
y
is m
o
st
commonly
described b
y
the P
h
arm
acokinetic/Pharmacod
y
n
a
mic (PK/PD)
m
odel. Since th
e PK m
odel is
a positive l
i
ne
ar
sy
st
em
, the de
sign of the
controll
er
can
b
e
tr
eat
ed
as a
po
sitive st
abi
liz
ati
on problem
.
In t
h
is paper
,
a
state f
eedba
ck c
ontrolle
r with po
sitive in
terv
al ob
server was desig
n
ed using a
linear
program
ming
approach b
y
taking into accoun
t
th
e
inter-indiv
i
dual
variab
ility
among patient in th
e PK
model. The designed co
ntroller was
assessed b
y
simulation
on a poo
l of pati
ents.
The
result shows that
the desig
n
of a fix controller for the whole popula
tion is
difficu
lt due to the conflict
between
perform
ance and
robustn
ess.
K
eyw
ords
:
Dept
h of
anaes
thesia
In
ter-ind
i
v
i
d
u
a
l v
a
riab
ility
Out
put
fee
dbac
k
c
ont
rol
Po
sitiv
e lin
ear
syste
m
Po
sitiv
e ob
server
Copyright ©
201
8 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Jing Jing C
h
ang,
Depa
rt
m
e
nt
of
C
o
m
put
er an
d
C
o
m
m
uni
cat
i
o
n Tec
h
nol
ogy
,
Facul
t
y
o
f
I
n
fo
rm
ati
on a
n
d
C
o
m
m
uni
cat
i
on
Tech
nol
ogy
,
Un
i
v
ersiti Tu
nk
u Abd
u
l
Rahman
,
Jal
a
n
Uni
v
ersi
t
i
B
a
nda
r B
a
rat
,
3
1
9
0
0
Kam
p
ar, P
e
ra
k, M
a
l
a
y
s
i
a
.
Em
a
il: ch
an
gj
j@u
t
ar.edu
.m
y
1.
INTRODUCTION
The d
r
u
g
de
l
i
v
ery
pr
ocess
of ge
ne
ral
anaest
h
esi
a
i
s
m
o
st
co
m
m
onl
y
desc
ri
be
d by
t
h
e
Pha
r
m
acoki
net
i
c
/
P
harm
acody
nam
i
c (PK/
PD
) m
odel
.
The
PK m
o
d
e
l is a lin
ear tim
e in
v
a
rian
t (LTI)
m
o
d
e
l
t
h
at
rel
a
t
e
s t
h
e dr
ug
do
sage t
o
d
r
u
g
co
nce
n
t
r
at
i
on i
n
bl
o
o
d
pl
asm
a
, whi
l
e PD m
odel
is a st
at
i
c
nonl
i
n
ear
m
o
d
e
l th
at relates th
e
d
r
u
g
con
cen
t
r
atio
n in
t
h
e
b
l
oo
d p
l
asm
a
to
th
e resu
ltin
g dru
g
effect
[1
].
On
e im
p
o
r
tan
t
p
r
op
erty of th
e PK m
o
d
e
l is th
at it is a p
o
s
itiv
e system; th
e state v
a
riab
les (drug
conce
n
tration
in each c
o
m
p
artm
ent) can ne
ver
be le
ss t
h
an zero.
Im
posing
positiveness in the
desi
gn
of
clo
s
ed-loo
p
sy
ste
m
al
lo
ws one to
si
m
p
lify
th
e stab
ility
an
alysis [2
] an
d
red
u
c
es th
e p
r
ob
le
m
to
a
real b
o
u
n
d
e
d
unce
r
t
a
i
n
t
y
gai
n
p
r
o
b
l
e
m
[3]
.
There
f
ore, t
h
e
cont
r
o
l
o
f
ge
neral a
n
aesthe
s
ia can be trea
ted as a stabilization
p
r
ob
lem
o
f
a po
sitiv
e system
.
Clo
s
ed-loop
st
ab
ilizatio
n
o
f
p
o
s
itiv
e lin
ear
syste
m
h
a
s b
e
en
co
nsid
ered
in
sev
e
ral
p
r
evio
u
s
wo
rk
s.
For e
x
am
ple, Kaczore
k [4] proposed a
suffi
c
ient condition for
state feedback controlle
r base
d
on
Ge
rsgorin's
th
eorem
an
d
q
u
a
dratic programmin
g
.
Lat
e
r, Leenh
eer
an
d Aeyels
[5] so
lv
e t
h
e st
ab
ilisatio
n
o
f
a state
feedbac
k
using alge
braic a
p
proac
h
. B
o
yd
et al [6] an
d
Gao
et
al
[7]
pr
o
pose
d
a
ne
cessary and s
u
fficient
co
nd
itio
n to
stab
ilised
th
e clo
s
ed
-loop
p
o
s
i
tiv
e lin
ear syst
e
m
fo
rm
u
l
ated as Lin
e
ar Mat
r
ix
In
equ
a
lity (LMI).
Ram
i
et al [8-9] also propose
d
a fee
d
back sta
b
ilisation
base
d
on
linear program
m
ing (LP
)
m
e
thod.
The LP a
p
proa
ch offe
rs se
veral adva
ntages
ove
r the
othe
r
m
e
thods: it provi
des
bot
h the necessa
ry
an
d
sufficien
t
co
nd
ition
to
g
u
a
ran
t
ee asym
p
t
o
tic stab
ili
ty o
f
th
e syst
e
m
, it h
a
s a lo
wer co
m
p
u
t
atio
n
a
l
co
m
p
lex
ity co
m
p
ared
to
qu
ad
ratic
p
r
o
g
rammin
g
or LM
I,
and it can
be
e
x
tended easily to unce
rtain
plants.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
a
n
J
E
l
ec En
g &
C
o
m
p
Sci
ISS
N
:
2
5
0
2
-
47
52
Posi
t
i
ve I
n
t
e
rv
al
St
at
e Fee
d
b
a
ck C
ont
r
o
l
l
e
r
f
o
r G
e
ner
a
l
A
n
aest
hesi
a
Syst
e
m
(
J
.J.
C
h
an
g)
1
001
Mo
reo
v
e
r, t
h
e
LP in
eq
u
a
lities can
b
e
u
s
ed
to d
e
sign
a
p
o
s
itiv
e in
terv
al ob
serv
er [10
]
. In
an
aesth
esia
cont
rol, t
h
e drug c
o
ncent
r
ation i
n
each c
o
m
p
artm
ent was not
pos
sible to be m
easure
d
in real tim
e
. Hence, a
n
obs
erver is nee
d
ed to estim
ate the states. Howe
ve
r, th
e classical Luenbe
rge
r
observe
r
doe
s not gua
r
a
n
tee the
p
o
s
itiv
en
ess of th
e esti
m
a
te
d
states. Th
is can
b
e
ach
ieved
b
y
u
s
ing
th
e LP app
r
o
a
ch
th
at g
u
a
ran
t
ees th
e
esti
m
a
ted
state
s
to
rem
a
in
in
th
e
n
onn
eg
ati
v
e orth
an
t.
C
o
n
v
e
n
t
i
onal
l
y
,
st
at
e feedba
ck co
nt
r
o
l
l
e
rs
have
bee
n
desi
gne
d
usi
n
g t
h
e
LM
I [1
1]
o
r
p
o
l
e pl
acem
e
n
t
[12
-
13
] m
e
th
od
s.
Howev
e
r, fo
r
p
r
ob
lem
wit
h
on
ly p
a
rtia
l in
fo
rm
atio
n
on
th
e state is av
ailab
l
e, static o
u
t
pu
t
st
abi
l
i
zat
i
on p
r
o
b
l
e
m
has not
been f
o
rm
ul
at
ed and s
o
lve
d
exactly as an LMI proble
m or pole pla
c
e
m
ent
ap
pro
ach [8
].
Fu
rt
h
e
rm
o
r
e, it can
b
e
d
i
fficu
l
t to
u
s
e po
le
p
l
ace
m
e
n
t
m
e
th
od
for
p
o
s
itiv
e
syste
m
sin
ce it i
s
no
t
ev
en
k
now
which
p
o
l
es are desireab
le t
o
ensu
re po
sitiv
ity o
f
th
e clo
s
ed
-l
o
o
p
system
.
Hen
ce,
th
e LP
ap
pro
ach
h
a
s t
h
e ad
v
a
n
t
ag
e
o
f
easy h
a
n
d
ling
of static ou
tpu
t
stab
ilizatio
n
p
r
ob
lem
for
p
o
s
itiv
e syste
m
s.
In t
h
i
s
pape
r,
u
n
cert
a
i
n
t
y
was
assum
e
d t
o
be
occu
rre
d i
n
P
K
m
odel
.
LP ap
pr
oac
h
was
use
d
t
o
de
si
g
n
th
e state-feedback
co
n
t
ro
ller
an
d th
e po
sitive in
terv
al
ob
serv
er,
b
y
tak
i
ng in
to
accoun
t th
e
p
o
ssib
l
e
v
a
riab
ilit
y
o
f
p
a
ram
e
ters in
th
e PK m
o
d
e
l.
2.
R
E
SEARC
H M
ETHOD
Sev
e
ral im
p
o
r
tan
t
no
tatio
n
s
are stated here.
R
n
+
d
e
notes
th
e n
onn
eg
a
tive
ort
h
ant
of the
n-
dim
e
nsional real space
R
n
.
M
T
de
not
es t
h
e t
r
a
n
s
pose
of t
h
e m
a
t
r
i
x
M
. Each
elemen
ts o
f
m
a
trix
M
is
rep
r
ese
n
t
e
d by
m
ij
where
i
i
s
t
h
e num
ber o
f
ro
w an
d
j
is
th
e n
u
m
b
e
r of co
lu
m
n
.
M
ij
≥
0
m
ean
s th
at
all th
e
ele
m
ents are
nonne
g
ative.
M
and
M
r
e
pr
esen
ts the up
p
e
r
bo
und
an
d low
e
r boun
d of
t
h
e
u
n
c
ertain
m
a
tr
ix
M.
Cx
y
Bu
Ax
x
(1
)
a.
Plant m
o
del
The
PK
m
odel
can
be
descri
b
e
d as
a f
o
ur
-co
m
partm
e
nt
m
o
del
an
d e
x
pres
sed i
n
t
h
e
f
o
l
l
o
wi
n
g
st
at
e
space E
q
uation:
wh
ere
e
C
C
C
C
x
3
2
1
,
.
1
0
0
0
and
0
0
0
,
0
0
0
0
0
0
0
1
0
0
31
3
1
13
21
2
1
12
1
3
31
1
2
21
13
12
10
C
V
B
k
k
k
V
V
k
k
V
V
k
V
V
k
V
V
k
k
k
k
A
e
e
C
1
,
C
2
,
C
3
and
C
e
den
o
t
e
t
h
e dr
ug
conce
n
t
r
at
i
on i
n
com
p
ar
tm
ent 1, 2,
3 and effect com
p
artment,
respectively.
V
i
is the volu
m
e
for com
p
artm
e
n
t
i
wh
ile
k
ij
is th
e
d
r
ug
tran
sfer
rate from com
p
ar
tment
i
to
j
.
u
is
t
h
e pro
pof
ol
i
n
fusi
o
n
rat
e
(m
l/
h),
ρ
i
s
t
h
e dru
g
conce
n
t
r
at
i
on (for
pr
op
ofol
,
ρ
= 1
0
m
g
/m
l
)
and
α
is a
norm
a
li
sati
on const
a
nt
(
α
=
60
m
i
n/
h).
Fo
r Schn
id
er PK
m
o
d
e
l, th
e
n
o
m
in
al
v
a
lu
e
o
f
co
m
p
artm
ent
vol
um
es and dru
g
transfer rates can be
fo
un
d in
[1
4-15
]. Howev
e
r, du
e to
in
ter-p
atien
t
v
a
riab
ilit
y,
it is ex
p
ected
t
h
at th
e tru
e
v
a
l
u
es will b
e
d
i
fferen
t
fro
m
th
e n
o
mi
n
a
l v
a
lu
es. Lu
ck
ily,
in
m
o
st
o
f
th
e b
i
o
l
o
g
i
cal
m
o
d
e
l
lin
g
s
, in
t
e
r-v
ariab
ility
re
m
a
in
s b
o
u
n
d
e
d
with
a
p
r
i
o
r
i
k
n
o
w
n
b
o
u
n
d
s
[
1
6
]
.
C
onsi
d
er
a 50 y
ear
ol
d
m
a
l
e
pat
i
e
nt
wei
g
ht
i
ng 7
0
k
g
an
d 1
70cm
t
a
l
l
.
A
possi
bl
e
lo
w
e
r
an
d upper
b
oun
d of
m
a
tr
ix
A
w
e
r
e
g
i
ven
as th
e
f
o
ll
ow
:
,
2420
.
0
0
0
2420
.
0
0
0035
.
0
0
0035
.
0
0
0
0679
.
0
0679
.
0
0
1958
.
0
3190
.
0
7979
.
0
,
4820
.
0
0
0
2420
.
0
0
0035
.
0
0
0035
.
0
0
0
0679
.
0
0679
.
0
0
1958
.
0
3190
.
0
9689
.
0
A
A
(2
)
B
and C
were
assum
e
d cert
a
i
n
an
d
were e
q
ual
t
o
.
1
0
0
0
and
0
0
0
039
.
0
C
B
T
PD m
o
del can
b
e
ex
pressed
by th
e fo
llowing static n
o
n
lin
ear Hill eq
u
a
tion
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
502
-47
52
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci, V
o
l. 10
,
No
.
3
,
Jun
e
2
018
:
10
00
–
1
006
1
002
e
e
e
C
C
C
BIS
BIS
BIS
BIS
50
0
max
0
)
(
(3
)
wh
ere B
I
S is
measu
r
ab
le p
a
ram
e
ter o
f
an
aesth
e
tic lev
e
l,
BIS
0
is the
bas
e
line effect in the a
b
se
nce
of
drug,
BIS
ma
x
is th
e
max
i
m
u
m
effect o
f
th
e dru
g
,
C
e
50
i
s
t
h
e c
o
n
cent
r
at
i
o
n t
h
at
pr
o
duces
50%
of
t
h
e
m
a
xim
u
m
drug
effect and
γ
determin
e th
e steep
n
e
ss
o
f
the Hill eq
u
a
tion
.
In
th
is p
a
per, it is assu
med
th
at BIS
0
=
10
0,
BIS
ma
x
= 0,
C
e
50
= 2
.
23
an
d
γ
=
1
.
72
.
Due to
th
e static n
a
ture
o
f
PD m
o
d
e
l, th
e
no
n
lin
ear effect
can
b
e
can
celled
ou
t by its in
v
e
rse,
PD
-1
.
Hence
,
t
h
e
pl
ant
ca
n
be
c
ont
rol
l
e
d
usi
n
g
l
i
n
ear c
o
nt
r
o
l
st
rat
e
gy
.
b.
State feedba
ck
sta
b
ilisatio
n
First, it is assumed that the states are available fo
r feed
b
a
ck
. Th
e ob
j
ecti
v
e is to
d
e
termin
e th
e g
a
in
matrix
K
in
th
e co
n
t
ro
l law
u = K
x
that st
abilizes the syste
m
Bu
Ax
x
w
h
ile guar
a
n
t
eeing
th
e syste
m
p
o
s
itiv
en
ess. Accord
ing
to
[8
], th
e
K
can be determ
ined suc
h
that
A + BK
is b
o
t
h
a Metzler an
d
a Hurwitz
matrix
.
These can
b
e
ach
i
ev
ed
b
y
th
e fo
llo
win
g
LP
i
n
equ
a
l
ities:
0
0
0
1
1
d
v
B
d
A
v
B
d
A
n
i
i
n
i
i
(4
)
A
nd
j
i
v
b
d
a
j
i
v
b
d
a
v
v
j
i
j
ij
j
i
j
ij
n
i
i
i
for
0
for
0
0
0
1
(5
)
whe
r
e
K
was
c
o
m
puted as
n
n
v
d
v
d
K
1
1
1
1
.
(6
)
c.
Positi
ve inte
rval obser
v
er
Consi
d
er the
followi
ng obse
rver system
Ax
x
Cx
y
(7
)
whe
r
e the t
r
aje
c
tory of
n
x
R
is assumed
to
b
e
un
kn
own
bu
t
n
onneg
a
tiv
e. Based
o
n
t
h
e classical Lu
en
b
e
rg
er
obs
er
ver
[
17]
,
t
h
e
fol
l
o
wi
n
g
l
i
near
o
b
se
rv
e
r
was
use
d
to approxim
a
t
e the states
x
ˆ
Ly
x
LC
A
x
ˆ
)
(
(8
)
whe
r
e L i
s
t
h
e obse
r
ve
r gai
n
.
The aim
here i
s
t
o
det
e
rm
i
n
e t
h
e obse
r
ver
gai
n
L
s
u
ch that the approximated
states
x
ˆ
are
nonnegative
a
n
d the error
x
x
ˆ
converges asym
ptotic
a
lly to
zero.
Accord
ing
to [1
0
]
, a
p
o
s
itiv
e
in
terv
al
ob
server can
b
e
d
e
sign
ed using
th
e fo
llo
wi
n
g
in
eq
ualities:
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesi
a
n
J
E
l
ec En
g &
C
o
m
p
Sci
ISS
N
:
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5
0
2
-
47
52
Posi
t
i
ve I
n
t
e
rv
al
St
at
e Fee
d
b
a
ck C
ont
r
o
l
l
e
r
f
o
r G
e
ner
a
l
A
n
aest
hesi
a
Syst
e
m
(
J
.J.
C
h
an
g)
1
003
0
0
)
(
diag
,
1
,
for
0
0
0
1
i
T
T
j
T
i
n
i
i
T
T
z
I
Z
C
d
A
n
j
i
z
c
d
z
C
d
A
(9
)
with
L
calculat
e
d as
n
n
z
d
z
d
L
1
1
1
1
.
(1
0)
d.
Inte
gral
ac
ti
o
n
To
i
n
clud
e
referen
c
e track
i
ng
an
d im
p
r
o
v
e
its d
i
sturb
a
n
c
e rej
ectio
n ab
ilities, th
e con
t
ro
l law
was
expa
nded to i
n
clude i
n
tegral
action
r
y
z
z
k
Kx
u
i
.
(1
1)
whe
r
e
r
i
s
t
h
e refe
rence
poi
nt
and
k
i
as the integral ter
m
. The augm
ented
sy
st
em
of t
h
e cl
osed
-l
o
op c
o
n
t
rol
l
e
r
was e
x
presse
d
as follows:
r
I
u
B
B
z
x
x
C
LC
A
LC
A
z
x
x
0
0
0
ˆ
0
0
0
0
0
ˆ
(1
2)
Figu
re
1 s
h
o
w
s the
o
v
erall
bloc
k
diag
ra
m
of th
e cl
os
ed-l
oo
p sy
ste
m
. The plant
m
odel has th
e
pr
o
p
o
f
ol in
fus
i
on rate, u as
the inp
u
t and
B
i
spectral
Index (BIS) as the output. BIS
is the was assum
e
d
un
k
n
o
w
n. B
I
S
is a wid
e
ly
use
d
in
de
x that m
easure
s
th
e
de
pth
of a
n
aesthe
s
ia. The
nonlinear effect int
r
oduce
d
Since t
h
e
patients
were
ass
u
m
e
d u
n
k
n
o
w
n
,
the
n
o
m
i
nal m
a
trix A
was
use
d
in
the
o
b
s
erve
r
bloc
k
d
u
ri
ng
si
m
u
lation.
Figu
re
1.
B
l
oc
k
diag
ram
of th
e o
b
ser
v
e
r
-
b
as
ed
state fe
edba
ck c
ont
rol
with integral action
3.
R
E
SU
LTS AN
D ANA
LY
SIS
B
a
sed o
n
the
m
e
thod
descri
bed in
Section
2, the c
ontr
o
lle
r gains
were
d
e
signe
d an
d c
o
m
puted to be
5103
.
0
3759
.
0
3660
.
0
3593
.
0
K
,
0464
.
0
0
0
0
L
, an
d
k
i
= 2.
The desi
gne
d
contr
o
ller wa
s
tested on 9 simulated
patients
with varying
k
10
and
k
e0
values, as tabulated in Table
1.
These two
values were
chosen due t
o
t
h
eir
higher impact
on t
h
e
variability of BIS
effect.
The
objecti
v
e
of the
controller is t
o
bri
n
g t
h
e
B
I
S value
do
w
n
t
o
50
, w
h
ich
is
the
rec
o
m
m
e
nded
inde
x d
u
ri
ng
sur
g
ical pr
oce
d
u
r
es. T
h
e co
ntr
o
ller wa
s a
ssessed
by
its indu
ction
ph
ase du
ratio
n (
I
D
)
,
perce
n
tage
of
ove
rs
ho
ot (
O
S
)
, a
nd i
n
tegrat
ed ab
sol
u
te
er
ro
r (
I
AE
) [
1
8]
. The
ID
was
defi
ned as t
h
e
tim
e
elapsed
from
the beginning of propof
ol adm
i
nistration until the BIS
falls to
below 60 for
30s [19].
A
short ID
is pre
f
era
b
le
because it re
duc
e
s th
e tim
e spent in t
h
e
ope
rating
room
. OS
m
easures the de
gree
of
overshoot
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
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502
-47
52
I
ndo
n
e
sian
J Elec Eng
& Com
p
Sci,
Vo
l. 10
,
No
.
3
,
Jun
e
2
018
:
10
00
–
1
006
1
004
an
d shou
ld
b
e
as low as
possib
l
e to
p
r
ev
en
t dr
ug
ov
erdose.
IAE is the integra
tion of absol
u
te difference
betwee
n the
B
I
S set-
poi
nt an
d
the
real B
I
S
.
Table
1. Test Population
Patient no.
k
10
(m
in
-1
)
k
e0
(m
in
-1
)
1 0.
283
0.
242
2 0.
283
0.
362
3 0.
283
0.
482
4 0.
369
0.
242
5 (
N
o
m
inal)
0.
369
0.
362
6 0.
369
0.
482
7 0.
454
0.
242
8 0.
454
0.
362
9 0.
454
0.
482
Table
2 a
n
d
Fi
gu
re
2 s
h
ows
the sim
u
lation r
e
sult o
f
the controller for all patie
nts. Res
u
l
t
shows
that
all BIS c
o
nverges t
o
the
targeted val
u
e.
T
h
e m
ean
v
a
lu
e of
OS is 13
.0
1%,
with
no BI
S lo
wer
than
4
0
.
Ho
we
ver
,
a lo
ng
ID
, with th
e
m
ean of 1
4
.
7
8 m
i
n, was ob
s
e
rve
d
. T
h
is d
u
r
ation
was lo
n
g
er to
3 m
i
n, whic
h is
co
nsid
er
ed
to
o lo
ng
f
o
r
clinica
l
practice a
n
d other
researc
h
[20].
Table 2. Performance
of
the
cont
roller
without initial bolus
Patien
t
n
o
.
ID (
m
in
)
OS (%
)
IAE
1 14.
50
19.
42
1362
9
2 13.
50
14.
70
1132
1
3 13.
08
12.
34
1056
4
4 15.
50
16.
33
1222
5
5 14.
58
12.
08
1045
8
6 14.
25
10.
12
9726
7 16.
50
13.
77
1121
1
8 15.
67
9.
98
9704
9 15.
42
8.
37
9021
M
ean
14.
78
13.
01
1087
3
Fig
u
r
e
2
.
Perfor
m
an
ce o
f
t
h
e
co
n
t
r
o
ller
witho
u
t
i
n
itial b
o
l
us. (
a
)
B
I
S
r
e
spo
n
s
e (b)
Pr
opof
o
l
i
n
fu
sion
r
a
te
Th
e ind
u
c
tion
p
h
a
se can
be gr
eatly r
e
d
u
c
ed
wh
en
an
i
n
itial
b
o
l
us of
pr
opof
o
l
was ad
m
i
n
i
ster
ed
.
Due
to the prese
n
ce
of close
d
-l
oo
p
contr
o
l, a low
e
r-tha
n
-
c
linical practice bol
us injec
tion was adm
i
nistered
d
u
ri
ng
the initial phase, i.e.,
250 m
l
/
h
at the first m
i
nute. Then, the cont
roller was initiated in t
h
e second m
i
nutes.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
d
onesia
n
J
E
l
ec En
g &
C
o
m
p
Sci
ISS
N
: 2
5
0
2
-
47
52
Positive Interval St
ate Feedback C
ontroller
fo
r G
e
ner
a
l A
n
aesthesi
a
Syste
m
(
J
.J.
C
h
an
g)
1
005
Table 3 and Figure 3 presents th
e si
m
u
lat
i
on result of the controlle
r wi
th an initial b
o
lus for all
patients. The
result shows that all BIS
conve
r
ges t
o
the ta
rgeted val
u
e. T
h
e
m
ean ID
was
r
e
duce
d
t
o
2
.
3
6
m
i
n.
All B
I
S readi
n
g reac
hed
60
within 3
.
0
3
m
i
n. H
o
weve
r,
the
m
ean OS wa
s shown to inc
r
ease from
13.01% to
16
.6
0%
.
Table 3. Performance
of
the
cont
roller
with initial bol
us
Patien
t
n
o
.
ID (
m
in
)
OS (%
)
IAE
1 2.
83
19.
22
1404
7
2 2.
08
20.
07
1285
5
3 1.
83
27.
79
1229
1
4 3.
00
14.
54
1843
5 .
17
12.
46
1052
0
6 1.
83
21.
28
9944
7 3.
33
11.
55
1047
7
8 2.
25
7.
36
7975
9 1.
92
15.
15
7871
M
ean
2.
36
16.
60
1086
9
Figure
3. Perform
ance of t
h
e
cont
ro
ller
with initial bol
us.
(a) BIS respon
se (b)
Propofol i
n
fusion
rate
While the ID can also be
s
h
orte
ned
by
increasin
g the
k
i
value, it will also cau
se a large overshoot
whic
h m
a
y
put the patient safety
at risk. B
e
sides thes
e two
con
f
licting pe
r
f
o
r
m
a
nce
criteria (ID a
nd O
S
), the
per
f
o
r
m
a
nce o
f
the
co
ntr
o
ller
has
to
be c
o
m
p
r
o
m
i
sed fo
r s
y
ste
m
robustness if t
h
e BIS
response
were
to be
kept within
t
h
e
range of 40-60 for
all pati
ents. This shows
that the i
n
ter-individua
l
variability is a
great
challenge in the desi
gn of a
safe a
n
d ef
ficient controller
for a
n
aesthesia syste
m
.
4.
CO
NCL
USI
O
N
An obse
rve
r
-based state fee
dbac
k
c
o
ntrol with
inte
gral
action
was
de
signe
d to
re
g
u
l
ate the B
I
S
signal u
s
in
g p
r
op
o
f
ol in
fusi
o
n
rate. T
h
e sta
t
e feedb
ack
ga
in an
d o
b
ser
v
e
r
gain
wer
e
de
signe
d u
s
in
g the LP
approach and t
o
ok i
n
to
consideration the pos
itiveness of
states as well as th
e uncertainty of t
h
e PK
m
odel.
Si
m
u
lation result shows t
h
at
all BIS was able to converg
e
to the set-point, but
w
ith a long i
n
duction
phase.
A bolus injection
of propofo
l during the initial stage was able to
reduce the induction phase, but will increase
the ove
rs
ho
ot
perce
n
tage
. Th
is sho
w
s that the desi
gn
of
a
fixe
d co
ntr
o
ller fo
r the w
h
ole po
pulatio
n is diffic
u
lt
due t
o
the la
rge inter-i
ndi
vidual va
riability exists am
ong
pa
tients. Indi
vidualised c
ont
rol
l
er m
a
y be the
key to
tackle patient
variability in order to
realise th
e closed-loop
cont
rol
of anaesthesia.
REFERE
NC
ES
[1]
H. Derendorf an
d B. Meibohm, “Modeling
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armacod
y
nami
c
(PK/PD) Relatio
nships: Concepts
and Perspectiv
es,”
Pharmaceutical Research
, vol. 16(2), pp. 176-8
5
, Feb
1999.
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I
S
SN:
2
502
-47
52
I
ndo
n
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& Com
p
Sci,
Vo
l. 10
,
No
.
3
,
Jun
e
2
018
:
10
00
–
1
006
1
006
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ck Stabili
za
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y
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o
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.
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ve S
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BIOGRAP
HI
ES
OF AUTH
ORS
Chang Jing Jing
is with Dep
a
rtment of Com
puter and Communication Techno
log
y
, University
Tunku Abdul
Rahman, Malay
s
ia
. She r
eceived her Ph.D. in Control
and Automation
Engine
ering in Universiti Putra
Mala
y
s
i
a
. Her
research int
e
re
sts include m
odelling
,
contro
l,
artif
ici
a
l
int
e
ll
ig
ence
and
biom
ed
ica
l
eng
i
ne
ering
.
S. S
y
afiie r
e
ceiv
ed his DEA
and
PhD degrees fro
m University
of
Vallado
lid, Spain in 2004
and
2007, respectiv
ely
,
in
th
e ar
ea
of s
y
stems engi
neering
and
automatic
control. In 2007, he
continu
e
as postdoctoral resear
ch
er in the ar
ea of
continuous acti
on reinforcemen
t learn
i
ng in the
same university
.
In 2008, he did
his post do
ctor
al
r
e
sear
ch in
Gent Univ
ersity
,
Belgium in
the
area of biomedical eng
i
neer
ing
and machine learning. From 200
9 to 2017 he wa
s appointed as
s
e
nior le
ctur
er a
t
departm
e
n
t
ch
e
m
ical and
enviro
nm
ental eng
i
ne
e
r
ing Univers
i
t
i
P
u
tra M
a
l
a
y
s
ia
.
In 2017 he join
ed industrial en
gineer
ing departme
nt in S
y
iah
Kuala University
. His resear
ch
inter
e
sts includ
e
m
achine le
arni
ng and control
th
eor
y
application in bi
omedical engin
eer
ing,
chemical engineering and
supply chain manag
e
ment.
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