TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.4, April 201
4, pp. 3185 ~ 3
1
9
2
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i4.4925
3185
Re
cei
v
ed Se
ptem
ber 19, 2013; Revi
se
d No
vem
ber
20, 2013; Accepted Decem
ber 9, 201
3
The Design of PID Controller Based on Hopfield Neural
Network
Wenxia Du
1
, Xiuping Zhao*
2
, Feng Lv
3
, Hailian Du
3
Coll
ed
ge of Ca
reer T
e
chnolo
g
y
, He
bei N
o
rm
al Univ
ersit
y
, N
O.20 Road E
a
st of 2nd Rin
g South, Yuh
ua
District, Shijiaz
hua
ng, He
bei,0
500
24, Ph./Fax: 00860
31
18
07
879
42
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: d
w
x2
0
0
4
051
3@1
63.com
1
, zhao
xiup
in
g07
111
@sin
a.com
2
,
lvfeng
@mai
l.tsingh
ua.e
du.cn
3
, duha
ili
an@
12
6.com
4
A
b
st
ra
ct
W
i
th the complexity i
n
creas
e in i
ndustri
a
l prod
uctio
n
process, the
traditio
nal Pr
o
portio
n
-
Integratio
n-Diff
e
renti
a
tion
(PI
D
) cont
r
o
l c
an
not
me
et the
r
equ
ire
m
e
n
ts
of
the c
ontrol
sy
stem
perfor
m
a
n
ce.
Becaus
e ne
ur
al netw
o
rk has
the abil
i
ty of ada
ptive, self-l
earn
i
ng a
nd
n
onli
n
e
a
r functi
on ap
proxi
m
ati
on,
control
equality
of system
is
im
pr
oved
if it is
combined wit
h
traditional PID. In the pa
per, Hopfield neural
netw
o
rk bas
ed
on H
ebb
rul
e
s i
s
used to
id
enti
f
y the
par
amet
ers of syste
m
, and th
en th
e st
ate spac
e
mo
d
e
l
is estab
lish
ed.
Hopfi
e
ld
Ne
ur
al n
e
tw
ork has
the f
uncti
on
o
f
opti
m
al c
a
lc
u
l
atio
n, PID con
t
roller
base
d
o
n
Hopfield neural network is desig
ned for
a
system
c
a
n optimi
z
e
t
he
pa
rameter
of PID in real-tim
e
and
improve c
ontro
l accuracy. Si
mulati
on resu
lt show
the perfor
m
a
n
ce i
ndex is
greatly i
m
pr
ov
ed.
Ke
y
w
ords
:
Hopfield neural netw
ork, control system
, PID
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
With the imp
r
oveme
n
t of the level of in
dus
tri
a
l produ
ction, the p
r
o
c
e
ss
become
s
mo
re
and mo
re co
mplicate
d
, high co
ntrol pe
rforma
nce of
system is
req
u
ired in
crea
si
ngly, espe
cia
lly
whe
n
the sy
stem involve
s
pa
ramete
r
uncertain
tie
s
,
traditional P
I
D co
ntrol
ca
n not meet t
h
e
requi
rem
ents of the control syste
m
[1]. Neu
r
al
network ha
s the
p
r
ope
rtie
s of
self-lea
rning
a
nd
self-o
rg
ani
zin
g
, it also ca
n approximat
e any non
lin
ear fun
c
tion
[2-4]. If neural net
wo
rk is
combi
ned
with traditional
PID controlle
r, appli
ed ra
nge of PID can be enla
r
g
ed, at the same
time, cont
rol
effect can
be
improved g
r
eatly. In
man
y
neural n
e
tworks, Hopfi
e
ld net
wo
rk
has
good p
e
rfo
r
m
ance in optim
al cal
c
ulation
[5-9]. F
eedb
a
ck
con
n
e
c
tion
is sele
cted a
m
ong ne
uron
s,
time-del
ay be
tween th
e in
puts a
nd o
u
tputs i
s
co
n
s
i
dere
d
, the dy
namic
pr
ocess of the
syst
em
can
be
de
scribed. In thi
s
pape
r, sy
ste
m
param
ete
r
s can
be id
e
n
tified by con
t
inuou
s Hopfi
e
ld
neural n
e
two
r
k (CHNN).
F
u
rthe
rmo
r
e,
CHNN i
s
u
s
e
d
to
optimize
co
ntrol
pa
ra
meters of
PID in
real
-time. Fo
r controlled
pro
c
e
ss, th
e
PID controller b
a
sed
Ho
pf
ield ne
ural
network
ca
n be
desi
gne
d to realize effective control.
2.
Con
t
inuous
Hop
f
ield Ne
ural Ne
t
w
o
r
k
(CHNN)
2.1. Net
w
o
r
k
Model
Hopfiel
d
net
work i
s
a hi
g
h
ly interconn
ect
ed
colle
cti
on of sim
p
le
pro
c
e
ssi
ng
neuron
s.
The p
h
ysi
c
ist
Ho
pfield
de
si
gned
mod
e
l u
s
ed
by a
nal
o
g
ci
rcuit, the
stru
cture
of
Hopfield m
odel
is
s
h
ow
n
in
F
i
gu
r
e
1
.
In Figu
re 1,
The
re
sista
n
ce
i
R
a
n
d
ca
pa
c
i
ta
nc
e
i
C
in parallel
sim
u
l
a
te time-
delay
cha
r
a
c
teri
stics of bi
ologi
cal neu
ron
s
.
Operati
onal
amplifier sim
u
lates nonli
n
ear pro
p
e
r
ties
of
neuron
s, that is
()
ii
v=f
u
，
whe
r
e
i
u
is the inte
rna
l
state of
ith
neuron, who
s
e output i
s
i
v
,
)
(
f
is the a
c
tivation fun
c
tion o
f
neuron, whi
c
h i
s
continu
ously differen
t
iable an
d
0
)
(
f
;
i
I
is the
externa
l
input;
ij
w
is
the con
n
e
c
tion strength
bet
we
en jth n
euron
and ith
neu
ro
n,
ji
ij
w
w
; N is the nu
mber of ne
urons in the
Ho
pfield network.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 3185 – 3
192
3186
A
c
c
o
r
d
i
n
g
t
o
K
i
r
c
h
h
o
f
f
'
s
l
a
w
s
,
the dyna
mics fo
rmula
t
ion of CHNN ca
n be obt
ained:
1
N
ii
ii
j
j
i
j
i
du
u
Cw
v
I
dt
R
(1)
The activatio
n
function of
neuron
)
(
f
is sel
e
cted in the fol
l
owin
g:
0
0
/
/
1
1
)
(
u
u
u
u
i
i
i
i
i
e
e
u
f
v
(2)
Whe
r
e
0
u
rep
r
e
s
ents the i
n
itia
l value of inp
u
t vo
ltage. Th
e dynami
c
p
r
oce
s
s of CHNN i
s
descri
bed by
Equation (1)
and Equatio
n
(2)
2.2. Energ
y
Function o
f
Net
w
o
r
k
The
stable
a
nalysi
s
of
Ho
pfield net
wo
rk b
a
ses on
e
nergy fu
nctio
n
, trainin
g
of
Hopfiel
d
netwo
rk i
s
to minimize ene
rgy function
E
,
1
11
1
1
0
11
()
2
i
v
NN
N
N
ij
i
j
i
i
i
ij
i
i
i
E
wv
v
v
I
f
v
d
v
R
(3)
If
ij
ji
ww
, the time derivative of energy fun
c
tio
n
E
is
:
2
1
1
[(
)
]
0
N
ii
i
i
i
ii
dv
d
f
v
d
v
dE
dE
C
dt
dv
d
t
d
v
dt
(4)
So the equilibrium point of
asymptotic st
abilit
y is the
minimum val
ue of energy
function.
Thoug
h it
will
always
settl
e to a
sta
b
le
state f
r
om
a
n
y initial
state, a
Hopfiel
d
network
usu
a
lly
gets tra
pped i
n
to local mini
mum state
s
.
In the high-g
a
i
n limit, the e
nergy fun
c
tio
n
can b
e
app
roximated to Equation
(
5
)
.
1
R
1
C
3
v
1
v
2
v
N
R
3
R
2
R
2
C
3
C
N
C
N
v
2
I
3
I
N
I
21
w
32
w
13
w
1
u
2
u
3
u
N
u
1
N
w
1
I
Figure 1. The Structu
r
e of
CHNN Mo
de
l
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
The De
sig
n
o
f
PID Controll
er Based on
Hopfiel
d
Neu
r
al Network (Wen
xia
Du)
3187
11
1
1
2
NN
N
ij
i
j
i
i
ij
i
Ew
v
v
v
I
(5)
Thro
ugh a si
mple analy
s
i
s
of the energy func
tion, the method of
solving opti
m
ization
probl
em
s used by CHNN can b
e
gott
en. Obje
ctive
function
s of
the pro
b
lem
is co
nverte
d
to
energy fun
c
tion of
network and
the va
ri
able
of p
r
obl
em
corre
s
po
nds with
the
status of
net
work,
the optimal solution of the
probl
em ha
s
been o
b
tain
e
d
the optimal
value co
uld b
e
solved a
s
t
h
e
energy functi
on co
nverg
e
s to t
he minimal value of ne
twork.
3.
S
y
st
em Ident
i
f
i
cat
i
on B
a
sed on CHNN
The state e
q
u
a
tion of linear discrete
syst
em is form
ula
t
ed in the followin
g
，
12
n
(1
)
(
)
(
)
()
[
(
)
,
()
()
]
xk
A
x
k
B
u
k
x
kx
k
x
k
x
k
,,
(6)
11
1
1
n
nn
n
aa
A
aa
11
1
1
m
nn
m
bb
B
bb
Whe
r
e
m
uR
rep
r
e
s
ent
s syste
m
input
，
n
x
R
repre
s
e
n
ts sy
stem state vector,
nn
A
R
is the
state
-
transitio
n, an
d
nm
B
R
is input
matrix
，
wh
ose
es
tima
te
d va
lu
es
is
r
e
pr
es
e
n
t
ed
b
y
ˆ
A
and
ˆ
B
. The
purp
o
se of system identificati
on is to est
i
mate the value of each
element in m
a
trix [10-12].
Becau
s
e th
ere are
nn
+
nm
elem
ents in m
a
tri
x
nn
A
R
and
nm
B
R
, Hopfield
netwo
rk requi
re
nn
+
nm
neu
ron
s
in o
r
d
e
r to
e
s
timate th
e el
ements,
in
which
ea
ch
ste
ady
state output correspon
ds
with t
he estima
tion of matrix A and B.
Assu
me the i
dentificatio
n model is:
ˆ
ˆ
ˆ
(1
)
(
)
(
)
x
kA
x
k
B
u
k
(7)
11
1
1
ˆ
ˆ
ˆ
ˆ
n
nn
n
aa
A
aa
11
1
1
ˆ
ˆ
ˆ
m
nn
m
bb
B
bb
Let
Equation (7) subt
ract
E
quat
ion (6), id
entification e
r
ror
(1
)
ek
could b
e
obtaine
d,
(1
)
(
1
)
(1
)
(1
)
(
)
(
)
e
k
xk
xk
x
kA
x
k
B
u
k
(8)
Define the o
b
j
ective functio
n
:
1
()
(
1
)
(
1
)
2
1
[
(
1
)
()
()
]
[
(
1
)
(
)
(
)
]
2
T
T
Ek
e
k
e
k
x
kA
x
k
B
u
k
x
k
A
x
k
B
u
k
(9)
Paramete
rs to be inde
ntified co
rrespon
d wi
th output
s of Hopfiel
d
netwo
rk, that
is:
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ISSN: 23
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TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 3185 – 3
192
3188
12
11
1
1
1
1
1
1
()
[
(
)
,
()
()
]
[a
,
,
;
;
;
]
T
nn
n
m
T
n
n
nn
n
n
nm
Vk
v
k
v
k
v
k
aa
a
b
b
b
b
After objectiv
e
function i
s
transfo
rme
d
appr
op
riately, it can be co
nne
cted with
energy
function Eq
u
a
tion (5
), an
d then conn
ection
weig
ht
W
and thresho
l
d
I
are d
e
termined. Fo
r
se
con
d
linea
r
disc
ret
e
sy
st
em:
2
11
2
1
1
2
12
2
2
2
2
11
2
1
1
2
12
2
2
2
2
11
2
2
2
11
2
2
00
0
00
0
00
0
00
0
00
0
00
0
xx
x
u
x
xx
x
u
x
x
xx
u
x
w
x
xx
u
x
ux
u
x
u
ux
u
x
u
1
2345
6
11
1
2
2
1
2
2
1
2
(
1
)
(
)
(
1
)
()
(
1
)
(
)
(
1
)
()
(
1
)
(
)
(
1
)
()
II
I
I
I
I
I
x
kx
k
x
kx
k
x
k
x
k
x
kx
k
x
k
u
k
x
k
u
k
The activatio
n
function of
neuron is:
12
()
11
i
ii
u
ii
uu
ek
vf
u
k
k
ee
(10)
Whe
r
e
0
1
u
,
k
re
prese
n
ts gai
n. The followi
ng fo
rmul
ation ca
n be derived from
above
equatio
n:
2
1
i
u
i
k
e
Vk
(11)
The time derivative of o
u
t
p
u
t
o
f
n
e
t
w
o
r
k
i
v
is:
ii
i
i
dv
dv
du
dt
du
dt
Set
i
Cc
, then:
22
2
1
()
2(
)
(1
)
2
,1
,
2
,
i
i
u
ii
u
i
N
i
ij
i
j
dv
k
V
ke
du
e
k
du
wI
i
N
dt
22
1
((
)
)
2
1,
2
,
N
ii
i
i
ij
i
j
i
dv
dv
du
k
V
k
wI
dt
du
dt
kc
iN
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
The De
sig
n
o
f
PID Controll
er Based on
Hopfiel
d
Neu
r
al Network (Wen
xia
Du)
3189
D
i
sc
re
tiz
a
tion is
s
h
ow
n
as
:
22
1
((
)
)
(1
)
(
)
(
)
(
)
2
N
i
ii
i
j
j
i
j
kv
k
vk
vk
w
v
k
I
k
t
kc
(12)
A new varia
b
l
e
is introd
uce
d
,
2
t
kc
The form
ula above can be
chan
ged into
,
22
1
(
1
)
(
)
[
()
()
]
(
)
N
ii
i
j
j
i
i
j
vk
vk
w
v
k
I
k
k
v
(13)
If we bring the weight
ij
w
and thre
sh
ol
d
i
I
into the above equati
on, assumin
g
(0
)
0
i
v
, we can
ge
t the param
eter e
s
timation of the sy
stem, wh
en
()
i
vk
conve
r
ge to
balan
ce p
o
int
by iteration.
4.
PID Control
Bas
e
d on CHNN
PID control system stru
ctu
r
e ba
sed o
n
CHNN is
shown as
in Figure.2,
Figure 2. PID Control Stru
cture Based o
n
Contin
uou
s HNN
Figure 2
sho
w
s that th
e
system
stru
ctu
r
e ha
s
two
Ho
pfield n
eural
netwo
rks.
On
e HNN i
s
use
d
to id
ent
ify the param
eters,
wh
en t
he
state
spa
c
e m
odel
of
controlled
pla
n
t is u
n
certai
n
sometim
e
s,
a
nother on
e i
s
used to
opti
m
ize
the
par
ameters
of traditional
PID
controlle
r, tha
t
is
the factor of p
r
opo
rtion
P
K
, integration
i
K
and di
fferentiation
d
K
,
define net
work output is:
T
d
i
p
T
K
K
K
v
v
v
V
]
[
]
[
3
2
1
Define the o
b
j
ective functio
n
of optimizat
ion as follo
w,
2
1
()
(
1
)
2
1
(1
)
(
)
(
)
(
1
)
(
)
(
)
2
T
Ek
e
k
rk
C
A
x
k
B
u
k
r
k
C
A
x
k
B
u
k
(
1
4
)
Syste
m
id
en
tifier
Optim
al calculation
)
(
k
r
Plant system
PI
D con
t
ro
ller
CH
NN
CH
NN
p
K
i
K
d
K
)
(
k
e
_
+
)
(
k
u
)
(
k
y
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 3185 – 3
192
3190
Whe
r
e:
(1
)
(
1
)
(1
)
(
1
)
(
)
(
)
ek
r
k
y
k
r
k
C
A
x
k
B
u
k
From th
e ab
o
v
e Equation
(5) an
d Equ
a
tion (1
4),
con
n
e
ction
wei
ght
W
and th
re
shol
d
I
are dete
r
min
ed. Assuming
:
12
3
()
1
,
(
0
)
0
0
,
(0)
[
(
0
)
(
0)
(0)]
[
000
]
T
T
rk
x
Vv
v
v
The o
u
tput o
f
HNN can b
e
obtain
ed from
Equatio
n
(12
)
, wh
en t
he outp
u
t of netwo
rk
achi
eved pe
rmitted rang
e.
5. Simulation
State control
of orde
r linea
r discrete system is de
scri
bed a
s
:
(1
)
(
)
(
)
()
0.3
6
8
0
0.
63
2
01
0
.
63
2
1
0.
36
8
xk
A
x
k
B
u
k
yC
x
k
AB
C
Whe
n
the
step fun
c
tion i
s
sele
cted a
s
inp
u
t
of the discrete
system, the
co
ntrolle
r i
s
desi
gne
d ba
sed on HCNN,
simulation
re
sult is sho
w
n
from Figu
re 3
to Figure 7.
Figure 3. Parameter E
s
timation of System Model
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TELKOM
NIKA
ISSN:
2302-4
046
The De
sig
n
o
f
PID Controll
er Based on
Hopfiel
d
Neu
r
al Network (Wen
xia
Du)
3191
Figure 4. Optimization Process Param
e
ter
p
K
and
i
K
Figure 5. Con
t
rol Re
sunlt b
y
using Optim
i
zed
p
K
and
i
K
To illustrate control results
of the neural
net
wo
rk PID
control is b
e
tter than the traditional
PID cont
rol,
we p
u
t the sa
me PI para
m
eters
(
0.2
096
p
k
，
0.0341
i
k
) on t
he traditio
n
al
PID
and ma
ke si
mulation on t
he sam
e
syst
em, the results are
sho
w
n i
n
Figure 9 an
d Figure 10.
Figure 6. Step Re
spo
n
se of the Simulation
Sys
t
em
Figure 7. Enlarged Partial
Response of
Traditio
nal PID
Simulation
re
sult
sho
w
s th
at co
ntrol
effect b
a
sed
on
Ho
pfield
neu
ral
netwo
r
k i
s
better
than that
ba
sed o
n
traditio
nal PI
D. T
h
e
sp
ecifi
c
m
e
ri
ts in
clud
e
sm
all oversh
oot, fast
re
spo
n
se
time, less time adju
s
tme
n
t, high pre
c
i
s
ion
contro
l and etc., it doesn’t rely on a fixed system
model. Co
mp
arison bet
we
en the two co
ntrolle
rs i
s
sh
own in Ta
ble
1.
Table 1. Co
m
pari
s
on of Pe
rforma
nce Index
Controller t
y
pe
Regulation time
(step)
Stead
y
-
stat
e erro
r
Traditional PID c
ontroller
35
0.6
PIDcontroller bas
ed on HN
N
30
0.1
0
50
10
0
15
0
20
0
-0
.
5
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
x 1
0
11
29
.
6
1
2
29
.
6
14
29
.
6
16
29
.
6
1
8
29
.
6
2
29
.
6
22
29
.
624
29
.
626
29
.
6
2
8
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
x 1
0
7
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02-4
046
TELKOM
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KA
Vol. 12, No. 4, April 2014: 3185 – 3
192
3192
6. Conclu
sion
A PID co
ntro
ller b
a
sed o
n
HNN is
propo
sed i
n
thi
s
pa
pe
r. Ho
pfield ne
ural
netwo
rk
based o
n
He
bb rule
s can
conve
r
ge
ra
p
i
dly, it us
ed t
o
identify an
d optimi
z
e th
e pa
ramete
rs of
system PID,
One
HNN is use
d
to ide
n
tify
the parameters, wh
en the
s
t
a
t
e s
p
ac
e
mo
de
l o
f
controlled
pla
n
t is u
n
ce
rtai
n, anothe
r o
n
e
is
us
e
d
to
optimize
the
para
m
eters
o
f
traditional P
I
D
controlle
r, sy
stem p
a
rame
ters
ca
n b
e
well
optim
ize
in real-tim
e. Simulation
result
sh
ow the
perfo
rman
ce i
ndex of control system i
s
g
r
eatly improv
ed.
Ackn
o
w
l
e
dg
ements
This
work h
a
s be
en sup
ported
by National Natural Scien
c
e
Found
ation
of China
(611
750
59),
Heb
e
i Edu
c
a
t
ion Dep
a
rtm
ent Prog
ram
(Q20
120
53
), Do
ctor F
oun
dation of He
bei
Normal Univ
ersity (L20
12
B13),
Youth
Found
ati
on
o
f
Heb
e
i Normal University (L20
11Q
08
),
Natural Scie
n
c
e Fou
ndatio
n of Hebei Province. Th
i
s
work ha
s al
so financi
a
lly suppo
rted by the
Teache
r sp
ecial resea
r
ch o
f
Hebei Norm
al University in edu
cation reform in 20
13
Year.
Referen
ces
[1]
Astrom KJ, Hagglund T
.
PID contro
llers: th
eory, d
e
sig
n
a
nd tu
nin
g
. Press of Instrument Societ
y
of
America, Res
e
arch T
r
iangle P
a
rk, NC, Secon
d
editi
on. 19
95
.
[2]
Xu S, Hu
ang
Y, Qu L, et al. F
P
GA Realiz
at
ion of PID Contro
ller Bas
ed on BP Ne
ural Net
w
o
r
k
.
T
E
LKOMNIKA Indon
esi
an Jou
r
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al Eng
i
ne
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ng.
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1
(10):
604
2-60
50.
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Hon
g
mei
L.
Appl
icatio
n R
e
searc
h
of
B
P
Ne
ural
Ne
t
w
ork
in
En
g
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each
i
ng
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uatio
n
.
T
E
LKOMNIKA Indon
esi
an Jou
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602-
460
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[4]
Z
h
iju
n YU. R
B
F
Neura
l
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e
t
w
orks O
p
timi
zation A
l
g
o
rith
m and A
p
p
lic
ation
on T
a
x F
o
recastin
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T
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491-
349
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[5]
Joy
a
G, Atencia MA, Sandoval F.
Ho
pfie
ld
ne
ural
net
w
o
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ks for optim
iz
ation
Stud
y
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the
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dy
nam
ics.
N
e
uro
c
om
pu
ti
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2
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1): 219
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[6]
Yao
L
i
an
g
. Co
mb
in
atoria
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imi
z
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opfie
ld n
e
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uro
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oham
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a
nna
n MA. Intell
ige
n
t ma
ximum
po
w
e
r p
o
int tr
ackin
g
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stem
usin
g
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e
ld n
eur
al
net
w
o
rk optim
i
z
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y
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i
c
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il
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[8]
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bari
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a
t
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data
trans
formati
on
tech
niq
ues
w
i
th H
opfie
ld ne
ural
net
w
o
rks
for
solvin
g travel
li
ng sal
e
sman
p
r
obl
em.
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i
th Appl
icatio
ns
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7
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1
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[9]
Hopfield
JJ.
N
eura
l
netw
o
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h
ysica
l systems w
i
th e
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er
ge
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ona
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e
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.
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hang
CO, Fada
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nlin
ear s
y
ste
m
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atio
n
usin
g a G
abor/H
opfie
ld
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w
o
rk.
IEEE
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r
ansactio
n
, Systems, Man a
nd Cy
b
e
rnetics
,
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(1): 124-1
33.
[11]
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T
a
tem, HG Le
w
i
s, PM Atkinson.
Super-res
o
lution target
identifi
c
a
tion from
rem
o
tely sens
ed
imag
es usi
ng
a Ho
pfiel
d
ne
u
r
al netw
o
rk
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and Remote S
ens
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r
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6.
[12]
Shi H
o
n
g
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a
i
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Z
u
-lian. S
y
ste
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ide
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tificati
on
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d
o
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NA
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g H
opfie
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g
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itio
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3.
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