April 2016
Intermediate to advanced
552 pages
17h 2m
English
Content preview from Bio-Inspired Computing and Networking
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Bio-Inspired Process Control
■
177
■ Sum—this part represents
K
i=1
M
i
j=0
in Equation 7.3
v
k
=
K
i=1
M
i
j=0
⎛
⎝
P
p=1
w
(p)
b
(p)
(i,j)
⎞
⎠
v
(i,j,k)
+
P
p=1
w
(p)
c
(p)
■ Autoregression—this part represents autoregression in Equation 7.3
ˆy
(narmax)
k
= v
k
+
N
i=1
⎛
⎝
P
p=1
w
(p)
a
(p)
i
⎞
⎠
y
k−i
Because all items are linear they can be ordered in any way. Let us invert the order
of the sum and autoregression in the cascade. Because the sum contains multiple
inputs, the autoregression must be applied to all its inputs:
ˆv
(r,j,k)
= v
(r,j,k)
+
N
i=1
⎛
⎝
P
p=1
w
(p)
a
(p)
i
⎞
⎠
ˆv
(r,j,k−i)
, r = 1, ..., K
ˆy
(narmax)
k
=
K
i=1
M
i
j=0
⎛
⎝
P
p=1
w
(p)
b
(p)
(i,j)
⎞
⎠
ˆv
(i,j,k)
+
P
p=1
w
(p)
c
(p)
The order reversion above is ...
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