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Fig. 4.7.
Identification of Van der Pol oscillator using linear regression (1000 step
regression) (
a
) Initialization on the attractor (limit cycle) (
b
) Initialization far from
the attractor
exogenous input (NARX model). The stochastic NARX(
p,r
) model equation
is
X
(
k
+1)=
f
[
X
(
k
)
,...,X
(
k
−
p
+1)
,V
(
k
+1)
,u
(
k
)
,...,u
(
k
−
r
+1)]
.
Regression order is
p
for the state and
r
for the control. The diagram of
the network, which is used for that purpose, is displayed on Fig. 4.8.
Fig. 4.8.
Learning diagram of a NARX based neural model to identify a controlled
dynamical system (see also Chap. 2, Fig. 2.31)
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