![](bg8.png)
cient in figure 12 describes the relation between the
identified and the observed language of an automa-
ton identified with k = 2. For n = k + 1, the model
strictly creates the observed language L
k+1
Obs
. It can be
seen that for larger values of n the automaton gener-
ates a larger language than L
n
Obs
. A certain part of the
additionally created words is probably not part of the
original system language which may lead to a need for
specific precautions in some model based techniques
like diagnosis. However, from theorem 1 it is clear
that each word with length n ≥ k + 1 of the original
language not observed so far is part of the identified
language. In the case of model based diagnosis for
example, this allows stating that there will be no false
alerts using the identified automaton as fault-free ref-
erence model (Roth et al., 2009).
Figure 12: Coefficient of identified and observed language.
6 CONCLUSIONS
In this paper practical implications of identification
of closed-loop discrete event systems have been ad-
dressed. It has been shown how the necessary data
can be obtained in the case of industrial closed-loop
systems. For many model-based techniques it is cru-
cial to have a model of the complete system behav-
ior. For the identification algorithm of (Klein, 2005) it
has been proved that the identified automaton is sim-
ulates the original system language of arbitrary length
if some conditions concerning the observed system
language hold.
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