Neural Identification of Controlled Dynamical Systems and Recurrent Networks - Neural Networks: Methodology and Applications - page 278

Fig. 4.19. Time unwrapping of the canonical form of a recurrent network along the
whole learning sequence

the training sequence is of length N . The state trajectory of the process is not
measured , hence cannot be used as state inputs during training. The state of
the network is set initially to the state of the process if the latter is available
(semidirected learning). If it is not the case, the input state of the network
is initialized to a likely value (a priori initialization). The unfolding of the
network canonical form is shown schematically on Fig. 4.19. That generates a
feedforward network. Any training algorithm of feedforward networks can be
used, subject to the constraint that all the weights of the copies are identical.
Therefore, the shared-weight technique must be used (see Chap. 2).
If the training sequences are too long, or if an adaptive training is required
(on-line training), the training sequences must be truncated to a finite dura-
tion, so that, for each training step, only a limited portion of past information
will be used. Let p be the duration of that period. Thus, at time n , only in-
formation pertaining to time n p + 1 to time n is taken into account. That

leads to a new notation: from now on, k will stand for the number of the copy
at step n ; k varies from 1 to p . The training scheme is similar to Fig. 4.19
with the following modifications:

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• The length of the sequence is not n time steps, but p time steps;

• The state inputs at the first of those p time-steps can be set in to two

different ways:
1. If the state of the process is fully measured, then the measured values
of the process may be assigned to these state inputs (at the first time-
step): then the algorithm is called semidirected ;
2. If the state of the process is not fully measured, those inputs must be
fed with the previously computed values for that specific copy (those
quantities were computed at learning step n 1). Then, the algorithm

is said “ undirected ” because the true state of the process is never taken
into account during the training process. In that case, that assignment

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