Neural Identification of Controlled Dynamical Systems and Recurrent Networks - Neural Networks: Methodology and Applications - page 231

4
Neural Identification of Controlled Dynamical
Systems and Recurrent Networks
M. Samuelides
Modeling of controlled dynamical systems or “process identification” is a
major application of neural networks. This topic was cursorily addressed in
Chap. 2. It is more systematically developed hereafter. Moreover, it is com-
pared to similar statistical methods that are commonly used, especially for
linear systems identification.
We start with the presentation of several examples of controlled dynam-
ical systems. We show that the addition of a “state noise” in order to take
into account the uncertainty of the model leads to viewing the evolution of
the state as a Markov process. Neuronal identification of nonlinear processes
is essentially a generalization of well known linear regression. We first recall
the elements of linear regression in the section “Regression, a tool for con-
trolled dynamic al system identification.” Based on examples, we show how
to compute the regression coe cients of an auto-regressive model. Then neural
identification is presented as a natural nonlinear regression methodology. Fol-
lowing section is devoted to on-line or adaptive identification of dynamical
systems. Our starting point is recursive identification of linear systems, which
is a mere generalization of the basic statistical Law of Large Numbers. Fur-
thermore, we develop the recursive prediction error method (RPEM), which
is a nonlinear extension thereof. Adaptive identification algorithms, including
neural identification algorithms, will be addressed.
In most applications, the state of the system cannot be completely known
because some state variables cannot be measured and because one cannot
avoid measurement errors. Therefore, filtering techniques are commonly used
to reconstruct the state of a dynamical process from the measurement results.
The popular technique of Kalman filtering is addressed in the section “Inno-
vation filter in a state model.” It is subsequently used for designing a neural
learning algorithm that may be used to identify dynamical processes. At the
end of the chapter, the sections “Recurrent neural networks” and “Learn-
ing for recurrent neural networks” are devoted to recurrent neural networks.
The most popular models of recurrent neural networks (Elman networks and