Page 112 - Neural Network Modeling and Identification of Dynamical Systems

3.3 ANN-BASED MODELING AND IDENTIFICATION OF DYNAMICAL SYSTEMS 101
immediately in the process of the dynamical 1. Dynamic networks (models) derived from
system operating. conventional feedforward networks by add-
ing TDL elements to their inputs make it pos-
sible to take into account the dynamics of the
3.3.2 Recurrent Neural Networks for change in the input (control) signal. This is
Modeling of Dynamical Systems because not only the current value of the in-

As already noted in Chapter 2, ANNs can be put signal but also several values (prehistory)
divided into two classes: static ANNs and dy- for several previous instants are fed to the in-
namic ANNs. put of the ANN model. Models of this type
include networks such as TDNN (FTDNN)
Layered feedforward networks are static net-
and DTDNN, discussed in Chapter 2.Anex-
works. Their characteristic feature is that their
ample of using a TDNN-type model to solve
outputs depend only on their inputs, i.e., to cal-
a particular application problem is discussed
culate the outputs of such ANN, only the cur-
below, in Section 2.4 of this chapter. The so-
rent values of the variables used as input are
lution of some other application problems
required.
using networks of this type is also considered
In contrast, the output of dynamic ANNs de-
in [51–58].
pends not only on the current values of the in-
2. Dynamic networks with feedbacks (recur-
puts. In dynamic ANNs, when calculating their
outputs, the current and/or previous values of rent networks) are a much more powerful
tool for modeling controlled dynamical sys-
the inputs, states, and outputs of the network
tems. This capability is provided by the fact
are taken into account. Different architectures
that it becomes possible to take into account
of dynamic ANNs use different combinations of not only the prehistory of control signals (in-
these values (that is inputs, states, and outputs, puts) but also the prehistory for the outputs
their current and/or previous values). We give and internal states (outputs of hidden layers).
corresponding examples in Chapter 2. Dynamic Recurrent networks of types NARX [15–23]
networks of this kind appear because a memory and NARMAX [1,24] are most often used
(for example, as a TDL element) is introduced to solve the problems of modeling, identifi-
into their structure in some way, which allows cation, and control of nonlinear dynamical
us to save the values of the inputs, states, and systems. We discuss examples of using the
outputs of the network for future use. The pres- NARX network to solve problems of simula-
ence of memory in dynamic networks enables us tion of aircraft motion in Chapter 4. A much
to work with time sequences of values, which more general version of the structural orga-
is fundamentally essential for ANN simulation nization of ANN models for nonlinear dy-
of dynamical systems. Thus, it becomes possi- namical systems is networks with LDDN
ble to use some variable value (control variable architecture [29]. This architecture includes,
as a function of time or state of the system) or as individual cases, almost any other neu-
a set of such values as the input of the ANN roarchitecture (both feedforward and recur-
model. The response of the system and its corre- rent), including NARX and NARMAX. The
sponding model will also represent some set of LDDN architecture, as well as the learning
variables, in other words, the trajectories of the algorithms for networks with such an archi-
system in its state space. tecture, allow, among other things, to build
As for the possible options for dynamic net- not only traditional-style ANN models (black
works used to model the behavior of controlled box type) but also hybrid ANN models (gray
systems, there are two main directions: box type). We discuss models of this type in