Page 56 - Neural Network Modeling and Identification of Dynamical Systems

44 2. DYNAMIC NEURAL NETWORKS: STRUCTURES AND TRAINING METHODS

FIGURE 2.11 Examples of a structural organization for feedforward dynamic neural networks. (A) Jordan network. (B) El-
man network. D in are source (input) data; D out are output data (results); L (0) is input layer; L (1) is hidden layer; L (2) is output
layer; TDL (1) is tapped delay line (TDL) of order 1.

FIGURE 2.12 Examples of a structural organization for feedforward dynamic neural networks. (A) Hopfield network.
(B) Hamming network. D in are source (input) data; D out are output data (results); L (0) is input layer; L (1) is hidden layer;
L (2) is output layer; TDL (1) is tapped delay line (TDL) of order 1.

In Fig. 2.13A the ANN model Nonlinear any topology of forward and backward connec-
AutoRegression with eXternal inputs (NARX) tions, that is, in a certain sense, this structural
[33–41] is shown, which is widely used in mod- organization of the neural network is the most
eling and control tasks for dynamical systems. common.
The same structural organization has a variant The set of Figs. 2.14–2.17 allows us to spec-
of this network, expanded by the composition ify the structural organization of the layers of
of the parameters considered. This is the ANN the ANN model: the input layer (Fig. 2.14)and
model Nonlinear AutoRegression with Moving working (hidden and output) layers (Fig. 2.15).
Average and eXternal inputs (NARMAX) [42, In Fig. 2.16 the structure of the TDL element is
43]. presented, and in Fig. 2.17 the structure of the
In Fig. 2.13B we can see an example of an neuron as the main element that is part of the
ANN model with the Layered Digital Dynamic working layers of the ANN model is shown.
Network (LDDN) structure [11,28]. Networks One of the most popular static neural net-
with a structure of this type can have practically work architectures is a Layered Feedforward