A First Course in FUZZY and NEURAL CONTROL

166 CHAPTER 5. NEURAL NETWORKS FOR CONTROL

of inputs and learn solely from training samples. As mathematical models for
biological nervous systems, artificial neural networks are useful in establishing
relationships between inputs and outputs of any kind of system.
Roughly speaking, aneural networkis a collection of artificial neurons. An
artificial neuronis a mathematical model of a biological neuron in its simplest
form. From our understanding, biological neurons are viewed as elementary
units for information processing in any nervous system. Without claiming its
neurobiological validity, the mathematical model of an artificial neuron [43] is
based on the following theses:

1. Neurons are the elementary units in a nervous system at which information
   processing occurs.


2. Incoming information is in the form of signals that are passed between
   neurons throughconnection links.


3. Each connection link has a properweightthat multiplies the signal trans-
   mitted.


4. Each neuron has an internal action, depending on abiasorfiring threshold,
   resulting in anactivation functionbeing applied to the weighted sum of
   the input signals to produce an output signal.

Thus, when input signalsx 1 ,x 2 ,...,xnreach the neuron through connection
links with associated weightsw 1 ,w 2 ,...,wn, respectively, the resulting input to
the neuron, called thenet input,istheweightedsum

Pn
i=1wixi.Ifthefiring
threshold isband the activation function isf, then the output of that neuron
is

y=f

√n

X

i=1

wixi−b

!

In thefirst computational model for artificial neurons, proposed by McCul-
loch and Pitts [43], outputs are binary, and the functionfis the step function

Figure 5.1. First model for artificial neuron

defined by

f(x)=

Ω

1 ifx≥ 0

0 ifx< 0