Chapter 5
NEURAL NETWORKS
FOR CONTROL
In this chapter, we will introduce computational devices known as neural net-
works that are used to solve a variety of problems, including aspects of the
control of complex dynamical systems. With standard control, we rely on a
mathematical model; with fuzzy control, we use a set of rules. When the infor-
mation available about a systemís behavior consists primarily of numerical data,
the methodology of neural networks is very useful. As you will see later, some
problems are best solved with a combination of fuzzy and neural approaches.
We set forth here the basic mathematical ideas used in neural networks for
control. Although neural networks have applications in manyfields, we will
attempt to address only the parts of neural network theory that are directly
applicable in control theory. We will address questions such as ìWhat are neural
networks?,î ìWhy do we need neural networks?,î and ìHow can we use neural
networks to solve problems?î The applications of neural networks in control will
beexpandeduponinlaterchapters.
5.1 Whatisaneuralnetwork?......................
It is well known that biological systems can perform complex tasks without
recourse to explicit quantitative operations. In particular, biological organisms
are capable of learning gradually over time. This learning capability reflects
the ability of biological neurons to learn through exposure to external stimuli
and to generalize. Such properties ofnervous systems make them attractive
as computation models that can be designed to process complex data. For
example, the learning capability of biological organisms from examples suggests
possibilities for machine learning.
Neural networks, or more specifically, artificial neural networks are mathe-
matical models inspired from our understanding of biological nervous systems.
They are attractive as computation devices that can accept a large number