Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 23

of normal operation, and the actual state of the process, the model of
normal operation must be accurate and run in real time.

• The model may be accurate, but too complex for real-time operation (e.g.,

for an application in monitoring and control).

If measurements are available, in addition to the equations of the—unsatisfac-
tory—knowledge-based model, it would be unadvisable to forsake altogether
the accumulated knowledge on the process and to design a purely black-box
model. Semi-physical modeling allows the model designer to have the best of
both worlds: the designer can make use of the physical knowledge in order to
choose the structure of the recurrent network, and make use of the data in
order to estimate the parameters of the model. An industrial application of
semi-physical modeling is described below, and the design methodology of a
semi-physical model is explained in Chap. 2.

1.1.6.2 Process Control

The purpose of a control system is to convey a prescribed dynamics to the
response of a process to a control signal or to a disturbance. In the case of
a regulator system the process must stay in a prescribed state in spite of
disturbances: the cruise control system of a car must keep the speed constant
(equal to the setpoint speed) irrespective of the slope of the road, wind gusts,
load variations, etc. A tracking system is designed to follow the variations of
the setpoint, irrespective of disturbances: in a fermenting plant, the heating
system must be controlled in order for the temperature to follow a prescribed
temperature profile, irrespective of the temperature of ingredients that may
be added during operation, of heat-producing chemical reactions that may
take place, etc. In order to achieve such goals, a model of the process must be
available; if necessary, the model must be nonlinear, hence be implemented as
a recurrent neural network. Chapter 5 is devoted to nonlinear neural control.

1.1.7 Recurrent Neural Networks Without Training for
Combinatorial Optimization

In the previous two sections, we emphasized the applications of recurrent
neural networks that take advantage of their forced dynamics : the model de-
signer is interested in the response of the system to control signals. By con-
trast, there is a special class of applications of recurrent neural networks that
takes advantage of their spontaneous dynamics, i.e., of their dynamics with
zero input.
Recurrent neural networks whose activation function is a step function
(McCulloch-Pitts neurons), have a dynamics that features fixed points: if such
a network is forced into an initial state, and is subsequently left to evolve under
its spontaneous dynamics, it reaches a stable state after a finite transient
sequence of states. This stable state depends on the initial state. The final