6.5. NEURAL NETWORKS IN INDIRECT NEURAL CONTROL 223
xlabel(íTime Stepí); ylabel(íPlant (solid) NN Output (dotted)í);Figure 6.24. Plant and trained neural network
response to specified inputStep 12. If the results are satisfactory, as illustrated in the simulation results
of Figure 6.24, then we have identified the nonlinear system and we can use
the trained neural network for control purposes. If however the results are not
satisfactory, some amount of experimentation would be required in selecting the
appropriate number of neurons in each of the hidden layers and/or increasing
the number of hidden layers, choosing a proper scaling factor, and by choosing
adifferent training algorithm. The reader is urged to conduct such experimen-
tation in order to obtain a better feel for how such parameters affect neural
network performance and training characteristics.
In the example discussed, it is clear that the neural network performs very
well in identifying the ìunknownî plant. Several models for identification are
discussed in the reference cited on page 219, at the beginning of this example.
We strongly recommend that the reader obtain further information regarding
system identification issues from this and other sources.
6.5.3 Instantaneous linearization
The most common approach to the control of nonlinear systems is to approx-
imate the system by a linear system, in the region of concern, and then to
design a controller for this linear system. Neural network model structures pro-
duce discrete nonlinear models, and as mentioned earlier, one way to design
the controller is to linearize its identified neural network model and apply stan-
dard linear controller designs. However,linearization of these discrete nonlinear
models can also be carried out at each sampling time by a process calledin-
stantaneous linearization. This process extracts a linear model from the