168 CHAPTER 5. NEURAL NETWORKS FOR CONTROL
Figure 5.3. Perceptronthe middle layer, called thehidden layer,haspnodes, and the output layer
hasmnodes. This is called an ìn-p-mî neural network.
Neurons (nodes) in each layer are somewhat similar. Neurons in the hidden
layer are hidden in the sense that we cannot directly observe their output. From
input patterns, we can only observe the output patterns from the output layer.
Of course, a multi-layer neural network can have more than one hidden layer.
The two-layer neural network depicted in Figure 5.4 is a typicalmulti-
layer perceptron(MLP), a multi-layer neural network whose neurons perform
the same function on inputs, usually a composite of the weighted sum and
adifferentiable nonlinear activation function, or transfer function, such as a
hyperbolic tangent function. Multi-layer perceptrons are the most commonly
used neural network structures for a broad range of applications.
5.2 Implementingneuralnetworks....................
Unlike computer systems that are programmed in advance to perform some
specific tasks, neural networks need to be trained from examples (supervised
learning) before being used. Specifically, as we will see next, a neural network
can be designed and trained to perform a specific task, for example, to construct
a control law for some control objective of a dynamical system.
The chosen architecture of the neural network is dictated by the problem at
hand. Once the neural network architecture is chosen, we need to have training
samples in order to train the neural network to perform the task intended. The
training of the neural network forms the most important phase in putting neural
networks to practical applications. Once the neural networks are successfully
trained, they are ready to use in applications as a computational device that
produces appropriate outputs from inputs.
We start out by giving an example of a logical function that can be imple-