Error backpropagation algorithm

Note that for small errors, Eq. (19.31) converges to the derivative of activation function at the point of the output value. With an increase of system dimensionality, the chances for local minima decrease. It is believed that the described phenomenon, rather than a trapping in local minima, is responsible for convergency problems in the error backpropagation algorithm. 

The second step of training is the error backpropagation algorithm carried on only for the output layer. Since this is a supervised algorithm for one layer only, the training is very rapid, 100-1000 times faster than in the backpropagation multilayer network. This makes the radial basis-function network very attractive. Also, this network can be easily modeled using computers, however, its hardware implementation would be difficult. 

A schematic diagram of the neural network-based adaptive control technique is shown in Fig. 4.9. A neural network identification model is trained using a static backpropagation algorithm to generate p(fc + 1), given past values of y and u. The identification error is then used to update the weights of the neural identification model. The control error is used to update the... 

Several different types of ANN are available and the most popular is the backpropagation approach. In this procedure, input patterns presented to the input layer, for example, signals from an array of chemical sensors, generate a flow of activation to the output layer. Errors in the output are then fed back to the input layer to modify the weights of the interconnections. It should be emphasized that backpropagation does not describe a network but represents a learning algorithm. In this way, the network can be trained with known parameters, such as sensor array responses to sets of known chemicals. 

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