| Neural networks have often been presented as almost magical devices able to tame unruly non-linear control problems when provided with nothing more than the input and output data from that circuit. Experience has proven that there is no such free lunch. Although neural networks do have desirable properties that make them very useful for control systems, they need more than haphazardly collected data to fulfill their potential.; The properties required of a data set used to design conventional linear controller have been worked out in great detail. This work develops the corresponding data requirements for neural networks. The minimum sample size needed to guarantee that the network converges to the training set has been found using statistical methods and a variant of the Lipschitz condition. Also, to obtain a valid controller, the data must meet the requirement of Persistence of Excitation. Two methods are developed to verify this; direct calculation for smaller data sets, and qualitatively by examining the power spectral densities for the larger data sets.; These techniques were applied to several real world data sets, a simulated data set, and several data sets collected from lab-scale tests. The results showed that the real world is much more variable than the simulated or lab-scale systems. Also, although the developed conditions did guarantee the neural network would converge to the training set, they did not guarantee that the network could maintain control of the plant once on-line. Comparatively minor changes in the underlying distributions of the data were sufficient to render the neural network useless.; Although the back-propagation neural networks used here trained to acceptable errors, they were generally unable to outperform multiple linear regression at predicting the future behavior of the systems. This greatly reduces their utility in control systems. |
