An H∞ control approach to robust learning of feedforward neural networks

A novel H∞ robust control approach is proposed in this study to deal with the learning problems of feedforward neural networks (FNNs). The analysis and design of a desired weight update law for the FNN is transformed into a robust controller design problem for a discrete dynamic system in terms of the estimation error. The drawbacks of some existing learning algorithms can therefore be revealed, especially for the case that the output data is fast changing with respect to the input or the output data is corrupted by noise. Based on this approach, the optimal learning parameters can be found by utilizing the linear matrix inequality (LMI) optimization techniques to achieve a predefined H∞ “noise” attenuation level. Several existing BP-type algorithms are shown to be special cases of the new H∞-learning algorithm. Theoretical analysis and several examples are provided to show the advantages of the new method.