Neural network approach for identification of Hammerstein systems

In this paper, four different on-line gradient-based learning algorithms for training neural network Hammerstein models are presented in a unified framework. These algorithms, namely the backpropagation for series-parallel models, the backpropagation, sensitivity method, and truncated backpropagation through time algorithm (BPTT) for parallel models are derived, analysed, and compared. For the truncated BPTT, it is shown that determination of the number of unfolding time steps, necessary to calculate the gradient with an assumed degree of accuracy, can be made on the basis of impulse response functions of sensitivity models. The algorithms are shown to differ in their computational complexity, gradient approximation accuracy, and convergence rates. Numerical examples are also included to compare the performance of the algorithms.