Quasi-parametric Recovery of Hammerstein System Nonlinearity by Smart Model Selection

In the paper we recover a Hammerstein system nonlinearity. Hammerstein systems, incorporating nonlinearity and dynamics, play an important role in various applications, and e¤ective algorithms determining their characteristics are not only of theoretical but also of practical interest. The proposed algorithm is quasi-parametric, that is, there are several parametric model candidates and we assume that the target nonlinearity belongs to the one of the classes represented by the models. The algorithm has two stages. In the …rst, the neural network is used to recursively …lter (estimate) the nonlinearity from the noisy measurements. The network serves as a teacher/trainer for the model candidates, and the appropriate model is selected in a simple tournament-like routine. The main advantage of the algorithm over a traditional one stage approach (in which models are determined directly from measurements), is its small computational overhead (as computational complexity and memory occupation are both greatly reduced). Keywords: system identi…cation, structure detection, Hammerstein system, wavelet neural network