Model Selection of Hammerstein System Nonlinearity under Heavy Noise

The paper deals with the problem of automatic model selection of the nonlinear characteristic in a block-oriented dynamic system. We look for the parametric model of Hammerstein system nonlinearity. From the finite set of candidate classes of parametric models we select the best one on the basis of the input-output measurement data, using the concept of nearest neighbour borrowed from pattern recognitions techniques. The algorithm uses the pattern of the true characteristic generated by its nonparametric estimates on the grid of fixed (e.g. equidistant) points. Each class generates parametrized learning sequence through the values on the same grid of points. Next, for each class, the optimal parameters are computed by the least squares method. Finally, the nearest neighbour approach is applied for the selection of the best model in the mean square sense. The idea is presented on the exemplary competition between polynomial, exponential and piece-wise linear models of the same complexity (i.e. number of parameters needed to be stored in memory). For all classes, the upper bounds of the integrated approximation errors of the true characteristic are computed and compared.