Approximation of Hammerstein/Wiener dynamic models

Abstract

In the analysis of several scientific and engineering problems nonlinear dynamic systems are modelled as systems composed by the series connection of a linear dynamic subsystem with a nonlinear memoryless unit. If the nonlinearity follows the linear subsystem, the system is called of Wiener type, otherwise the system is called of Hammerstein type. In this work a nonparametric approach to the approximation of Wiener/Hammerstein models is proposed. The approach is based on the use of Laguerre filter banks to approximate the linear subsystem, and an artificial neural network to approximate the memoryless nonlinearity. Building on existing results of approximating properties of Laguerre filters and neural networks, theoretical convergence results of the approximating scheme to the underlining Hammerstein/Wiener model are reported. It is emphasized that the suggested approach requires much milder assumptions than those needed by other procedures previously proposed in the literature. In particular, no knowledge of the linear system order and time delay is needed, and the nonlinearity need not to be invertible and/or of polynomial type.