Unknown Input Reconstruction Observer for Hammerstein-Wiener Systems in the Errors-in-Variables Framework

Abstract

In this paper an approach for reconstructing an unknown input in the case when input and output signals are both subject to measurement uncertainties, i.e. errors-in-variables framework, is presented. The algorithm is applicable to Hammerstein-Wiener systems, i.e. systems composed from a dynamic linear system followed and preceded by a memoryless nonlinearity. It is based on a parity equations concept and forms an extension of the idea developed previously by the authors for linear systems. The only requirement is that the function used to describe the component static output nonlinearity must be strictly monotonic. The order of the parity space can be treated as a tuning parameter allowing for a trade-off between the smoothness of the reconstructed unknown input and a phase lag to be obtained. An analytical solution of the overall problem is obtained by using a Lagrange multiplier method.