Identification of MISO nonlinear systems via the semiparametric approach

In this paper we examine a class of multiple-input, single output (MISO) nonlinear systems of the block-oriented structure. In particular, we focus on MISO Hammerstein systems being the cascade connection of a multivariate nonlinearity with a linear dynamical subsystem. In order to alleviate an apparent curse of dimensionality occurring in the problem of estimating the nonlinearity, we propose to a semi-parametric strategy for identification of the nonlinear system. This is carried out by projecting the d-dimensional input signal onto one dimensional subset which, in turn, is mapped by a uni variate nonparametric function to an internal unobserved signal of the system. Such a parsimonious representation allows us to overcome the curse of dimensionality as the accuracy of our identification algorithms is independent of d. We identify the system via the semi-parametric version of the least squares. The statistical accuracy of the resulting estimates is obtained via the theory of M- estimation. These theoretical findings are verified in numerous simulation studies.