Nonparametric identification of MISO Hammerstein system from structured data

Abstract

The problem of nonparametric identification of a multivariate nonlinearity in a D-input Hammerstein system is examined. It is demonstrated that if the input measurements are structured, in the sense that there exists some hidden relation between them, i.e. if they are distributed on some (unknown) d-dimensional space M in R ^D, d < D, then the system nonlinearity can be recovered at points on M with the convergence rate O(n ^−1/(2+d)) dependent on d. This rate is thus faster than the generic rate O(n ^−1/(2+D)) achieved by typical nonparametric algorithms and controlled solely by the number of inputs D.

Keywords

MISO Hammerstein system / nonparametric system identification / structured data / convergence rate

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