NONPARAMETRIC IDENTIFICATION OF MISO HAMMERSTEIN SYSTEM FROM STRUCTURED DATA

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.