A simple nonlinear system modeling algorithm designed to work with limited
\emph{a priori }knowledge and short data records, is examined. It creates an
empirical Volterra series-based model of a system using an lq-constrained
least squares algorithm with q≥1. If the system m(⋅)
is a continuous and bounded map with a finite memory no longer than some known
τ, then (for a D parameter model and for a number of measurements N)
the difference between the resulting model of the system and the best possible
theoretical one is guaranteed to be of order N−1lnD, even for
D≥N. The performance of models obtained for q=1,1.5 and 2 is tested
on the Wiener-Hammerstein benchmark system. The results suggest that the models
obtained for q>1 are better suited to characterize the nature of the system,
while the sparse solutions obtained for q=1 yield smaller error values in
terms of input-output behavior