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 $l_{q}$-constrained least squares algorithm with $qgeq 1$. If the system $mleft( cdot right) $ is a continuous and bounded map with a finite memory no longer than some known $tau$, 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 $sqrt{N^{-1}ln D}$, even for $Dgeq N$. 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.
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