Non-linear system modelling based on constrained Volterra series estimates
(2017) I E T Control Theory and Applications — Vol. 11, n° 15, p. 2623-2629 (2017)
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- A simple non-linear system modelling algorithm designed to work with limited a priori knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an lqlq-constrained least squares algorithm with q≥1q≥1. If the system m(⋅)m⋅ is a continuous and bounded map with a finite memory no longer than some known ττ, 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−−−−−−−√N−1lnD, even for D≥ND≥N. The performance of models obtained for q=1,1.5q=1,1.5 and 2 is tested on the Wiener–Hammerstein benchmark system. The results suggest that the models obtained for q>1q>1 are better suited to characterise the nature of the system, while the sparse solutions obtained for q=1q=1 yield smaller error values in terms of input-output behaviour.
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Śliwiński, P., Marconato, A., Wachel, P., & Birpoutsoukis, G. (2017). Non-linear system modelling based on constrained Volterra series estimates. I E T Control Theory and Applications, 11(15), 2623-2629. https://doi.org/10.1049/iet-cta.2016.1360 (Original work published 2017)