# Nonlinear system modeling based on constrained Volterra series estimates

arXiv: https://arxiv.org/abs/1804.07258 · HTML: https://mlsanity.com/paper/1804.07258/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2018.

## Built on by (most cited first, 2 of 2)

- [Deep Subspace Encoders for Nonlinear System Identification](https://mlsanity.com/paper/2210.14816/) (2022)
- [Orthogonal Transforms in Neural Networks Amount to Effective Regularization](https://mlsanity.com/paper/2305.06344/) (2023)

## Abstract (arXiv)

A simple nonlinear system modeling 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 lq-constrained least squares algorithm with q≥ 1. If the system mleft( · right)  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-1ln D, 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.