Noniterative tensor network‐based algorithm for Volterra system identification

Abstract

Volterra model serves as one of the powerful alternatives to approximate nonlinear dynamics on the basis of input/output observations. The kernel representation of a Volterra model is attractive since it is linear in the kernel coefficients and always stable. Although the kernel representation suffers from the curse of dimensionality, the demand for storage requirements can be relieved via a tensor network (TN) technique. This allows one to approximate complicated coupled nonlinear dynamics with high degree and even multi-input multi-output (MIMO) Volterra models. The iterative feature of existing TN-based algorithms poses challenges for the algorithms to converge to an appropriate solution with both good prediction accuracy and minor overfitting problems. In this article, noniterative TN-based algorithms with two tuning factors to solve either a linear or ridge regression are proposed for MIMO Volterra system identification. The proposed algorithms do not suffer convergence problems due to its noniterative feature and perform active low-rank approximations to reduce overfitting problems. Simulations compare different algorithms and investigate the effects for different excitation signals.

Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials

“…The algorithms classically used for NSI depend on the selection of a suitable model to represent the data. Some valid and widely used models are the Volterra series expansion [4][5][6], Hammerstein model [7][8][9][10][11], Wiener model [12][13][14][15] and the nonlinear auto-regressive moving average model with exogenous inputs (NARMAX) and its derivatives [16][17][18][19][20][21].…”