Parameter estimation for nonlinear Volterra systems by using the multi-innovation identification theory and tensor decomposition

The Volterra model can represent a wide range of nonlinear dynamical systems. However, its practical use in nonlinear system identification is limited due to the exponentially growing number of Volterra kernel coefficients as the degree increases. This paper considers the identification issue of discrete-time nonlinear Volterra systems and uses a tensorial decomposition called PARAFAC to represent the Volterra kernels which can provide a significant parametric reduction compared with the conventional Volterra model. Applying the multi-innovation identification theory, the recursive algorithm by combining the l(2)-norm is proposed for the PARAFAC-Volterra models with the Gaussian noises. In addition, the multi-innovation algorithm combining with the logarithmic p-norms is investigated for the nonlinear Volterra systems with the non-Gaussian noises. Finally, some simulation results illustrate the effectiveness of the proposed identification methods. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

The Volterra model, although capable of representing a wide range of nonlinear dynamical systems, faces limitations in practical use for nonlinear system identification due to the exponential growth of Volterra kernel coefficients. This paper introduces a tensorial decomposition called PARAFAC to reduce the number of parameters in representing Volterra kernels compared to the traditional Volterra model. The proposed recursive algorithm, based on the multi-innovation identification theory and l(2)-norm, effectively handles PARAFAC-Volterra models with Gaussian noises, while the multi-innovation algorithm combined with logarithmic p-norms is studied for nonlinear Volterra systems with non-Gaussian noises. Simulation results demonstrate the effectiveness of the proposed identification methods.