Low-rank tensor recovery for Jacobian-based Volterra identification of parallel Wiener-Hammerstein systems

TL;DR

This paper introduces a novel tensor recovery approach for identifying parallel Wiener-Hammerstein systems by leveraging Jacobian sampling, simplifying the process compared to traditional Volterra kernel decomposition methods.

Contribution

It proposes a new method that uses Jacobian sampling points to transform the identification problem into a tensor recovery task, avoiding complex constraints.

Findings

Jacobian matrix becomes a linear projection of a tensor with rank equal to the number of branches

The approach simplifies the identification process for parallel Wiener-Hammerstein systems

Tensor recovery techniques can effectively identify system structure from Jacobian samples

Abstract

We consider the problem of identifying a parallel Wiener-Hammerstein structure from Volterra kernels. Methods based on Volterra kernels typically resort to coupled tensor decompositions of the kernels. However, in the case of parallel Wiener-Hammerstein systems, such methods require nontrivial constraints on the factors of the decompositions. In this paper, we propose an entirely different approach: by using special sampling (operating) points for the Jacobian of the nonlinear map from past inputs to the output, we can show that the Jacobian matrix becomes a linear projection of a tensor whose rank is equal to the number of branches. This representation allows us to solve the identification problem as a tensor recovery problem.