Exact solution to the least squares realization problem as a multiparameter eigenvalue problem
Year: 2025
Type: article
Abstract: We consider the least squares (LS) realization of an autonomous single-output linear time-invariant dynamical model for a given sequence of output data. As opposed to standard system identification practices, which often rely on (heuristic) iterative optimization techniques, we propose an exact solution to this non-convex optimization problem: the globally optimal solution(s) are identified by means of a deterministic eigenvalue procedure. In particular, we illustrate that for all (local) minimizers, the corresponding misfit can be characterized as the result of filtering an unknown signal twice through a finite-impulse response filter. Exploiting this insight, we propose a novel (rectangular) multiparameter eigenvalue problem (MEP), the eigentuples of which allow to retrieve all local and global minimizers of the identification problem. The proposed MEP is of great theoretical interest and offers new insights into the structure of the LS realization problem, which we explore in detail. We provide numerical examples to illustrate our findings.
Source: Automatica
Authors: Sibren Lagauw, Lukas Vanpoucke, Bart De Moor
Institution: KU Leuven
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,760
OpenAlex ID: W4417519997