On Robustness of Kernel-Based Regularized System Identification

TL;DR

This paper introduces a kernel-based uncertainty set for regularized system identification, demonstrating its effectiveness in enhancing robustness against input disturbances through theoretical proofs and extensive numerical experiments.

Contribution

It establishes a novel equivalence between kernel-based regularized estimation and robust least-squares with a specific uncertainty set, providing a new theoretical foundation for robustness.

Findings

Kernel-based uncertainty set improves robustness to input disturbances.

The approach is theoretically grounded and validated through numerical experiments.

Robust least-squares with kernel-based sets outperforms traditional methods.

Abstract

This paper presents a novel feature of the kernel-based system identification method. We prove that the regularized kernel-based approach for the estimation of a finite impulse response is equivalent to a robust least-squares problem with a particular uncertainty set defined in terms of the kernel matrix, and thus, it is called kernel-based uncertainty set. We provide a theoretical foundation for the robustness of the kernel-based approach to input disturbances. Based on robust and regularized least-squares methods, different formulations of system identification are considered, where the kernel-based uncertainty set is employed in some of them. We apply these methods to a case where the input measurements are subject to disturbances. Subsequently, we perform extensive numerical experiments and compare the results to examine the impact of utilizing kernel-based uncertainty sets in the identification procedure. The numerical experiments confirm that the robust least square identification approach with the kernel-based uncertainty set improves the robustness of the estimation to the input disturbances.