Kernel-based system identification improving robustness to input disturbances: A preliminary study on its application to AR models

Hiroe, T.; Ide, Kazunari; Sase, Ryo; Sugie, Toshiharu

doi:10.23919/ecc51009.2020.9143711

Cited by 1 publication

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“…The idea of multiple regularizations together with advanced hyperparameter tuning techniques are used for improving the performance of model estimation [23][24][25][26]. Recently, it has been empirical observed that kernel-based approaches can improve the robustness of the estimation to the input disturbances [27].…”

Section: Introductionmentioning

confidence: 99%

On Robustness of Kernel-Based Regularized System Identification

Khosravi¹,

Smith²

2021

Preprint

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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.

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