Finite-Sample LTI System Identification from a Misspecified Finite Model Set
Abstract
We consider the problem of finite-sample identification of an unknown LTI system from a finite hypothesis class. In contrast to existing results that assume the hypothesis class contains the true system, we consider the misspecified setting, where the true system does not belong to the hypothesis class. We first characterize the resulting estimation target and its dependence on the data-generation scheme. We then establish a finite-sample lower bound on the failure probability that any identification algorithm must incur. Finally, we analyze the robustness of an existing exponential weighting-based identification algorithm to the misspecification and derive a finite-sample upper bound on its failure probability. Our results illustrate when using a misspecified finite hypothesis class can provide an advantage over identification without prior knowledge of the candidate systems.
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BibTeX
@misc{chatzikiriakos2026finitesample,
title = {{Finite-Sample LTI System Identification from a Misspecified Finite Model Set}},
author = {Nicolas Chatzikiriakos and Andrea Iannelli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40387},
eprint = {2610.40387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40387},
}
RIS
TY - UNPB
TI - Finite-Sample LTI System Identification from a Misspecified Finite Model Set
AU - Nicolas Chatzikiriakos
AU - Andrea Iannelli
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40387
UR - https://arxiv.org/abs/2610.40387
AB - We consider the problem of finite-sample identification of an unknown LTI system from a finite hypothesis class. In contrast to existing results that assume the hypothesis class contains the true system, we consider the misspecified setting, where the true system does not belong to the hypothesis class. We first characterize the resulting estimation target and its dependence on the data-generation scheme. We then establish a finite-sample lower bound on the failure probability that any identification algorithm must incur. Finally, we analyze the robustness of an existing exponential weighting-based identification algorithm to the misspecification and derive a finite-sample upper bound on its failure probability. Our results illustrate when using a misspecified finite hypothesis class can provide an advantage over identification without prior knowledge of the candidate systems.
ER -