mlsanityData to 14 Oct 2026

Near optimal finite time identification of arbitrary linear dynamical systems

arXiv 1812.01251 ↗First posted 4 Dec 2018eess.SY cs.SYcited by 89

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Abstract (arXiv)

We derive finite time error bounds for estimating general linear time-invariant (LTI) systems from a single observed trajectory using the method of least squares. We provide the first analysis of the general case when eigenvalues of the LTI system are arbitrarily distributed in three regimes: stable, marginally stable, and explosive. Our analysis yields sharp upper bounds for each of these cases separately. We observe that although the underlying process behaves quite differently in each of these three regimes, the systematic analysis of a self--normalized martingale difference term helps bound identification error up to logarithmic factors of the lower bound. On the other hand, we demonstrate that the least squares solution may be statistically inconsistent under certain conditions even when the signal-to-noise ratio is high.

Key facts. Cited by 89 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Dec 2018.

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Citing papers per year: 2021: 18; 2022: 19; 2023: 20; 2024: 12; 2025: 11; 2026: 9.

89 papers.

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38 more
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50 most cited of 89 All 89 (JSON)