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PreprintCC BY 4.0arXiv

Finite Sample Identification of Analytic Nonlinear Systems

  • Negin Musavi
  • Ziyao Guo
  • Geir E. Dullerud
  • Yingying Li
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Abstract

This paper studies the identification of linearly parameterized nonlinear (LPN) systems. Although LPN systems share the same linear parameterization structure as linear systems, they are more challenging to identify. In particular, previous work has shown, through a counterexample based on a piecewise-affine system, that non-active exploration is generally insufficient for LPN system identification. In this paper, we consider LPN systems with real-analytic feature functions. We show that non-active exploration is sufficient for the identification of this class of systems by establishing non-asymptotic convergence rates of least-squares estimation and set-membership estimation. In addition, we provide counterexamples to show that non-active exploration may not be sufficient for system identification for non-real-analytic systems, even if those systems are infinitely differentiable. We present numerical experiments to further support and validate our theoretical results.

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Cite

BibTeXRIS
BibTeX
@misc{musavi2026finite,
  title = {{Finite Sample Identification of Analytic Nonlinear Systems}},
  author = {Negin Musavi and Ziyao Guo and Geir E. Dullerud and Yingying Li},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29908},
  eprint = {2608.29908},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29908},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Finite Sample Identification of Analytic Nonlinear Systems
AU  - Negin Musavi
AU  - Ziyao Guo
AU  - Geir E. Dullerud
AU  - Yingying Li
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29908
UR  - https://arxiv.org/abs/2608.29908
AB  - This paper studies the identification of linearly parameterized nonlinear (LPN) systems. Although LPN systems share the same linear parameterization structure as linear systems, they are more challenging to identify. In particular, previous work has shown, through a counterexample based on a piecewise-affine system, that non-active exploration is generally insufficient for LPN system identification. In this paper, we consider LPN systems with real-analytic feature functions. We show that non-active exploration is sufficient for the identification of this class of systems by establishing non-asymptotic convergence rates of least-squares estimation and set-membership estimation. In addition, we provide counterexamples to show that non-active exploration may not be sufficient for system identification for non-real-analytic systems, even if those systems are infinitely differentiable. We present numerical experiments to further support and validate our theoretical results.
ER  -