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Deterministically Optimal Robust Exact Differentiators of Arbitrary Order — arXiv:2609.15564

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.15564
License (as archived): CC0-1.0
Archived: 2026-10-16T00:39:24.321Z
SHA-256 of the archived text: 09aa6dbe6c955441858ce8363bc52434c3973e8099bc6eb1cb791ed3075bbcfb
Stable URL of this page: https://metraipolis.com/documento/dc_aa92ea91d5eb

How to cite

Deterministically Optimal Robust Exact Differentiators of Arbitrary Order — arXiv:2609.15564 — arXiv (en), https://arxiv.org/abs/2609.15564 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_aa92ea91d5eb (Metraipolis archive dc_aa92ea91d5eb, sha256 09aa6dbe6c955441858ce8363bc52434c3973e8099bc6eb1cb791ed3075bbcfb)

BibTeX

@misc{dcaa92ea91d5eb,
  title = {Deterministically Optimal Robust Exact Differentiators of Arbitrary Order — arXiv:2609.15564},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.15564},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_aa92ea91d5eb; sha256 09aa6dbe6c955441858ce8363bc52434c3973e8099bc6eb1cb791ed3075bbcfb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.15564. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Estimation of the derivatives of a function with bounded high-order derivative in the presence of bounded measurement noise is considered, in a deterministic setting. Theoretical fundamental limitations of causal differentiators in terms of the lowest achievable worst-case differentiation error and desired properties such as exactness---the zero-error estimation of derivatives in the absence of noise---and robustness---the small sensitivity of the estimate under small perturbations---are established for the first time for arbitrary differentiation order. Differentiators that achieve these theoretically lowest bounds on their differentiation error are formally defined, fully characterized, and their properties are studied. In particular, deterministically optimal differentiators---those featuring optimal differentiation error bounds among the class of exact differentiators---are shown to exist by means of a novel construction exhibiting, in addition to exactness from the beginning, a very strong form of robustness.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-15 in math.OC).
Categorie arXiv: Optimization and Control (math.OC) ; Systems and Control (eess.SY).
Pagina del lavoro: https://arxiv.org/abs/2609.15564 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T00:16:48.842Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).