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Stochastic MPC under Heavy-Tailed Disturbances: An Extreme Value Theory Approach — arXiv:2609.21170

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21170
License (as archived): CC0-1.0
Archived: 2026-10-10T03:11:54.745Z
SHA-256 of the archived text: ccc74dec79a1ff83b305e895928a9bbb1c51f1f0b65d78666989a1507d8f192f
Stable URL of this page: https://metraipolis.com/documento/dc_94268cbd2fee

How to cite

Stochastic MPC under Heavy-Tailed Disturbances: An Extreme Value Theory Approach — arXiv:2609.21170 — arXiv (en), https://arxiv.org/abs/2609.21170 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_94268cbd2fee (Metraipolis archive dc_94268cbd2fee, sha256 ccc74dec79a1ff83b305e895928a9bbb1c51f1f0b65d78666989a1507d8f192f)

BibTeX

@misc{dc94268cbd2fee,
  title = {Stochastic MPC under Heavy-Tailed Disturbances: An Extreme Value Theory Approach — arXiv:2609.21170},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21170},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_94268cbd2fee; sha256 ccc74dec79a1ff83b305e895928a9bbb1c51f1f0b65d78666989a1507d8f192f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21170. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Safety-critical control systems must contend with disturbances whose extreme deviations occur far more frequently than classical light-tailed models predict. Existing stochastic MPC (SMPC) formulations tighten constraints using an assumed distribution, a moment bound, or a finite scenario sample, each of which degrades under an unknown heavy-tailed disturbance. This paper develops an SMPC formulation for linear systems under heavy-tailed disturbances that is only assumed to be regular varying, replacing these approaches with an explicit extreme value theory (EVT) characterization of the tube error tail that is asymptotically exact. We further show that closed-loop dynamics induce temporal clustering of rare excursions across the prediction horizon, and characterize this clustering through a closed-form extremal index estimable from data. The resulting $\theta$-corrected constraint bounds the probability of a rare-event episode over the horizon, rather than only the marginal per-step exceedance probability. Simulation on a nonlinear unicycle navigating past an obstacle under Student-$t$ disturbances validates both approaches and demonstrates reduced frequencies of safety constraint violations.

Tema degli esploratori: calcolo e infrastrutture (retro-catalogo arXiv: annunci del 2026-09-21 in eess.SY).
Categorie arXiv: Systems and Control (eess.SY).
Pagina del lavoro: https://arxiv.org/abs/2609.21170 — 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 2026-10-10T02:58:16.892Z dalla pagina https://arxiv.org/catchup/eess.SY/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).