Pith Number

pith:6ZFXME7J

pith:2026:6ZFXME7JW6WLPUO3M66VHIDQMM

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Learning a Contracting KKL-observer with Local Optimal Guarantees

Clara Luc\'ia Galimberti, Daniele Astolfi, Johan Peralez, Madiha Nadri, Vincent Andrieu

Neural networks learn KKL observers that stay globally contracting yet locally match the minimum-energy estimator.

arxiv:2605.13453 v1 · 2026-05-13 · eess.SY · cs.SY

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Claims

C1strongest claim

We derive a condition on the latent dynamics such that the observer locally mimics the behavior of a Minimum Energy Estimator (Mortensen observer). We then employ Deep Learning to approximate the KKL transformation and the latent dynamics, using neural network architectures that structurally enforce the contraction property.

C2weakest assumption

That a suitable latent dynamics satisfying the derived local-optimality condition exists for the target systems and that neural networks with contraction-enforcing architectures can accurately approximate the required KKL transformation and latent dynamics.

C3one line summary

Learns contracting KKL observers via deep learning that locally match minimum energy estimators with global stability guarantees.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Andrieu, V. and Praly, L. (2006). On the existence of a Kazantzis–Kravaris/Luenberger observer.SIAM Journal on Control and Optimization, 45(2), 432–456. Beik Mohammadi, H., Hauberg, S., Arvanitidis, G 2006

[2] Figueroa, N., Neumann, G., and Rozo, L. (2024). Neural contractive dynamical systems. InICLR, 49097–49120 2024

[3] Bernard, P., Andrieu, V., and Astolfi, D. (2022). Observer design for continuous-time dynamical systems.Annual Reviews in Control, 53, 224–248 2022

[4] Brivadis, L., Andrieu, V., Bernard, P., and Serres, U. (2023). Further remarks on KKL observers.Systems & Control Letters, 172, 105429 2023

[5] Buisson-Fenet, M., Bahr, L., Morgenthaler, V., and Di Meglio, F. (2023). Towards gain tuning for numerical KKL observers.IFAC-PapersOnLine, 56(2), 4061–4067 2023

Receipt and verification

First computed	2026-05-18T02:44:41.851983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f64b7613e9b7acb7d1db67bd53a070631770bb138910666f0af714267cde0d00

Aliases

arxiv: 2605.13453 · arxiv_version: 2605.13453v1 · doi: 10.48550/arxiv.2605.13453 · pith_short_12: 6ZFXME7JW6WL · pith_short_16: 6ZFXME7JW6WLPUO3 · pith_short_8: 6ZFXME7J

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6ZFXME7JW6WLPUO3M66VHIDQMM \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f64b7613e9b7acb7d1db67bd53a070631770bb138910666f0af714267cde0d00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7ed70b267837ea3d379896634a211f99a735c9cbb0a5dd13a9288a8c092f03c",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-05-13T12:48:47Z",
    "title_canon_sha256": "3ad60a874f67d65bc430eec67ae9e345eceb50b3ffe5b0bc57bdde6815261672"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13453",
    "kind": "arxiv",
    "version": 1
  }
}