Pith Number

pith:ZICFKXT5

pith:2026:ZICFKXT5GUBSIVF57WOKT3UN6U

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Nonlinear backstepping with saturation for low-thrust station-keeping of libration point orbits

Ant\'onio Nunes, Pedro Batista, S\'ergio Br\'as

A saturation-inclusive nonlinear backstepping controller provides almost global exponential stability for low-thrust station-keeping on Earth-Moon libration point orbits.

arxiv:2604.15028 v1 · 2026-04-16 · eess.SY · astro-ph.EP · astro-ph.IM · cs.SY

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\pithnumber{ZICFKXT5GUBSIVF57WOKT3UN6U}

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Record completeness

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Almost global uniform exponential stability guarantees are attained, as shown through Lyapunov's stability theory. Saturation of the actuators is formally included in the controller design, such that these guarantees hold even in the event of saturation.

C2weakest assumption

The high-fidelity model of the dynamics accurately captures the real Earth-Moon gravitational environment and that the Lyapunov analysis assumptions remain valid for the targeted quasi-periodic orbits under operational errors and external perturbations.

C3one line summary

A saturated nonlinear backstepping controller achieves almost global uniform exponential stability for low-thrust station-keeping of Earth-Moon libration point orbits under a high-fidelity model.

References

51 extracted · 51 resolved · 0 Pith anchors

[1] R. W. Farquhar, The Control and Use of Libration-point Satellites, Technical report, NASA (1970) 1970

[2] J. Breakwell, A. Kamel, M. Ratner, Station-keeping for a translunar communication station, Celestial Mechanics 10 (1974) 357–373 1974

[3] W. Wiesel, W. Shelton, Modal control of an unstable periodic orbit, Journal of the Astronautical Sciences 31 (1983) 63–76 1983

[4] C. Simó, G. Goméz, J. Llibre, R. Martinez, Stationkeeping of a quasiperiodic halo orbit using invariant manifolds, in: ESA Special Pub- lication, Vol. 255 of ESA Special Publication, 1986, pp. 65–70 1986

[5] C. Simó, G. Gómez, J. Llibre, R. Martínez, J. Rodríguez, On the optimal station keeping control of halo orbits, Acta Astronautica 15 (6) (1987) 391–397. 47 1987

Receipt and verification

First computed	2026-06-11T01:10:36.246165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca04555e7d35032454bdfd9ca9ee8df51b869de1d6f660ff2938d976ce518fee

Aliases

arxiv: 2604.15028 · arxiv_version: 2604.15028v1 · doi: 10.48550/arxiv.2604.15028 · pith_short_12: ZICFKXT5GUBS · pith_short_16: ZICFKXT5GUBSIVF5 · pith_short_8: ZICFKXT5

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZICFKXT5GUBSIVF57WOKT3UN6U \
  | 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: ca04555e7d35032454bdfd9ca9ee8df51b869de1d6f660ff2938d976ce518fee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "591771336b4b81a2f069390fe314e91afc37b58d50300f4fc2dbf8186fb42101",
    "cross_cats_sorted": [
      "astro-ph.EP",
      "astro-ph.IM",
      "cs.SY"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-04-16T13:58:14Z",
    "title_canon_sha256": "d85349c56e188cf4fe63545ef6cf9d5edbb0e90828fb11e840a982d27cdc1c91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.15028",
    "kind": "arxiv",
    "version": 1
  }
}