Pith Number

pith:4KDK2PBY

pith:2026:4KDK2PBY2XPVYAKNKNK35R2K7L

not attested not anchored not stored refs pending

Impulse-to-Peak-Output Norm Optimal State-Feedback Control of Linear PDEs

Javad Mohammadpour Velni, Sachin Shivakumar, Tristan Thomas

Partial integral equations turn impulse-to-peak analysis and optimal state-feedback design for linear PDEs into solvable convex optimization problems.

arxiv:2604.03399 v2 · 2026-04-03 · math.OC · cs.SY · eess.SY

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\usepackage{pith}
\pithnumber{4KDK2PBY2XPVYAKNKNK35R2K7L}

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Record completeness

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3 Author claim open · sign in to claim

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

we utilize this PIE framework, and associated Lyapunov techniques, to formulate the I2P response analysis problem as a solvable convex optimization and obtain provable bounds for the I2P-norm of linear PDEs. Moreover, by establishing strong duality between primal and dual formulations of the optimization problem, we develop a constructive method for I2P optimal state-feedback control of PDEs

C2weakest assumption

The partial integral equation representation is an exact and complete state-space model for the linear PDEs considered, allowing Lyapunov-based convex optimization to produce non-conservative bounds and controllers without hidden approximation errors.

C3one line summary

The authors use partial integral equations and Lyapunov techniques to cast impulse-to-peak norm analysis as convex optimization and derive optimal state-feedback controllers for linear PDEs via strong duality.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T03:05:05.442725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e286ad3c38d5df5c014d5355bec74afada8a24556b0431c268799f5b976df1c4

Aliases

arxiv: 2604.03399 · arxiv_version: 2604.03399v2 · doi: 10.48550/arxiv.2604.03399 · pith_short_12: 4KDK2PBY2XPV · pith_short_16: 4KDK2PBY2XPVYAKN · pith_short_8: 4KDK2PBY

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4KDK2PBY2XPVYAKNKNK35R2K7L \
  | 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: e286ad3c38d5df5c014d5355bec74afada8a24556b0431c268799f5b976df1c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2fc88c933485003a91bfb0115de407e8d25258113cdc9ad5ca2b374c2f2f7d3",
    "cross_cats_sorted": [
      "cs.SY",
      "eess.SY"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-03T19:01:27Z",
    "title_canon_sha256": "1c1fe6278b35b7bb564bc9663affc0aaab04510e4106be1fd8d2eb2425609fe2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.03399",
    "kind": "arxiv",
    "version": 2
  }
}