{
  "abstract": "We solve the four-dimensional Hamilton-Jacobi-Bellman (HJB) equation for two diffusively coupled Stuart-Landau-like oscillators to obtain full-state optimal feedback control. A sweep over coupling strength reveals a sharp change in the numerically optimal strategy: below a threshold coupling value, the controller steers the phase difference toward anti-phase while keeping both oscillators near the limit cycle, as reduced-order models would suggest. Above this threshold, the HJB solution changes qualitatively; the controller transiently collapses one oscillator's amplitude to near zero, thereby enabling large phase repositioning near the origin before rebuilding its amplitude. Direct gradient-based and stochastic optimization do not recover this lower-cost collapse trajectory from the initializations considered, suggesting that it occupies a region of the control landscape that is difficult to access by direct search. A joint sweep over nonisochronicity and coupling shows that collapse can occur even for an isochronous oscillator: phase repositioning near the origin can favor an off-cycle strategy. Nonisochronicity provides an additional energetic benefit through a phase-velocity surplus at small amplitude, quantitatively accounting for the observed reduction in control cost. Comparisons with uncoupled and coupled phase-reduced baselines show that phase models become increasingly inaccurate and cost significantly more energy for strong coupling. Results for coupled Van der Pol oscillators further demonstrate that exploitation of off-cycle dynamics is not specific to the Stuart-Landau-like oscillators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16449",
  "author_total": 3,
  "authors": [
    {
      "name": "Faranak Rajabi"
    },
    {
      "name": "Frédéric Gibou"
    },
    {
      "name": "Jeff Moehlis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvbgbahxvnzn2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16449",
  "fulltext_url": null,
  "id": "fvbgbahxvnzn2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16449",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
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      "arxiv",
      "cs.SY"
    ],
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      "arxiv",
      "eess.SY"
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      "arxiv",
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      "arxiv",
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      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
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  "openalex": "W7213434625",
  "pdf_url": "https://arxiv.org/pdf/2609.16449",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvbgbahxvnzn2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16449",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16449"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Beyond Phase Reduction: Amplitude Collapse in Optimal Control of Coupled Oscillators",
  "title_text": "Beyond Phase Reduction: Amplitude Collapse in Optimal Control of Coupled Oscillators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/fvbgbahxvnzn2",
  "venue": "arXiv",
  "versions": []
}