{
  "abstract": "This paper presents novel extremum seeking algorithms inspired by RMSProp dynamics and based on Lie bracket approximation techniques. To inherit the behavior of the classical continuous-time RMSProp algorithm, we introduce an extremum seeking scheme that exploits second-order Lie brackets, allowing the excitation of squared gradient terms in the resulting Lie bracket system. Moreover, we propose two modified RMSProp-type algorithms that can be implemented using only first-order Lie bracket approximations, thereby reducing the complexity of the extremum seeking control design. The three resulting extremum seeking algorithms are compared through numerical simulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06505",
  "author_total": 2,
  "authors": [
    {
      "name": "Victoria Grushkovskaya"
    },
    {
      "name": "Christian Ebenbauer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ag1xavkaky1d0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06505",
  "fulltext_url": null,
  "id": "ag1xavkaky1d0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06505",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Extremum Seeking Control Systems"
    ]
  ],
  "openalex": "W7212066266",
  "pdf_url": "https://arxiv.org/pdf/2609.06505",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ag1xavkaky1d0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06505",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06505"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Lie bracket approximations of RMSprop for Extremum Seeking Control",
  "title_text": "Lie bracket approximations of RMSprop for Extremum Seeking Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/ag1xavkaky1d0",
  "venue": "arXiv",
  "versions": []
}