{
  "abstract": "We study optimal input design over a finite horizon for linear dynamical systems. The goal is to minimize a weighted inverse-covariance (information) criterion subject to an energy budget. The set of covariances achievable by causal policies is convex but lacks a tractable explicit description, ruling out projection-based methods. We show that Frank--Wolfe applies naturally: each linear minimization subproblem is a budget-constrained finite-horizon linear quadratic (LQ) problem, solvable by a Riccati recursion and one-dimensional bisection over a Lagrange multiplier. Using smoothness of the objective over the feasible set, we establish an $\\mathcal{O}(1/M)$ convergence rate for the objective value, while strong convexity yields an $\\mathcal{O}(1/\\sqrt{M})$ rate for the iterates. We further extend the framework to input design for system identification with unknown dynamics and adaptive online LQR, and illustrate the approach numerically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08751",
  "author_total": 4,
  "authors": [
    {
      "name": "Fethi Bencherki"
    },
    {
      "name": "Bruce Lee"
    },
    {
      "name": "Nikolai Matni"
    },
    {
      "name": "Anders Rantzer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqc25cz24qc54.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08751",
  "fulltext_url": null,
  "id": "fqc25cz24qc54",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08751",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Optimization"
    ]
  ],
  "openalex": "W7211992567",
  "pdf_url": "https://arxiv.org/pdf/2609.08751",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fqc25cz24qc54.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08751",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08751"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal input design via Frank-Wolfe",
  "title_text": "Optimal input design via Frank-Wolfe",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/fqc25cz24qc54",
  "venue": "arXiv",
  "versions": []
}