{
  "abstract": "This paper studies a finite-horizon mixed $H_2/H_\\infty$ feedback Nash game for stochastic evolution equations on a separable Hilbert space. The drift generator is unbounded, the remaining coefficients are bounded, and the one-dimensional Brownian diffusion depends on the state, control, and disturbance. The $H_2$ channel is an LQ state--control energy. For the disturbance channel, the stochastic LQ uniform-convexity characterization yields equivalence between strict induced $L^2$ attenuation and unique strongly regular mild Riccati solvability. Simultaneous bounded-generator approximation of the Lyapunov equation and the state justifies quadratic identities for strongly continuous mild operator solutions. These identities verify both Nash inequalities and full-output strict attenuation from a strongly regular coupled Riccati pair. An invertible feedback block and a contraction argument establish locally unique coupled solutions on a sufficiently short terminal interval for every positive attenuation level. For a specified stochastic heat-equation model at $γ=0.09$, a uniform invariant rectangle further proves full-horizon existence, bounded infinite-dimensional feedbacks, and operator-norm spectral convergence. Numerical computations reproduce the projected gains and compare selected best responses. Global coupled solvability for general coefficients remains an explicit hypothesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00756",
  "author_total": 4,
  "authors": [
    {
      "name": "Mingyang Shen"
    },
    {
      "name": "Weihai Zhang"
    },
    {
      "name": "Qingxin Meng"
    },
    {
      "name": "Maoning Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1fn566ryvy30.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00756",
  "fulltext_url": null,
  "id": "d1fn566ryvy30",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00756",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7215988491",
  "pdf_url": "https://arxiv.org/pdf/2610.00756",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1fn566ryvy30.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00756",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00756"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Riccati Approach to Mixed $H_2/H_\\infty$ Closed-Loop Games for Infinite-Dimensional Stochastic Systems",
  "title_text": "A Riccati Approach to Mixed H_2/H_∞ Closed-Loop Games for Infinite-Dimensional Stochastic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/d1fn566ryvy30",
  "venue": "arXiv",
  "versions": []
}