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A minimality property of the value function in optimal control over the Wasserstein space

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  • Additional Information
    • Contributors:
      Universidad Tecnica Federico Santa Maria Valparaiso (UTFSM); Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI); Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie); Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU); This work was supported by the Center for Mathematical Modeling (CMM) and ANID-Chile under BASAL funds for Center of Excellence FB210005 and Fondecyt Regular 1231049.
    • Publication Information:
      HAL CCSD
    • Publication Date:
      2024
    • Collection:
      Normandie Université: HAL
    • Abstract:
      An optimal control problem with (possibly) unbounded terminal cost is considered in P2(Rd), the space of Borel probability measures with finite second moment. We consider the metric geometry associated with the Wasserstein distance, and a suitable weak topology rendering P2(Rd) locally compact. In this setting, we show that the value function of a control problem is the minimal viscosity supersolution of an appropriate Hamilton-Jacobi-Bellman (HJB) equation. Additionally, if the terminal cost is bounded and continuous, we show that the value function is the unique viscosity solution of the HJB equation.
    • Relation:
      hal-04427139; https://hal.science/hal-04427139; https://hal.science/hal-04427139/document; https://hal.science/hal-04427139/file/Hermosilla_Prost.pdf
    • Online Access:
      https://hal.science/hal-04427139
      https://hal.science/hal-04427139/document
      https://hal.science/hal-04427139/file/Hermosilla_Prost.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.15622A17