For conflict-controlled dynamical systems satisfying the conditions of generalized uniqueness and uniform boundedness, the solvability of the minimax problem in the class of generalized controls is studied. The issues of consistency of such an extension are considered; i. e., the possibility of approximating generalized controls in the space of strategic measures by embeddings of ordinary controls is analyzed. For this purpose, the dependence of the set of measures on the general marginal distribution specified on one of the factors of the base space is studied. The continuity of this dependence in the Hausdorff metric defined by the metric corresponding to the *-weak topology in the space of measures is established. The density of embeddings of ordinary controls and control-noise pairs in sets of corresponding generalized controls in the *-weak topologies is also shown.
Translated title of the contributionCONTINUOUS DEPENDENCE OF SETS IN A SPACE OF MEASURES AND A PROGRAM MINIMAX PROBLEM
Original languageRussian
Pages (from-to)277-299
Number of pages23
JournalТруды института математики и механики УрО РАН
Volume30
Issue number2
DOIs
Publication statusPublished - 1 Jun 2024

    Level of Research Output

  • VAK List
  • Russian Science Citation Index

    ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics
  • Computational Mechanics
  • Computer Science Applications

ID: 58465653