D.A. Serkov, A.G. Chentsov. On the construction of a nonanticipating selection of a multivalued mapping ... P. 232-246

We study the properties of multivalued mappings of general form with respect to the possibility of finding their nonanticipating selections. The property of nonanticipation is formulated for an arbitrary domain by specifying some family of “test” subsets. Sufficient conditions for the existence of a nonanticipating selection of a nonanticipating multivalued mapping are proposed: the values of the mapping must be nonempty compact sets, and the family of “test” subsets must be totally ordered by inclusion. We illustrate the results by showing their applicability to the pursuit–evasion differential game in the form of P. Varaya and J. Lin.

Keywords: quasistrategy, nonantiсipation, selection, topology

Received May 15, 2019

Revised June 19, 2019

Accepted June 24, 2019

Funding Agency: This work was supported by the Presidium of the Russian Academy of Sciences within the project “Newest Methods of Mathematical Modeling in the Study of Nonlinear Dynamic Systems.”

Dmitrii Aleksandrovich Serkov, Dr. Phys.-Math. Sci., Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Prof., Ural Federal University, Yekaterinburg, 620083 Russia, e-mail: serkov@imm.uran.ru

Alexander Georgievich Chentsov, Dr. Phys.-Math. Sci, RAS Corresponding Member, Prof., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620083 Russia, e-mail: chentsov@imm.uran.ru

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Cite this article as: D.A. Serkov, A.G. Chentsov. On the construction of a nonanticipating selection of a multivalued mapping, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 232–246.