Chikrii A.A., Rappoport I.S.
A modified method of resolving functions for control game problems with integral constraints

The authors consider linear differential games with integral constraints. Sufficient conditions for the game termination in a finite guaranteed time are formulated for the case where the Nikolsky condition is not satisfied. Multivalued mappings that generate the upper and lower resolving functions of special type are introduced. The modified schemes of the Nikolsky direct method and the method of resolving functions are proposed, which ensure the game termination in a finite guaranteed time in the class of quasi-strategies and stroboscopic strategies. The most recent theoretical results are illustrated by the reference Pontryagin’s example with objects of the same type. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: integral constraints, linear differential game, multivalued mapping, resolving functions, stroboscopic strategy, Game theory, Integral equations, Condition, Control problems, Direct method, Integral constraints, Linear differential games, Modified scheme, Multivalued mappings, Resolving functions, Stroboscopic strategy, Mapping

Cite:
Chikrii A.A., Rappoport I.S. (2023). A modified method of resolving functions for control game problems with integral constraints. Cybernetics and Systems Analysis, 59 (4), 82–93. doi: https://doi.org/10.1007/s10559-023-00593-z http://jnas.nbuv.gov.ua/article/UJRN-0001415726 [In Ukrainian].