Modifications of the Pontryagin conditions in the problem of approach of conflict-controlled objects / Chikrii, / Rappoport. (2022)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2022, 58 (6))

Chikrii A.A., Rappoport I.S.
Modifications of the Pontryagin conditions in the problem of approach of conflict-controlled objects

The authors consider the problem of approach of controlled objects in dynamic game problems and formulate modified sufficient conditions for the game termination in a finite guaranteed time in the case where the Pontryagin condition is not satisfied. Instead of the Pontryagin selector, which does not exist, some shift functions are considered and used to introduce special multivalued mappings. They generate the upper and lower resolving functions of special type, and based on them, modified schemes of the first Pontryagin’s method and of the method of resolving functions are proposed, which ensures the completion of the conflict-controlled process in the class of quasi-strategies and counter-controls. Pontryagin’s control example with objects of the same type illustrates the new theoretical results. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: measurable selector, multivalued mapping, quasilinear differential game, resolving function, stroboscopic strategy, Game theory, Condition, Controlled objects, Differential games, Dynamic game, Measurable selector, Multivalued mappings, Quasi-linear, Quasilinear differential game, Resolving functions, Stroboscopic strategy, Mapping


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Cite:
Chikrii A.A., Rappoport I.S. (2022). Modifications of the Pontryagin conditions in the problem of approach of conflict-controlled objects. Cybernetics and Systems Analysis, 58 (6), 95–105. doi: https://doi.org/10.1007/s10559-023-00527-9 http://jnas.nbuv.gov.ua/article/UJRN-0001368553 [In Ukrainian].


 

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