title: To the problem of the pursuit in quasilinear differential lag games
metadata.name: dc.contributor.author
metadata.value: Mukhsinov, Edgor M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-01-19T19:11:03Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-01-19T19:11:03Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Mukhsinov E. M. To the problem of the pursuit in quasilinear differential lag games. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2022, vol. 18, iss. 3, pp. 328–336.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.303
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38863
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In the field of the theory of differential games defined in a finite-dimensional space, fundamental works were carried out by L. S. Pontryagin, N. N. Krasovskiy, B. N. Pshenichny, L. S. Petrosyan, M. S. Nikol’skiy, N. Yu. Satimov and others. L. S. Pontryagin and his students consider differential games separately, from the point of view of the pursuer and from the point of view of the evader, which inevitably connects the differential game with two different problems. In this paper, in a Hilbert space, we consider the pursuit problem in the sense of L. S. Pontryagin for a quasilinear differential game, when the dynamics of the game is described by a differential equation of retarded type with a closed linear operator generating a strongly continuous semigroup. Two main theorems on the solvability of the pursuit problem are proved. In the first theorem, a set of initial positions is found from which it is possible to complete the pursuit with a guaranteed pursuit time. The second theorem defines sufficient conditions on the optimality of the pursuit time. The results obtained generalize the results of works by P. B. Gusyatnikov, M. S. Nikol’skiy, E. M. Mukhsinov, and M. N. Murodova, in which it is described by a differential equation of retarded type in a Hilbert space. Our results make it possible to study delayed-type conflict-controlled systems not only with lumped, but also with distributed parameters.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 18; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: pursuit problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: delay differential game
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hilbert space
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimality of pursuit time
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: To the problem of the pursuit in quasilinear differential lag games
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 14514-Текст статьи-47915-1-10-20221010.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38863/1/14514-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-47915-1-10-20221010.pdf
resources.format: Adobe PDF
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