Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2022, Volume 18, Issue 3, Pages 328–336
DOI: https://doi.org/10.21638/11701/spbu10.2022.303
(Mi vspui538)
 

Applied mathematics

To the problem of the pursuit in quasilinear differential lag games

E. M. Mukhsinov

Tajik State University of Law, Business and Politics, 2, 17th mkr-n, Khujand, 735700, Republic of Tajikistan
References:
Abstract: 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.
Keywords: pursuit problem, delay differential game, Hilbert space, optimality of pursuit time.
Received: August 25, 2021
Accepted: June 21, 2022
Document Type: Article
UDC: 519.837
MSC: 91A24, 49N75
Language: Russian
Citation: E. M. Mukhsinov, “To the problem of the pursuit in quasilinear differential lag games”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 18:3 (2022), 328–336
Citation in format AMSBIB
\Bibitem{Muk22}
\by E.~M.~Mukhsinov
\paper To the problem of the pursuit in quasilinear differential lag games
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2022
\vol 18
\issue 3
\pages 328--336
\mathnet{http://mi.mathnet.ru/vspui538}
\crossref{https://doi.org/10.21638/11701/spbu10.2022.303}
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