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## Archive of Issues

Russia; Uzbekistan Izhevsk; Tashkent
Year
2018
Volume
28
Issue
2
Pages
193-198
 Section Mathematics Title Multiple capture of a given number of evaders in the problem of a simple pursuit Author(-s) Petrov N.N.a, Narmanov A.Ya.b Affiliations Udmurt State Universitya, National University of Uzbekistanb Abstract In the finite-dimensional Euclidean space, the problem of a group of pursuers pursuing a group of evaders is considered, which is described by the system $$\dot z_{ij} = u_i - v_j,\quad u_i, v_j \in V.$$ The set of admissible controls is a convex compact, and the target's sets are the origin of coordinates. The aim of the group of pursuers is to carry out an $r$-fold capture of at least $q$ evaders. Additionally, it is assumed that the evaders use program strategies and that each pursuer can catch no more than one evader. We obtain necessary and sufficient conditions for the solvability of the pursuit problem. For the proof we use the Hall theorem on the system of various representatives. Keywords differential game, group pursuit, pursuer, evader UDC 517.977 MSC 49N75, 91A23 DOI 10.20537/vm180205 Received 3 June 2018 Language Russian Citation Petrov N.N., Narmanov A.Ya. Multiple capture of a given number of evaders in the problem of a simple pursuit, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 2, pp. 193-198. References Pshenichnyi B.N. Simple pursuit by several objects, Cybernetics, 1976, vol. 12, no. 3, pp. 484-485. https://link.springer.com/article/10.1007/BF01070036 Grigorenko N.L. Simple pursuit-evasion game of pursuit group and one evader, Vestnik Moskov. Univ. Ser. XV. Vychisl. Mat. Kibernet., 1983, no. 1, pp. 41-47 (in Russian). Blagodatskikh A.I. Simultaneous multiple capture in a simple pursuit problem, Journal of Applied Mathematics and Mechanics, 2009, vol. 73, no. 1, pp. 36-40. DOI: 10.1016/j.jappmathmech.2009.03.010 Petrov N.N., Prokopenko V.A. On a problem of the pursuit of a group of evaders, Differ. Uravn., 1987, vol. 23, no. 4, pp. 725-726 (in Russian). Sakharov D.V. On two differential games of simple group pursuit, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2012, issue 1, pp. 50-59 (in Russian). DOI: 10.20537/vm120106 Blagodatskikh A.I. Multiple capture in a Pontriagin's problem, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2009, issue 2, pp. 3-12 (in Russian). DOI: 10.20537/vm090201 Petrov N.N. Multiple capture in Pontryagin's example with phase constraints, Journal of Applied Mathematics and Mechanics, 1997, vol. 61, no. 5, pp. 725-732. DOI: 10.1016/S0021-8928(97)00095-6 Petrov N.N., Solov'eva N.A. Multiple capture in Pontryagin’s recurrent example with phase constraints, Proceedings of the Steklov Institute of Mathematics, 2016, vol. 293, suppl. 1, pp. 174-182. DOI: 10.1134/S0081543816050163 Petrov N.N., Solov'eva N.A. Multiple capture in Pontryagin’s recurrent example, Automation and Remote Control, 2016, vol. 77, no. 5, pp. 855-861. DOI: 10.1134/S0005117916050088 Chikrii A.A. Conflict-controlled processes, Boston-London-Dordrecht: Kluwer Acad. Publ., 1997. XX, 404 p. DOI: 10.1007/978-94-017-1135-7 Blagodatskikh A.I. Simultaneous multiple capture in a conflict-controlled process, Journal of Applied Mathematics and Mechanics, 2013, vol. 77, no. 3, pp. 314-320. DOI: 10.1016/j.jappmathmech.2013.09.007 Petrov N.N., Solov'eva N.A. A multiple capture of an evader in linear recursive differential games, Trudy Inst. Mat. i Mekh. UrO RAN, 2017, vol. 23, no. 1, pp. 212-218 (in Russian). DOI: 10.21538/0134-4889-2017-23-1-212-218 Petrov N.N., Solov'eva N.A. Problem of group pursuit in linear recurrent differential games, Journal of Mathematical Sciences, 2018, vol. 230, no. 5, pp. 732-736. DOI: 10.1007/s10958-018-3779-z Petrov N.N. On a certain problem of pursuit of a group of evaders, Autom. Remote Control, 1996, vol. 57, no. 6, pp. 808-813. Hall M. Combinatorial Theory, Waltham-Toronto-London: Blaisdell Publishing Company, 1967. Translated under the title Kombinatorika, Moscow: Mir, 1970. Full text