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## Archive of Issues

Russia Izhevsk
Year
2015
Volume
25
Issue
1
Pages
12-20
 Section Mathematics Title On the capture of two evaders in a non-stationary pursuit-evasion problem with phase restrictions Author(-s) Vinogradova M.N.a Affiliations Udmurt State Universitya Abstract We consider a linear problem of pursuing two evaders by a group of persecutors in case of equal dynamic opportunities of all participants and under phase restrictions imposed on the states of evaders. We assume that the evaders use the same control. The movement of each participant has the form $\dot z + a (t) z = w.$ Geometric constraints on the control are strictly convex compact set with smooth boundary, and terminal sets are the origin of coordinates. It is assumed that the evaders do not leave the convex cone. The aim of a group of pursuers is to capture two evaders; the aim of a group of evaders is opposite. We say that a capture holds in the problem of pursuing two evaders if among the specified number of pursuers there are two of them who catch the evaders, possibly at different times. We obtain sufficient conditions for capturing two evaders in terms of initial positions. The results obtained are illustrated by examples. Keywords differential game, phase restrictions, piece-program strategy, counterstrategy UDC 517.977 MSC 49N70, 49N75 DOI 10.20537/vm150102 Received 25 February 2015 Language Russian Citation Vinogradova M.N. On the capture of two evaders in a non-stationary pursuit-evasion problem with phase restrictions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 1, pp. 12-20. References Pshenichnyi B.N. Simple pursuit by several objects, Kibernetika, 1976, no. 3, pp. 145-146 (in Russian). Chernous'ko F.L. A problem of evasion from many pursuers, Journal of Applied Mathematics and Mechanics, 1976, vol. 40, no. 1, pp. 11-20. 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Nauki, 2011, no. 1, pp. 3-7 (in Russian). Petrov N.N. To the non-stationary problem of the group pursuit with phase restrictions, Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2010, vol. 2, no. 4, pp. 74-83 (in Russian). Bannikov A.S., Petrov N.N. On a nonstationary problem of group pursuit, Proceedings of the Steklov Institute of Mathematics, 2010, vol. 271, issue 1 supplement, pp. 41-52. Petrov N.N. Controllability of autonomous systems, Differ. Uravn., 1968, vol. 4, no. 4, pp. 606-617 (in Russian). Full text