Simple pursuit with phase constraints in a class of impulse strategies
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2012), pp. 48-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present paper deals with a simple group pursuit problem in a class of impulse strategies. The first part considers the impulse strategy of an evader with phase restrictions on the evader's state. It is assumed that the evader does not leave a convex polyhedral set. We obtain sufficient conditions for the capture of the evader by one of the pursuers. The second part deals with the impulse strategies of pursuers. Sufficient conditions for the capture of an evader by one of the pursuers under the assumption that the evader does not leave a convex polyhedral set, are stated.
Keywords: differential game, group pursuit, impulse strategy.
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E. V. Kotlyachkova. Simple pursuit with phase constraints in a class of impulse strategies. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2012), pp. 48-52. http://geodesic.mathdoc.fr/item/VUU_2012_3_a4/

[1] Krasovskii N. N., Teoriya upravleniya dvizheniem (Theory of control of motion), Nauka, Moscow, 1968 | MR

[2] Chikrii A. A. Machikhin I. I., “Linear differential games with impulse control of players”, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 11, no. 1, 2005, 212–224 | MR | Zbl

[3] Krivonos Yu. G., Machikhin I. I., Chikrii A. A., Dinamicheskie sistemy s razryvnymi traektoriyami (Dynamical systems with discontinuous trajectories), Nauk. Dumka, Kiev, 2005

[4] Petrov N. N., “The problem of group pursuit strategies in a class of impulsive pursuit”, Izv. Ross. Akad. Nauk Teor. Sist. Upr., 2009, no. 1, 38–44 | MR | Zbl

[5] Blagodatskikh A. I., Petrov N. N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob'ektov (Confict interaction of groups of controlled objects), Udmurt State University, Izhevsk, 2009 | MR | Zbl

[6] Petrov N. N., “To the time-dependent problem of group pursuit with phase constraints”, Mathematical Game Theory and its Applications, 2:4 (2010), 74–83 | Zbl

[7] Bannikov A. S., Petrov N. N., “On non-stationary problem of group pursuit with phase restrictions”, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 16, no. 1, 2010, 40–51

[8] Bannikov A. S., “About a problem of positional capture of one evader by group of pursuers”, Vestn. Udmurt. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 1, 3–7

[9] Vagin D. A., Petrov N. N., “On a problem of group pursuit with phase constraints”, Prikl. Mat. Mekh., 2002, no. 2, 234–241 | MR

[10] Vinogradova M. N., “On the capture of two evaders in a simple pursuit–evasion problem with phase restrictions”, Vestn. Udmurt. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 4, 3–8

[11] Petrov N. N., “Controllability of autonomous systems”, Differ. Uravn., 4:4 (1968), 606–617 | MR | Zbl