Ibragimov, G. I. A group pursuit game. (English. Russian original) Zbl 1113.91009 Autom. Remote Control 66, No. 8, 1214-1223 (2005); translation from Avtom. Telemekh. 2005, No. 8, 24-35 (2005). Summary: A differential game of pursuit of an evader by \(m\) dynamic pursuers under simple motion is studied. The time of game completion is fixed. Pursuers’ controls obey integral constraints, whereas the evader control obeys either an integral constraint or a geometric constraint. A differential game with cost defined by the distance between the evader and his nearest pursuer at the game completion instant is studied. Optimal strategies for players are constructed and the game cost is determined. MSC: 91A23 Differential games (aspects of game theory) 91A24 Positional games (pursuit and evasion, etc.) 49N75 Pursuit and evasion games 91A06 \(n\)-person games, \(n>2\) PDFBibTeX XMLCite \textit{G. I. Ibragimov}, Autom. Remote Control 66, No. 8, 1214--1223 (2005; Zbl 1113.91009); translation from Avtom. Telemekh. 2005, No. 8, 24--35 (2005) Full Text: DOI References: [1] Isaaks, R., Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control, and Optimization, New York: Wiley, 1952. Translated under the title Differentsial’nye igry, Moscow: Mir, 1967. [2] Pontryagin, L.S., Izbrannye trudy (Selected Works), Moscow: Nauka, 1988. [3] Krasovskii, N.N., Upravlenie dinamicheskoi sistemoi (Control of a Dynamic System), Moscow: Nauka, 1985. [4] Subbotin, A.I. and Chentsov, A.G., Optimizatsiya garantii v zadachakh upravleniya (Optimization of the Guarantee in Control Problems), Moscow: Nauka, 1981. · Zbl 0542.90106 [5] Chernous’ko, F.L., Evading Several Pursuers, Prikl. Mat. Mekh., 1976, vol. 40, no.1, pp. 14–24. [6] Petrov, N.N., A Group Pursuit Game under Phase Constraints, Prikl. Mat. Mekh., 1988, vol. 52, no.6, pp. 1030–1033. [7] Ivanov, R.P. and Ledyaev, Yu.S., Optimality of the Pursuit Time in a Differential Game with Several Pursuers under Simple Motion, Tr. MIAN SSSR, 1981, vol. 158, pp. 87–97. · Zbl 0509.90098 [8] Pashkov, A.G. and Teorekov, S.D., A Game of Optimal Pursuit of One Evader by Two Pursuers, Prikl. Mat. Mekh., 1983, vol. 47, no.6, pp. 898–903. [9] Rikhsiev, B.B., Differentsial’nye igry s prostymi dvizheniyami (Differential Games with Simple Motion), Tashkent: Fan, 1989. · Zbl 0813.90141 [10] Sinitsyn, A.V., Cost Function of a Game of Pursuit by Several Pursuers, Prikl. Mat. Mekh., 1993, vol. 57, no.1, pp. 52–57. [11] Ibragimov, G.I., A Game of Optimal Pursuit of an Evader by Several Pursuers, Prikl. Mat. Mekh., 1998, vol. 62, vol. 2, pp. 199–205. · Zbl 0973.91009 [12] Ibragimov, G.I., A Game Problem on a Closed Convex Set, Mat. Trudy, vol. 4, no.2, pp. 96–112. · Zbl 0998.91006 [13] Ibragimov, G.I. and Kuchkarov, A.Sh., Optimality of Pursuit Time in a Differential Game in a Half-Space under Integral Constraints, Uzbek. Math. Zh., 1996, no. 1, pp. 15–22. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.