On some sufficient conditions for optimality of the pursuit time in the differential game with multiple pursuers. (English. Russian original) Zbl 1125.91310

Autom. Remote Control 67, No. 4, 529-537 (2006); translation from Avtom. Telemekh. 2006, No. 4, 16-24 (2006).
Summary: Consideration was given to the problem of optimal pursuit of one object by multiple objects. The player’s moves obey the ordinary differential equations. Geometrical constraints are imposed on the player controls. Sufficient conditions were obtained for optimality of the pursuit time, and the optimal player strategies were constructed.


91A23 Differential games (aspects of game theory)
91A24 Positional games (pursuit and evasion, etc.)
49N70 Differential games and control
91A06 \(n\)-person games, \(n>2\)
Full Text: DOI


[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] Krasovskii, N.N., Upravlenie dinamicheskoi sistemoi (Control of the Dynamic System), Moscow: Nauka, 1985.
[3] Subbotin, A.I. and Chentsov, A.G., Optimizatsiya garantii v zadachakh upravleniya (Optimization of Guarantee in Control Problems), Moscow: Nauka, 1981. · Zbl 0542.90106
[4] Petrosyan, L.A., Differentsial’nye igry presledovaniya (Differential Pursuit Games), Leningrad: Leningr. Gos. Univ., 1977.
[5] Petrosyan, L.A. and Rikhsiev, B.B., Presledovanie na ploskosti (Planar Pursuuit), Moscow: Nauka, 1991.
[6] Rikhsiev, B.B., Differentsial’nye igry s prostymi dvizheniyami (Differential Games with Simple Moves), Tashkent: Fan, 1989. · Zbl 0813.90141
[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 Teorekhov, S.D., On a Game of Optimal Pursuit of One Object by Two Objects, Prikl. Mat. Mekh., 1983, vol. 47, no. 6, pp. 898–903.
[9] Sinitsyn, A.V., Construction of the Cost Function in the Game of Pursuit by Several Objects, Prikl. Mat. Mekh., 1993, vol. 57, no. 1, pp. 52–57.
[10] Ibragimov, G.I., One Game of Optimal Pursuit of One Object by Two Objects, Prikl. Mat. Mekh., 1998, vol. 62, no. 2, pp. 199–205. · Zbl 0973.91009
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.