phone +7 (3412) 91 60 92

Archive of Issues

Russia Izhevsk
Section Mathematics
Title Weak evasion of a group of rigidly coordinated evaders in the nonlinear problem of group pursuit
Author(-s) Blagodatskikh A.I.a
Affiliations Udmurt State Universitya
Abstract A natural generalization of differential two-person games is conflict controlled processes with a group of controlled objects (from at least one of the conflicting sides). The problems of conflict interaction between two groups of controlled objects are the most difficult-to-research. The specificity of these problems requires new methods to study them. This paper deals with the nonlinear problem of pursuing a group of rigidly coordinated evaders (i.e. using the same control) by a group of pursuers under the condition that the maneuverability of evaders is higher. The goal of evaders is to ensure weak evasion for the whole group. By weak evasion we mean non-coincidence of geometrical coordinates, speeds, accelerations and so forth for the evader and all pursuers. The position control is constructed for all possible initial positions of the participants; this control guarantees a weak evasion for all evaders.
Keywords weak evasion, group pursuit, nonlinear differential games, conflict controlled processes
UDC 517.977.8, 519.837.4
MSC 49N70, 49N75
DOI 10.20537/vm140401
Received 1 October 2014
Language Russian
Citation Blagodatskikh A.I. Weak evasion of a group of rigidly coordinated evaders in the nonlinear problem of group pursuit, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 4, pp. 3-17.
  1. Isaacs R. Differential games: a mathematical theory with applications to warfare and pursuit, control and optimization, New York: John Wiley and Sons, 1965, 384 p. Translated under the title Differentsial'nye igry, Moscow: Mir, 1967, 479 p.
  2. Krasovskii N.N., Subbotin A.I. Positsionnye differentsial'nye igry (Positional differential games), Moscow: Nauka, 1974, 456 p.
  3. Petrosyan L.A. Differentsial'nye igry presledovaniya (Differential games of pursuit), Leningrad: Leningrad State University, 1977, 222 p.
  4. Grigorenko N.L. Matematicheskie metody upravleniya neskol'kimi dinamicheskimi protsessami (Mathematical methods of control over multiple dynamic processes), Moscow: Moscow State University, 1990, 197 p.
  5. Chikrii A.A. Konfliktno upravlyaemye protsessy (Conflict-controlled processes), Kiev: Naukova Dumka, 1992, 380 p.
  6. Satimov N.Yu., Rikhsiev B.B. Metody resheniya zadachi ukloneniya ot vstrechi v matematicheskoi teorii upravleniya (Methods of solving the evasion problem in mathematical control theory), Tashkent: Fan, 2000, 176 p.
  7. Blagodatskikh A.I., Petrov N.N. Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob''ektov (Conflict interaction of groups of controlled objects), Izhevsk: Udmurt State University, 2009, 266 p.
  8. Petrov N.N., Petrov N. Nikandr. On a differential game of “cossacks-robbers”, Differ. Uravn., 1983, vol. 19, no. 8, pp. 1366-1374 (in Russian).
  9. Blagodatskikh A.I. Evasion of rigidly coordinated escaping objects from a group of inertial objects, Journal of Computer and Systems Sciences International, 2004, vol. 43, no. 6, pp. 966-972.
  10. Blagodatskikh A.I. Weak evasion of a group of coordinated evaders, Journal of Applied Mathematics and Mechanics, 2005, vol. 69, no. 6, pp. 891-899.
Full text
Next article >>