DIFFERENTIAL L-CAPTURE AND EVASION GAMES WITH INERTIAL PLAYERS UNDER GEOMETRIC CONSTRAINTS ON CONTROLS: DIFFERENTIAL L-CAPTURE AND EVASION GAMES WITH INERTIAL PLAYERS UNDER GEOMETRIC CONSTRAINTS ON CONTROLS

Бахром Саматов; Мохисанам Тургунбоева

doi:10.52754/16948645_2023_2_202

Авторлор

Таджиахматович Наманганский государственный университет
Ахмадулло кизи Наманганский государственный университет

DOI:

https://doi.org/10.52754/16948645_2023_2_202

Ачкыч сөздөр:

Differential game, l-capture, evasion, pursuer, evader, geometric constraint, strategy, guaranteed time of l-capture

Аннотация

This paper is devoted to solve l-capture and evasion problems for a differential game of two players, a pursuer and an evader, with inertial motions. We impose geometric constraints on controls of the players. Originally, we devise an l-approach strategy, on the basis of Chikrii’s method of resolving functions, for a pursuer and we present new sufficient conditions of l-capture. Here as l-capture, we refer the moment when a pursuer approaches an evader at the range l>0. In the evasion problem we define the strategy guaranteeing an evader to diverge from a pursuer at the distance greater than l>0. Besides that, new sufficient conditions of evasion have been shown.

Библиографиялык шилтемелер

Isaacs R. Differential games. John Wiley and Sons, New York. 1965, 340 p.

Pontryagin L.S. Selected Works. MAKS Press, Moscow. 2014, 551 p.

Krasovsky N.N. Game-Theoretical Control Problems/ Subbotin A.I. Springer, New York. 1988, 517 p. DOI: https://doi.org/10.1007/978-1-4612-3716-7

Petrosyan L.A. Games with “a Survival Zone”. Occasion L-catch / Dutkevich V.G. Vestnik Leningrad State Univ., 1969, Vol.3, № 13, p. 31-38.

Nahin P.J. Chases and escapes: The Mathematics of Pursuit and Evasion. Princeton University Press, Princeton. 2012, p. 272. DOI: https://doi.org/10.1515/9781400842063

Pshenichnyi B.N. Simple pursuit by several objects. Cybernetics and Systems Analysis, 1976, Vol. 12, № 5, p. 484-485. DOI: https://doi.org/10.1007/BF01070036

Satimov N.Yu. Methods for solving the pursuit problem in the Theory of Differential Games. Izd-vo NUUz, Tashkent. 2003. P. 203

Azamov A.A. On the quality problem for simple pursuit games with constraint. Serdica Bulgariacae math., 1986, Vol. 12, № 1, p. 38-43.

Samatov B.T. Problems of group pursuit with integral constraints on controls of the players. Cybernetics and Systems Analysis, 2013, Vol. 49, № 6, p. 907-921. DOI: https://doi.org/10.1007/s10559-013-9581-5

Samatov B.T. Differential game with a lifeline for the inertial movements of players / Soyibboyev U.B. Ural Mathematical Journal, Vol. 7, № 2, p. 94-107. DOI: https://doi.org/10.15826/umj.2021.2.007

Khaidarov B.K. Positional l-catch in the game of one evader and several pursuers. Prikl. Matem. Mekh., 1984, Vol. 48, № 4, p. 574-579. DOI: https://doi.org/10.1016/0021-8928(84)90006-6

DIFFERENTIAL L-CAPTURE AND EVASION GAMES WITH INERTIAL PLAYERS UNDER GEOMETRIC CONSTRAINTS ON CONTROLS