DIFFERENTIAL l-CATCH AND l-ESCAPE GAMES IN THE CASE OF NON-STATIONARY GEOMETRIC CONSTRAINTS ON CONTROLS
DOI:
https://doi.org/10.52754/16948645_2024_1(4)_48Keywords:
l-catch, Differential, evasion, pursuer, evade, geometric constraint, strategy, guaranteed time of l-catchAbstract
This paper is devoted to the l-catch and l-escape differential games with two players, called pursuer and evader, whose controls adhere to non-stationary geometric constraints of various types. Such problems are quite relevant for the processes where the rates of control parameters fluctuate consistently during the time. First, the pursuit problem is discussed and a pursuer strategy guaranteeing the l-catch is defined using the method of Chikrii’s resolving functions. Then, the evasion problem is dealt with by means of a specific control function of evader.
References
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. – 272. P. 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
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