THE  -CAPTURE PROBLEM FOR INERTIAL MOTIONS UNDER INTEGRAL CONSTRAINTS

Mohisanam Turgunboyeva

Mualliflar

Turgunboyeva Mohisanam Akhmadullo kizi

Namangan State University

Annotasiya

In this paper, we consider the -capture problem in a differential game with inertial objects (a pursuer and an evader). These objects have controls that are subject to integral constraints and start with identical initial velocity vectors in Euclidean space. We propose an approach strategy for the pursuer to solve the problem, and we also find a sufficient condition for -capture. Furthermore, we introduce the concept of a guaranteed time of -capture. Our strategy is based on Chikrii's method of resolving functions. The pursuer aims to approach the evader at a specific distance, while the evader tries to avoid the -approach or, if that's not possible, delay the occurrence of the -approach.

Kalit so‘zlar:

Differential game, object, constraint, -capture, guaranteed time.

Bibliografik manbalar

Azamov A. (1986) On the quality problem for simple pursuit games with constraint. SerdicaBulgariacae math. Publ.Sofia, Vol.12, No.1, p. 38–43.

Azamov A.A., Samatov B.T. (2010) The P-Strategy: Analogies and Applications. The Fourth International Conference on Game Theory and Management, St. Petersburg, Vol.4, P. 33–47.

Chikrii A.A. (1997) Conflict-Controlled Processes. Kluwer, Dordrecht, DOI 10.1007/978-94-017-1135-7

Grigorenko N.L. (1990) Mathematical Methods of Control for Several Dynamic Processes. Izdat. Gos. Univ., Moscow.

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

Krasovsky N.N. (1985) Control of a Dynamical System. Nauka, Moscow, 520 p. (In Russian)

Khaidarov B.K. (1984) Positional l-catch in the game of one evader and several pursuers, Prikl. Matem. Mekh.,48, No. 4, p. 574–579.

Nahin P.J. (2012) Chases and Escapes: The Mathematics of Pursuit and Evasion. Princeton University Press, Princeton. 272 p.

Pontryagin L.S. (2014) Selected Works. MAKS Press, Moscow. 551 p. (In Russian)

Pshenichnyi B.N. (1976) Simple pursuit by several objects. Cybernetics and System Analysis. Vol. 12, No. 5, 484–485. DOI 10.1007/BF01070036

Petrosjan L.A. (1993) Differential games of pursuit. Series on optimization. Vol.2. World Scientific Poblishing, Singapore.

SatimovN.Yu. (2003) Methods for Solving the Pursuit Problem in the Theory of Differential Games. Izd-voNUUz, Tashkent. (In Russian)

Samatov B.T. (2013) Problems of group pursuit with integral constraints on controls of the players II. Cybernetics and Systems Analysis, Vol. 49, No. 6, P. 907–921. DOI 10.1007/s10559-013-9581-5

THE -CAPTURE PROBLEM FOR INERTIAL MOTIONS UNDER INTEGRAL CONSTRAINTS

Mualliflar

Annotasiya

Kalit so‘zlar:

Bibliografik manbalar

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Qanday qilib iqtibos keltirish kerak

Nashr

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