This article is cited in 1 paper

MATHEMATICS

$\Pi$-strategy for a differential game of pursuit with integral constraints of a generalized type

B. T. Samatov^a, Horilov Mahmud Abdumalikovich^a, Juraev Bahodirjon Inomjon ugli<sup>b

a</sup> Namangan State University, ul. Uychi, 316, Namangan, 116019, Uzbekistan
^b Andijon State University, ul. Universitetskaya, 129, Andijan, 170100, Uzbekistan

Abstract: The paper investigates a differential game of simple pursuit, when the controls of two opposing players are subject to integral constraints of a generalized type. The generalization of the proposed restriction lies in the fact that it includes previously known restrictions such as integral, geometric, linear, exponential and their mixtures. In general, it includes 25 types of pursuit problems with such different types of constraints. To solve the pursuit problem under such generalized constraints, we propose a parallel pursuit strategy ($\Pi$-strategy for short) and find sufficient conditions for the solvability of this problem. At the end of the article, tables are provided that list each particular type of game, the conditions for its solvability, the resolving function (which determines the corresponding $\Pi$-strategy), and the time of capture.

Keywords: differential game, nonlinear integral constraint, pursuer, evader, strategy, pursuit, guaranteed capture time.

UDC: 517.977

MSC: 49N70, 49N79, 91A24

Received: 08.01.2023
Accepted: 31.03.2023

Language: English

DOI: 10.35634/vm230208

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