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Uzbekistan Andijan; Namangan
Year
2023
Volume
33
Issue
2
Pages
293-311
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Section Mathematics
Title $\Pi$-strategy for a differential game of pursuit with integral constraints of a generalized type
Author(-s) Samatov B.T.a, Horilov M.A.a, Juraev B.I.b
Affiliations Namangan State Universitya, Andijan State Universityb
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
DOI 10.35634/vm230208
Received 8 January 2023
Language English
Citation Samatov B.T., Horilov M.A., Juraev B.I. $\Pi$-strategy for a differential game of pursuit with integral constraints of a generalized type, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 2, pp. 293-311.
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