Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls

Gafurjan Ibragimov, Ikrombek Yusupov and Massimiliano Ferrara ()
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Gafurjan Ibragimov: Department of Digital Economics and Agrotechnologies, University of Digital Economics and Agrotechnologies, Tashkent 100022, Uzbekistan
Ikrombek Yusupov: Department of Mathematics, Andijan State University, Andijan 170100, Uzbekistan
Massimiliano Ferrara: Department of Law, Economics and Human Sciences and Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy

Mathematics, 2023, vol. 11, issue 2, 1-10

Abstract: We studied a simple motion differential game of two pursuers and one evader in R 2 . The control functions of players are subjected to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered complete. The pursuers attempt to complete the game as earlier as possible. The evader attempts to avoid being captured or delays the capture time. We found an equation for the optimal pursuit time and construct the optimal strategies of players.

Keywords: differential game; Grönwall constraints; pursuers; evader; optimal pursuit time; optimal strategy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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