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Russia Izhevsk
Section Mathematics
Title The problem of simple group pursuit with phase constraints in time scales
Author(-s) Petrov N.N.a
Affiliations Udmurt State Universitya
Abstract In the finite-dimensional Euclidean space $\mathbb R^k,$ the problem of pursuit of one evader by a group of pursuers with equal opportunities for all participants is considered, which is described in a given time scale $T$ by a system of the form $$z_i^{\Delta} = u_i - v,$$ where $f^{\Delta}$ is the $\Delta$-derivative of the function $f$ in the time scale $T$. The set of admissible controls is a ball of unit radius with the center at the origin. Terminal sets are the coordinate origin. Additionally, it is assumed that the evader does not leave the convex polyhedral set with a nonempty interior during the game. Sufficient conditions for the solvability of the pursuit and evasion problems are obtained. In the research, the method of resolving functions is used as the basic one.
Keywords differential game, group pursuit, pursuer, evader, phase restriction, time scale
UDC 517.977
MSC 49N79, 49N70, 91A24
DOI 10.35634/vm200208
Received 1 February 2020
Language Russian
Citation Petrov N.N. The problem of simple group pursuit with phase constraints in time scales, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 2, pp. 249-258.
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