N.N. Petrov. On a problem of pursuing a group of evaders in time scales ... P. 163-171

A problem of pursuing a group of evaders by a group of pursuers with equal capabilities for all the participants is considered in a finite-dimensional Euclidean space $\mathbb R^k$. In a given time scale $T$, the problem is described by a system
$$ z_i^{\Delta}=u_i-v,$$
where $f^{\Delta}$ is the $\Delta$-derivative of $f$ in the time scale $T$. The set of admissible controls is a ball of unit radius centered at the origin. The terminal sets are the origin. In addition, it is assumed that all the evaders use the same control and, during the game, stay within a convex polyhedral set with nonempty interior. Sufficient conditions are obtained for the solvability of the problem of capturing at least one evader. The method of resolving functions is used as a basis of this research.

Keywords: differential game, pursuer, evader, group pursuit, time scale

Received March 29, 2021

Revised May 11, 2021

Accepted Junе 7, 2021

Funding Agency: This research was funded by the Ministry of Science and Higher Education of the Russian Federation in the framework of state assignment No. 075-00232-20-01, project FEWS-2020-0010 and under grant 20-01-00293 from the Russian Foundation for Basic Research.

Nikolai Nikandrovich Petrov, Dr. Phys.-Math. Sci., Prof., Udmurt State University, Izhevsk, 426034 Russia, e-mail: kma3@list.ru

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Cite this article as: N.N. Petrov. Matrix resolving functions in a linear problem of group pursuit with multiple capture, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 3, pp. 163–171.