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Linear Group Pursuit Problem with Fractional Derivatives, Simple Matrices, and Different Possibilities of Players

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Abstract

In a finite-dimensional Euclidean space, we consider the problem of pursuit by a group of pursuers of one evader, which is described by a system of equations with a Caputo derivative of order \(\alpha \), where the sets of feasible controls are convex compact sets. We obtain sufficient conditions for the solvability of pursuit and evasion problems, in the study of which the method of resolving functions is used.

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Funding

This work was financially supported by the Russian Science Foundation, project 21-71-10070, https://rscf.ru/en/project/21-71-10070/.

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Authors and Affiliations

  1. Udmurt State University, Izhevsk, 426034, Russia

    N. N. Petrov & A. I. Machtakova

  2. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620108, Russia

    N. N. Petrov & A. I. Machtakova

Authors
  1. N. N. Petrov
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  2. A. I. Machtakova
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Correspondence to N. N. Petrov or A. I. Machtakova.

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Translated by V. Potapchouck

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Petrov, N.N., Machtakova, A.I. Linear Group Pursuit Problem with Fractional Derivatives, Simple Matrices, and Different Possibilities of Players. Diff Equat 59, 933–944 (2023). https://doi.org/10.1134/S0012266123070078

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  • DOI: https://doi.org/10.1134/S0012266123070078

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