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A Pursuit–Evasion Differential Game with Slow Pursuers on the Edge Graph of a Simplex. I

  • MATHEMATICAL GAME THEORY AND APPLICATIONS
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Abstract

We consider a differential game with several pursuing points and one evading point moving along the 1-skeleton (i.e., the edge graph) of an arbitrary simplex in three-dimensional space or a complete fourth-order graph with rectifiable edges with given maximal velocities of points. The exact statement of the problem is given. Using the strategy of parallel pursuit for the slow pursuer and one numerical characteristic of the simplex expressing its proximity to a regular tetrahedron, we give a complete solution of the performance problem for a three-dimensional simplex. The second part will be devoted to higher-dimensional cases.

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ACKNOWLEDGMENTS

The article is dedicated to an anniversary date of Prof. L.A. Petrosyan, who has made a great contribution to the development of the Tashkent school of the theory of differential games.

Funding

This work was supported by the Ministry of Innovative Development of the Republic of Uzbekistan, project no. OT-F4-84.

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Authors and Affiliations

  1. Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, 100170, Uzbekistan

    A. A. Azamov

  2. Andijan State University, Andijan, 170100, Uzbekistan

    T. T. Ibaydullayev

Authors
  1. A. A. Azamov
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  2. T. T. Ibaydullayev
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Corresponding authors

Correspondence to A. A. Azamov or T. T. Ibaydullayev.

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Translated by V. Potapchouck

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Azamov, A.A., Ibaydullayev, T.T. A Pursuit–Evasion Differential Game with Slow Pursuers on the Edge Graph of a Simplex. I. Autom Remote Control 82, 1996–2005 (2021). https://doi.org/10.1134/S000511792111014X

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  • DOI: https://doi.org/10.1134/S000511792111014X

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