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<p>In finite-dimensional Euclidean space we address the problem of pursuit of two evaders by a group of pursuers with equal opportunities for all participants. It is assumed that the motion of the players in a given time scale is described by a linear system with a simple matrix. The terminal sets are the origin. Sufficient conditions for the capture of at least one evader by one pursuer and sufficient conditions for the capture of at least one evader by two pursuers are obtained. The study is based on the method of resolving functions, which makes it possible to obtain sufficient conditions for solvability of the problem in some guaranteed time.</p>

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The Linear Problem of Pursuing Two Coordinated Evaders in Time Scales

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Elena Mozhegova,
  • Nikolay Petrov

摘要

In finite-dimensional Euclidean space we address the problem of pursuit of two evaders by a group of pursuers with equal opportunities for all participants. It is assumed that the motion of the players in a given time scale is described by a linear system with a simple matrix. The terminal sets are the origin. Sufficient conditions for the capture of at least one evader by one pursuer and sufficient conditions for the capture of at least one evader by two pursuers are obtained. The study is based on the method of resolving functions, which makes it possible to obtain sufficient conditions for solvability of the problem in some guaranteed time.