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<p>In a&#xa0;finite-dimensional Euclidean space, a&#xa0;pursuit problem involving a&#xa0;group of pursuers and an evader is considered. The dynamics are described by a&#xa0;system of second-order differential equations on a&#xa0;given time scale. The initial positions of the players and their initial velocities at a&#xa0;fixed initial time are specified. The pursuers use nonanticipative strategies, while the evader uses a&#xa0;programmed strategy. The set of admissible controls for each player is the unit ball centered at the origin, and the terminal set is the origin. The objective of the pursuers is to capture the evader, while the evader seeks to avoid capture. The study is based on the method of resolving functions. A&#xa0;sufficient condition for the capture of the evader is derived in terms of the initial velocities and the game parameters.</p>

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Second-Order pursuit problem on time scales

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Elena S. Mozhegova

摘要

In a finite-dimensional Euclidean space, a pursuit problem involving a group of pursuers and an evader is considered. The dynamics are described by a system of second-order differential equations on a given time scale. The initial positions of the players and their initial velocities at a fixed initial time are specified. The pursuers use nonanticipative strategies, while the evader uses a programmed strategy. The set of admissible controls for each player is the unit ball centered at the origin, and the terminal set is the origin. The objective of the pursuers is to capture the evader, while the evader seeks to avoid capture. The study is based on the method of resolving functions. A sufficient condition for the capture of the evader is derived in terms of the initial velocities and the game parameters.