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<p>In a&#xa0;finite-dimensional normed space, an antagonistic differential game is considered, in which the vectograms of the players’ controls are balls whose radii are functions of time. The motion is constructed using polygonal lines. We assume the possibility of a&#xa0;single breakdown that leads to a&#xa0;change in the dynamics of the first player. The moment of occurrence of a&#xa0;breakdown is not known in advance. The goal of the first player is to lead the phase vector to a&#xa0;terminal set, which is a&#xa0;ring with given inner and outer radii, at a&#xa0;given time. The goal of the second player is the opposite. The control of the first player is constructed using the principle of minimization of the guaranteed result. Necessary and sufficient conditions have been found for the termination of the game. The corresponding guaranteeing controls of players have been constructed.</p>

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Single-type differential game with a ring-shaped terminal set and a possible breakdown

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Igor’ V. Izmest’ev,
  • Aleksandr M. Barinov

摘要

In a finite-dimensional normed space, an antagonistic differential game is considered, in which the vectograms of the players’ controls are balls whose radii are functions of time. The motion is constructed using polygonal lines. We assume the possibility of a single breakdown that leads to a change in the dynamics of the first player. The moment of occurrence of a breakdown is not known in advance. The goal of the first player is to lead the phase vector to a terminal set, which is a ring with given inner and outer radii, at a given time. The goal of the second player is the opposite. The control of the first player is constructed using the principle of minimization of the guaranteed result. Necessary and sufficient conditions have been found for the termination of the game. The corresponding guaranteeing controls of players have been constructed.