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<p><i>We consider the</i> <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\ell \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation><i>-capture problem, where the movements of the players are described by differential equations of the same type as in the Pontryagin example. To solve this problem, two separate cases are studied. In the first case, the difference in the initial positions and the difference in the initial velocities of the players are assumed to be linearly dependent. In the second case, these vectors are assumed to be linearly independent. In each case, constructive quasistrategies for the pursuer are proposed, and necessary and sufficient conditions for capture are obtained. Bibliography: 13 titles.</i></p>

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THE \(\ell \)-CAPTURE PROBLEM IN A DIFFERENTIAL GAME WITH CONFLICT-CONTROLLED INERTIAL PLAYERS

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Bahrom Samatov,
  • Mokhisanam Turgunboeva

摘要

We consider the \(\ell \) ℓ -capture problem, where the movements of the players are described by differential equations of the same type as in the Pontryagin example. To solve this problem, two separate cases are studied. In the first case, the difference in the initial positions and the difference in the initial velocities of the players are assumed to be linearly dependent. In the second case, these vectors are assumed to be linearly independent. In each case, constructive quasistrategies for the pursuer are proposed, and necessary and sufficient conditions for capture are obtained. Bibliography: 13 titles.