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<p>We construct an evasion strategy in a general evasion differential game, played on the Euclidean space, with one evader and any finite number of pursuers where the dynamics of the objects are given by a system of linear differential equations. Our construction of the evasion strategy is based on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(a_i - \tau _i\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>a</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>τ</mi> <mi>i</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> method. We show that if the evader can successfully implement this strategy, then it can win the game against all possible strategy choices of the pursuers.</p>

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On the Existence of an Evasion Strategy in a Linear Differential Game with Integral Constraints

  • 期刊论文

  • 发表日期：

    2025年1月4日

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  • Bruno Antonio Pansera,
  • Gafurjan Ibragimov,
  • Shravan Luckraz

摘要

We construct an evasion strategy in a general evasion differential game, played on the Euclidean space, with one evader and any finite number of pursuers where the dynamics of the objects are given by a system of linear differential equations. Our construction of the evasion strategy is based on the \(a_i - \tau _i\) a i - τ i method. We show that if the evader can successfully implement this strategy, then it can win the game against all possible strategy choices of the pursuers.