An evasion differential game of one evader and many pursuers is studied. The dynamics of state variables \(x_1,\ldots , x_m\) are described by linear differential equations. The control functions of players are subjected to integral constraints. If \(x_i(t) \ne 0\) for all \(i \in \{1,\ldots ,m\}\) and \(t \ge 0\), then we say that evasion is possible. It is assumed that the total energy of pursuers doesn’t exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible.

中文翻译：

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具有整体约束的一个躲避者和多个追随者的线性躲避微分博弈

研究了一个躲避者和多个追赶者的躲避差异游戏。状态变量\（x_1，\ ldots，x_m \）的动力学由线性微分方程描述。游戏者的控制功能受到整体约束。如果对所有\ {i \ in \ {1，\ ldots，m \} \）和\（t \ ge 0 \）都具有\（x_i（t）\ ne 0 \），那么我们说逃避是可能的。假定追随者的总能量不超过逃避者的能量。我们构建的规避策略，并证明了对任意正整数米逃税是可能的。