For a dynamical system whose motion is described by neutral-type differential equations in Hale’s form, we consider a minimax–maximin differential game with a quality index evaluating the motion history realized up to the terminal time. The control actions of the players are subject to geometric constraints. The game is formalized in classes of pure positional strategies with a memory of the motion history. It is proved that the game has a value and a saddle point. The proof is based on the choice of an appropriate Lyapunov–Krasovskii functional for the construction of control strategies by the method of an extremal shift to accompanying points.

中文翻译：

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中立型系统位置微分博弈论

对于动力学系统，其运动由Hale形式的中立型微分方程描述，我们考虑一个minimax-maximin微分游戏，其质量指标可评估直至终端时间为止的运动历史。玩家的控制动作受到几何约束。这款游戏以带有运动历史记忆的纯位置策略类形式化。事实证明，该游戏具有价值和鞍点。该证明是基于通过极端移至伴随点的方法选择适当的Lyapunov–Krasovskii函数来构建控制策略的。