Abstract

We study a differential game problem for an infinite system of binary differential equations. The control functions of pursuer and evader are subjected to integral constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space \(l_{2}\) and the aim of the evader is opposite. An equation for the optimal pursuit time is obtained and optimal controls of players are constructed. Also, an auxiliary optimal control problem is solved to prove the main result of the paper.

中文翻译：

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一类无限二元微分方程组的最优追寻微分博弈问题

 抽象的

我们研究无限二元微分方程组的微分博弈问题。追击者和躲避者的控制函数受到积分约束。追赶者试图将系统的状态带到希尔伯特空间的原点\(l_{2}\)，而逃避者的目标则相反。得到了最优追踪时间的方程并构造了玩家的最优控制。同时还解决了一个辅助最优控制问题来证明本文的主要结果。