Time-optimal differential games with a lifeline are considered. In such games, there are two sets of interest: the first player tries to guide the system into a target set as soon as possible, while the second player counteracts him and wins if the system reaches another set (called the lifeline). A numerical method for solving time-optimal games with a lifeline is suggested. With this method, the value function is designed as a viscosity solution to the corresponding boundary-value problem for the Hamilton–Jacobi equation. The convergence of the method is established.

中文翻译：

---

用生命线求解时间最优微分对策的数值方法

考虑带有生命线的时间最优差分博弈。在此类游戏中，有两套有趣的东西：第一个玩家尝试将系统尽快引导到目标集中，而第二个玩家反击他，并在系统到达另一组时获胜（称为生命线）。提出了一种用生命线求解时间最优游戏的数值方法。使用这种方法，将值函数设计为汉密尔顿–雅各比方程的相应边值问题的粘性解。建立了方法的收敛性。