A Numerical Method for Solving Time-Optimal Differential Games with a Lifeline

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.