Numerical method for solving time-optimal differential games with lifeline

This paper discusses classic time-optimal differential games with lifeline. In such games, together with a target set, whereto the first player tries to guide the system, another set is chosen (namely, it is called lifeline), with reaching which the second player wins. Numerical method solving time-optimal games with lifeline is suggested. This method constructs the value function as a viscosity solution of the corresponding boundary value problem for the Hamilton–Jacobi equation. A convergence of the method is proved.