Model Problem in a Line with Two Pursuers and One Evader

An antagonistic differential game is considered where motion occurs in a straight line. Deviations between the first and second pursuers and the evader are computed at the instants T 1 and T 2, respectively. The pursuers act in coordination. Their aim is to minimize the resultant miss, which is equal to the minimum of the deviations happened at the instants T 1 and T 2. Numerical study of value function level sets (Lebesgue sets) for qualitatively different cases is given. A method for constructing optimal feedback controls is suggested on the basis of switching lines. The results of a numerical simulation are shown.