Unified approach for two-target game analysis

Abstract

A two-target differential game is defined from the outset by a qualitative (game-of-kind) formulation. The solution of such a game is the decomposition of the space of admissible initial conditions into zones of different outcomes: two winning zones, one for each player, the zone of nowinning (draw) and (if the intersection of the two target sets is not empty) a zone of eventual mutual winning (mutual kill). In this paper it is shown that the solution of any two-target game can be constructed, based on solving first two single-target pursuit-evasion games of kind (one for each target set) in a systematic way.