On the theory of three-person differential games

A differential game of three players with dynamics described by linear differential equations under geometric constraints on the control parameters is considered. Sufficient conditions are obtained for the existence of the first player's strategy guaranteeing that the trajectory of the game reaches a given target set for any admissible control of the second player and avoids the terminal set of the third player. An algorithm of constructing the first player's strategy guaranteeing the game's termination in finite time is suggested. A solution of a model example is given.