On linear differential games with convex integral constraints

We consider the problem of the approach of a trajectory of a linear conflict-controlled process to a linear subspace in the case of general integral constraints on the player's controls. Using the technique of set-valued mappings and convex analysis (epigraph of a function, recession cone), we obtain sufficient conditions for problem solvability in the class of measurable controls. The relation to a dual description based on conjugate functions is specified. Termination conditions for a game with impulse controls are established. The results are exemplified by means of model problems with various types of constraints on the players' controls.