On a directed metod in a linear differential gamesIn evklideng space the differential game described by the equation with late argument is considered. The managing parameters of the pursuing and escaping player get out as measurable vector functions and accept meanings from some not empty compact subset of elkland space. Such measurable functions are called as allowable controls pursuing and escaping of the players, accordingly.
The article is devoted to study of a game task of controls of pensile of trajectories at presence of delay and the sufficient condition of solvability of a task of controls of pensile of trajectories is received. At study of game we identify ourselves to the persecutor. In this case our purpose consists in reduction of a pensile of trajectories on terminal set. In a case, when a task of controls of pensile of trajectories solvability, speak, that in the given game the pensile of trajectories from initial set can be translated to terminal set for final time.
The tasks when initial set onedot, were studied by many authors. Therefore, the case is of interest, when the initial set contains more than one element. In a case, when the initial set contains one element, the strategy of the persecutor is under construction, proceeding from the given initial situation. In a case, when the initial set contains more than one element, the difficulty consists that for all initial situations from initial set the same strategy is under construction and the kind of controls of the persecutor is constructed.
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