On the procedure of choosing the instants of correction in the problem of control with constrained number of switchings

The problem of evading the given target set at the final time instant was c onsidered. The distinguishing feature of its formulation is the constraint on the number of corrections of the programmed controls of the evading play er. In the works of A. G. Chentsov, the differential game with constrained number of corrections was formalized and the decision procedure of the seco nd player was shown to be the triple of the positional strategy, number of required switchings, and law of correction defining the instant of switchin g in the course of processing the realized trajectory. For a class of linea r differential games, the present work proposed an algorithm for stepwise c onstruction of the motions corresponding to the decision procedure of the e vading player.