Abstract
Antagonistic linear differential games with a fixed instant of termination and a continuous terminal pay function are considered. The control action of the first (minimizing) player is assumed to be scalar and bounded in modulus. The vector control of the second player is restricted by a geometrical constraint. An assertion is proved concerning the sufficient condition and, when this is satisfied, the optimal negative feedback positional control of the first player can be specified using the switching surface which separates the space of the game into two parts, in each of which there is its own limit value of the control action. The proposed control procedure is stable with respect to inaccuracies in the numerical construction of the switching surface.
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