We consider a linear conflict-controlled process of two players with a terminal set in the form of the sum of a linear subspace and a convex compact set in its orthogonal complement. The process is considered from the point of view of the first player. His goal is to steer the controlled object to the terminal set. It is assumed that the first player knows the dynamic characteristics of the controlled object, the phase variables and the control of the second player. We give sufficient conditions under which the first player can guarantee the steering of the phase vector of the game to the terminal set. We provide a form of a positional countercontrol of the first player guaranteeing the termination of the process. This positional countercontrol is designed to operate within the logic of step-by-step positional control of the aggregate system that includes the real controlled object and a model (a guide) and implements tracking of the guide’s movement in the form of an extreme aiming procedure which is executed step-by-step in a discrete system and possesses the same stability against informational noise as achieved in a scheme with the guide. Examples are provided.
N. L. Grigorenko (Fri,) studied this question.