Abstract
A game-theoretic problem of guidance /1, 2/ is studied for non-linear controlled objects in the case when the control domains of the players depend on the phase coordinates. A procedure for constructing the reference functions of the domains of accessibility by the objects in question is described under specified conditions. The conditions under which the reference functions of the domains of accessibility are differentiable with respect to the initial position are given. The results obtained make it possible to use the rule of extremal aiming /1, 2/ to solve the guidance problem. The condition of regularity of the game /1/ is introduced in the usual manner, and is confirmed by finding a solution to a finite-dimensional extremal problem. It is shown that in the regular case the extremal strategies give the game-theoretic guidance problem a saddle point.
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