A nonlinear differential evasion game

The evasion problem for nonlinear differential games with a target set which is a linear subspace is considered. A sufficient condition for the possibility of avoidance of contact with all points not belonging to the target set is obtained. Examples are considered. This article borders on the investigations of L. S. Pontryagin, E. F. Mishchenko, and B. N. Pshenichnyi.Translated from Matematicheskie Zametki, Vol. 21, No. 3, pp. 415–425, March, 1977.