Oscillatory conflict-control processes

Abstract

Some quasi-linear dynamical processes functioning under conditions of conflict [1, 3–8] are considered, on the assumption that Pontryagin's condition [1] holds only in certain intervals of the real half-line (this may occur, in particular, when a homogeneous system is performing periodic oscillations [2]). The method of resolvent functions [3, 4] is used to establish sufficient conditions for the group pursuit problem [3, 4] to be solvable. A typical special case is examined and the group pursuit problem is solved for a second-order system [6]. The results have a bearing on the research reported in [3–5].