The controllability problem for conflict-controlled processes

The problem of bringing a trajectory of a quasilinear conflict control process to a given set from arbitrary initial positions is studied. Although in the conflict-free variant the controllability problem of a dynamical system is among the central ones, little is known about the analogous problem in a game situation. In this note the authors, use the method of solving functions to obtain sufficient conditions on the parameters of the process which ensure the solvability of the problem. The results are illustrated by model examples.