Matychyn I. Quasilinear Conflict Controlled Processes with Variable Structure

The dissertation is devoted to the conflict controlled processes with variable structure, namely quasilinear differential games with variable structure. In the paper three kinds of quasilinear differential games with variable structure, for which the dimension of phase space can change by switches, are considered and investigated. So the games with discontinuous trajectories and finite number of switches as well as games with participation of several players are studied. For these games on the basis of the Method of Resolving Functions pursuing strategies are designed, which allowed obtaining the sufficient conditions of approach with the terminal set. For the differential games with variable structure with finite number of switches the approach problem is formulated and solved, in which the pursuer is not obliged to make all switches. Theoretical results are supported by model examples demonstrating efficiency of approaches presented in the paper.