A Method of Approximate Reachable Set Construction on the Plane for a Bilinear Control System with Uncertainty.

The paper deals with the problem of approximate construction of the reachable set on the plane for a bilinear control system with uncertainty. In the proposed approach of problem solving the uncertainty in the matrix of the system is considered as the control of the second player, that allows to apply solution methods similar to the approaches of the differential games theory. Unlike differential games here the second player acts in conjunction with the first thereby expanding the capabilities of the control system. This approach, with changes in the properties of the components of the system to diametrically opposite ones, fits within the framework of the concept of radical reimplementation. The paper proposes the solution algorithm that is based on operations with polygons and is intended for constructing reachable sets on the plane. On the basis of this algorithm a computer program was developed. This programm was used for a number of numerical experiments. [ABSTRACT FROM AUTHOR]