Controllability by Initial Data in a Variable Structure Problem for the Particles Tracing Problem

In this paper, a new approach to studying problems with variable structure is considered. Omitting the optimization issue, the controllability problem is posed. A new approach is considered that combines the ideas of convex analysis of a linear problem for a nonlinear case. This allows us to proceed to the study of support functions for solving the problem. The Correction and Aiming Theorems describing a problem with a variable structure with one switching are presented and proven, and examples of their application are considered.