One method of attraction to the solvability set in the convergence problem

The research is devoted to the solution of a convergence problem of a non-linear dynamic system to the target compact set in the n-dimensional Euclidean space at a fixed moment of time. A step-by-step method with respect to time is provided to construct an approximate resolving control. One of the main methods used to solve the convergence problem is the method of extreme attraction to the solvability set. The method described in the research differs from the method of extreme attraction by the choice of control for each step in the time, that provides maximal attraction of the dynamical system to the sections of the solvability set. The presented research describes the method of construction of the approximate resolving control and gives the estimates of the divergence of the generated control from the target set.