Analysis of mathematical works of A.G. Kostyuchenko.
Necessary and sufficient conditions for controlled system final phase state guaranteed estimation is determined based on properties of attainability sets for problem solution of prediction possible system phase state on fixed points of time. Required sets of attainability approximation conditions by convex polyhedrons are obtained. System final phase state vector belongs to required set estimation is mathematically grounded. This provides acceptability verification of attainability problems obtained solutions taking into account principles of political, strategical and economical expediency.