Аннотация:A multi-faceted methodology for solving problems of discrete terminal control of dynamic objects under resource constraints is discussed. It is based on the formalism of multi-dimensional optimization and three theoretical constructions, such as predictive extrapolation of controlled object movements, the principle of immersion of the input optimization problem in a number of simpler computational problems algorithmically, and the mechanism of extreme guidance. Due to polyhedral formalization, all considered optimization problems have a polyhedral structure and are reduced to linear programming problems. As an example, the problem of advanced pulse control of stabilization of the lateral movement of a hovercraft is considered.