The polyhedral methodology for solving problems of discrete terminal control by dynamic objects under resource constraints conditions is discussed. It is based on formalism of multidimensional optimization and three theoretical constructions like predictive extrapolation of controlled object's movements, the immersion principle of the input optimization problem to a number of more simple computational problems algorithmically, and also the mechanism of extreme guidance. Due to polyhedral formalization, all the considered optimization problems have the polyhedral structure and are reduced to linear programming problems. As an example, the problem of advanced impulse control for stabilization of the lateral hovercraft's movement is considered.