ИСТИНА

An optimal control problem on a fixed time segment is considered. For each control selected from a set of controls, there is a unique phase trajectory defined on thе segment. Three points are selected on this time segment: two end points and one intermediate point. The left end of the segment is fixed. The intermediate point and the right-hand end are associated with linear programming problems. Each of these problems is formulated in a finite-dimensional space, the dimension of which is determined by the dimension of the phase trajectory. In the formulation of the problem, it is required to draw a phase trajectory by choosing a control, so that the trajectory, starting from the fixed left end, passes through the intermediate one and reaches the right end point of the time interval. It is required that the values of the trajectory at these points coincide with the optimal solutions of the intermediate and boundary value problems of linear programming. To solve the problem, a mathematically evidential and substantiated iterative computational process is proposed. The convergence of the method is proved in all components of problem solution. We emphasize that only evidence-based computing technologies transform mathematical models into tools for making guaranteed decisions.