ON THE COMPUTATIONAL EFFICIENCY OF THE ALGORITHM OF THE NUMERICAL SOLUTION OF OPTIMAL CONTROL PROBLEMS FOR MODELS OF LEONTIEFF TYPE

Abstract

The paper shows the efficiency of the numerical algorithm for the class of problems that is considered by the example of optimal control, hard control, start control and hard starting control for the Leontieff type models. There are presented actual results of computational experiment. As the initial condition is used Showalter - Sidorov condition. This eliminates the restrictions caused by the need to initial checking the data that existed when using Cauchy conditions. The introduction presents various problems of optimal control. Is given their economic interpretation. The first section presents a theorem an existence of a unique solution the problem of optimal control, kind of exact and approximate solutions, the main stages of the algorithm for finding approximate solutions, theorem on the convergence of the approximate solution to the exact one. The second section presents the results of a computational experiment of solving the problem of optimal control. The third section presents the results of a computational experiment of solving the problem of hard control. The fourth section contains the results of numerical experiments solving the problem of start control and the problem of hard starting control. The fifth section presents the results of computational experiments with different parameters of the algorithm as an example a model of Leontieff type. It is shown that the change of parameters leads to small computational error, indicating the computational efficiency.