Methods of Optimal Control in the Model of Economic Growth

摘要

A model of the growing economy of a certain country is described. The influence of two factors is investigated: the development of scientific and technical progress; consumption of non-renewable energy. The considered dynamic nonlinear model is based on the use of production functions. It is assumed that the country's economy includes three sectors: the knowledge sector (technological), the production sector; sector of extraction of one non-renewable energy resource. The optimal control problem is formulated, which consists in maximizing the functional of the total discounted consumption in the considered time period. It is proved that in the model under consideration two qualitatively different control modes are possible: control leading to the boundedness of the functional under consideration; management, giving the possibility of its infinite growth. The latter mode is possible with a certain ratio of the parameters of the production function describing the economy. In these terms, the bifurcation condition is formulated. In addition to the parameters of the production function used in the economy model, it includes the ratio between the initial values of capital productivity and the ratio of capital in the knowledge sector to capital in the manufacturing sector.