OPTIMIZATION OF THE PROCESS OF CONTROLLING THE DYNAMICS OF NONLINEAR SYSTEM AND ITS NUMERICAL IMPLEMENTATION
V.G. Shabanova, T.F. Mamedova, O.E. Kaledin
In this paper, we present the results of the stability study on the part of variables of a numerical solution of the system by the method of asymptotic equivalence. It is realized on the theory of characteristic exponents that follow from the Lyapunov stability method. With the help of mathematical transformations, the systems are simplified, and the ability of their “mutual transformation” on the basis of asymptotic equivalence appears. The properties of the solutions of such equations are known, and the objective function is sufficiently small in the investigated region. However, “smallness” in each specific problem is individual, which affects the form of equivalent equations. In the case of parametric optimization of the criteria, “smallness” acquires the mechanism of inheritance of certain important properties of solutions of comparative and asymptotic equations. As an object of study of the dynamics of nonlinear processes, an economic-mathematical model that reflects the multilevel structure of the agro-industrial complex (APC) was used. The latter consists of an industry producing means of production for all links of the agro-industrial complex, agriculture that produces food and agricultural raw materials. The matrix of initial values for numerical realization was formed on the basis of real statistical data of branch enterprises for a certain period, which is formed from equal time intervals. The result of statistical data processing is a function reflecting the current financial and economic situation of the enterprise. Its parametric analysis gives an opportunity to build a long-term forecast for the future period of the economic activity of the enterprise. At the same time, it is necessary to take into account the external factors of the organization’s financial policy, which enables the head to affect the quantitative and qualitative economic indicators of the enterprise, choosing the most promising development paths.
Keywords: : оptimization of control factors, basic production assets, three-sector model of economic growth, nonlinear dynamic system, process stability, asymptotic equivalence, agro-industrial complex.