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The article considers an automatic control system that implements the combined control principle with invariance with respect to the action of controlled disturbances. When constructing an invariant system of automatic control, the principle of two-channel Petrova B.N. was used. According to this principle, the mathematical model of corrective communication includes mathematical models of the control object on the channels of action of controlled disturbances and the control channel. The dynamic accuracy of the system of automatic control invariant to controlled perturbations depends on the accuracy of these models in particular their parameters. The simulation results confirm that the dynamic accuracy of the system significantly depends on the value of the transmission factor in the mathematical model of the corrective relationship and this dependence is extreme. The transmission factor of the corrective link model is equal to the ratio of the transfer factor of the control object model through the controlled perturbation channel to the transfer factor of the object model over the control channel. Under conditions of parametric uncertainty and non-stationary properties of the control object, the values of these coefficients at the stage of synthesis of the automatic control system can be obtained only approximately and change significantly during operation. Therefore, it is proposed to determine the optimal value of the correction factor of the corrective connection directly during the operation of the control system in real time using an extreme search algorithm with extreme memory. The article gives an example of the structural scheme of such a system. It provides not only the implementation of directly extreme search algorithm, but also special algorithms for automatically turning on and off the search algorithm. The use of these algorithms allows not to keep the search algorithm constantly on and as a result to reduce the stabilization error. Studies of the system were conducted by simulation in the Simulink environment of the MatLab system. The simulation results confirm the efficiency of the developed system and the efficiency of its operation in the conditions of changing the transmission coefficients in the channels of the control object during its operation. When changing the transfer coefficients in the channels of the control object, the system automatically starts the search algorithm and determines the new optimal value of the transmission ratio of the corrective connection, which reduces the stabilization error in the channel of controlled perturbation. [ABSTRACT FROM AUTHOR]

The article substantiates the expediency of modeling the development of national industry taking into account how the main interconnected key sectors of Ukrainian economy (not only processing and extractive industries, but also agriculture) are developing, as well as taking into account the factors that cause changes in this development over time. Based on previous researches, multiplicative production function has been chosen as the base for building the model, which was modified by taking into account the peculiarities of the Fourth Industrial Revolution and the specifics of individual industries in Ukraine. The economic-mathematical model of long-term development of specified branches of economy of Ukraine in the conditions of digitalization was proposed, in which the value added in the branch is the dependent variable, and the classic components of production functions (labor and the capital) are the independent variables, as well as the new factor - digitalization, and factors, specific to individual industries (world food price index for agriculture and world raw material price index for the extractive industry). A specific feature of the model is also the use of correction factors that reflect the change in the return of factors over time and increase the accuracy of calculations. In addition, separate models have been developed to calculate each of the main factors, based on the dynamics of investments, taking into account the recursive influence of value added, propensity to invest, the condition of the world economy and other specific factors. The calculation of value added in agriculture, extractive and processing industries of Ukraine in 2010-2019 was performed using the model. The adequacy of the model was validated based on the results of its parameterization, which showed sufficient accuracy for the implementation on practice, as the average absolute error of approximation ranges from 2.94% to 4.14% depending on the industry, with abnormal 2014-2015 excluded from the calculations. The value of GDP in the country as a whole was calculated on the basis of the results of value added calculations by key industries. Taking into account the fact that the proposed set of models does not include all industries, a regression model was used to calculate GDP, to which value added for the identified key industries was used as factor. It is established that the proposed model is quite accurate and can be used to calculate the GDP of Ukraine on the basis of value added calculations in agriculture, extractive and processing industries. Given the prospects of practical use of the model for management decisions, the elasticity of the main driving factor (investments) of the development of individual industries was assessed for the main variables, which, in particular, showed that the exchange rate of hryvnia to the US dollar has a negative impact on investments, and the most pronounced - on investments in fixed assets of the processing industry. This questions the widespread idea that the devaluation of the hryvnia stimulates domestic production. [ABSTRACT FROM AUTHOR]

The article analyzes production functions, investigates the features of the Cobb-Douglas function in its multiple variations. On the basis of the analysis carried out, as well as the practical needs of modeling the production systems, the necessity of modeling the production function with the account for the change in the output of production factors over time, is substantiated. As well as with the account for the factor of the modern industrial revolution, characterized by the digitalization of manufacturing. An approach to the development of a function is proposed, which takes into account the change in the output of production factors over time in the context of digitalization. The corresponding production function was modeled based on the example of the manufacturing industry over 2000-2019 in Germany, which is a country that is among the first to introduce modern technologies, including digital ones. The results of modeling the value added using the production function with and without the account for the change in the weight coefficients of the factors over time are presented. It was found that adding the correction factors that define the change in weight coefficients for the factors of the production function over time increased the accuracy of the calculations. Also, a decrease in the resulting (after taking into account the coefficient change over time) exponent coefficient was revealed in the digitalization factor and its increase in the factor of fixed assets involved in the production process (the cost of machinery and equipment) - the output on fixed assets increases annually, and the output of the digitalization factor decreases by about the same extent. It was found that since the relative output of digitalization decreases over time, if there is a need to achieve growth in output through digitalization, it has to be carried out at a growing pace, that is, investments should increase over time. In addition, the earlier investments are introduced, the greater the effect they will give. When modeling the sectors of the Ukrainian economy, it‟s advisable to use correction coefficients calculated based on the German data, rather than calculate them based on past periods on the basis of Ukrainian data. From the point of view of practical calculations, this is justified not only by the belated repetition of the technological development processes of developed countries by developing ones (that is, Ukrainian enterprises are introducing the same technologies, but with a delay of 5-10 years or more), but also by the greater relevance of German statistics to the needs of modeling. [ABSTRACT FROM AUTHOR]