The article examines the problem of managing a democratic socio-economic system in the face of a shortage of a vital commodity (such as the COVID-19 vaccine). The citizens' approval of the actions of the authorities to increase the production and supply of this product contributes to political stability. The possibilities of increasing the supply of a vital commodity depend on random factors. In the face of such uncertainty, in the age of artificial intelligence, the management of a socio-economic system can be based on machine learning and adaptation. In this case, it is necessary to take into account the activity of the elements of the system associated with the presence of their own goals, which do not necessarily coincide with the goal of the system as a whole. These elements can influence adaptation and machine learning procedures to achieve their goals. The research is carried out on a three-level model of a democratic socio-economic system. At its top level is a member of society - a citizen who evaluates the politician who is at the middle level of the system. In turn, the politician can influence the increase in the supply of a vital commodity, including both its purchase on the market and production at a local plant belonging to the lower level of the system. Political stability is guaranteed if the citizen regularly approves the actions of the politician to increase the supply of vital goods. But the plant's management knows its own production potential better than the politician. Thus, this leadership can manipulate the volume of its own production in order to gain more support from the politician. A politician may also manipulate the opportunities available to him in order to achieve personal goals. To avoid manipulation of the supply of a vital product under conditions of uncertainty, a socio-economic management mechanism is proposed, including an economic and political mechanism. The economic mechanism includes a procedure for adaptive forecasting of the production of a vital commodity, as well as a procedure for supporting this production. The political mechanism includes a procedure for machine self-learning of a citizen, as well as a procedure for assessing the activity of a politician. Sufficient conditions for the synthesis of the optimal mechanism of socio-economic management are found, in which random opportunities to increase the supply of a vital commodity are fully used, including both purchases on the market and production at a local plant. An example of such a socio-economic mechanism is considered on the example of the supply of the COVID-19 vaccine to England.

The article examines the problem of ensuring the political stability of a democratic social system with a shortage of a vital commodity (like vaccine against COVID-19). In such a system, members of society - citizens assess the authorities. Thus, actions by the authorities to increase the supply of this commodity can contribute to citizens' approval and hence political stability. But this supply is influenced by random factors, the actions of competitors, etc. Therefore, citizens do not have sufficient information about all the possibilities of supplying, and it is difficult for them to make the right decisions. Such citizen unawareness can be exploited by unscrupulous politicians to achieve personal targets. Therefore, it is necessary to organize public control in order to motivate politicians to use all available opportunities in supplying. The goal of the paper is to build such a digital mechanism of public control of the politicians by citizens, which would best assess and stimulate the activities of the authorities to improve the supply of a vital commodity. In the age of artificial intelligence, such digital public control in the face of uncertainty can be based on digital machine learning. In addition, it is necessary to take into account and model the activities of politicians associated with the presence of their own targets that do not coincide with public ones. Such politicians can use the learning of citizens for their own targets. The objective of the article is to build an optimal digital mechanism of public control in a two-level model of a democratic social system – a digital society. At its top level there is the Citizen, who gives an assessment for the Politico located at the lower level. In turn, the Politico can influence the supplying of a vital commodity. Political stability is guaranteed if the Citizen regularly approves of the Politico's actions to increase this supply. But the Politico may not use the opportunities available to him to offer a commodity to achieve a personal target. To avoid this, the Politico’s control mechanism is proposed. It includes the procedure for digital learning of the Citizen, as well as a procedure for assessing the Politico activity. Sufficient conditions have been found for the synthesis of such the Politico’s control mechanism, at which stochastic possibilities of increasing the supply of a vital commodity are used. The example of such the Politico’s control mechanism is considered on the case of supply of the COVID-19 vaccine in England.

The article deals with a problem of a speed control of a DC electric drive of a reverse rolling mill under the conditions of its mechanics parameters drift and influence of disturbances. The analysis of existing methods to solve it is made. As a result, two intelligent methods are chosen: the neural network (proposed by the authors) and the fuzzy logic based tuners of linear controllers, the efficiency of which are to be compared. The neural tuner consists of two neural networks calculating the controller parameters of the electric drive, and a rule base that determines at what moments and speed to train these networks. A general description of the fuzzy tuner is also provided. Experimental studies are made using a model of the electric drive of the rolling mill under the above mentioned conditions. The obtained results show that the neural tuner, contrary to the fuzzy one, keeps the speed overshoot within the required limits and also reduces the time of disturbance rejection by 30%.

A two-loop cascade control system of a DC drive is considered in this research. The task is to keep transients quality in both speed and armature current loops. It is solved by a usage of P- and PI-controller parameters neural tuner, which operates in real time and does not require a plant model. The tuner is trained online during its functioning in order to follow the plant parameters change, but usage of too high values of a learning rate may result in instability of the control system. So, the upper bound of the learning rate value calculation method is proposed. It is based on Lyapunov’s second method application to estimate the system sustainability. It is applied to implement adaptive control of a mathematical model of a two-high rolling mill. Obtained results show that the proposed method is reliable. The tuner allowed to reduce the plant energy consumption by 1–2% comparing to conventional P-controller.

The scope of this research is a problem of correct initialization and further correction of a neural network learning rate. It is one of the main hyperparameters, which helps to increase a convergence rate of a training process. There are known techniques of time-based decay, step decay and exponential decay, in which the learning rate is initialized manually and then corrected downwards proportionally to some value. In contrast, in this paper, it is proposed to focus on an excitation level of a regressor - an output amplitude of a previous network layer. The formulas, which are based on the recursive least squares method, are derived to calculate the learning rate for each network layer, and their convergence is proved. Using them, the initial learning rate can be chosen arbitrarily, and not only can such rate decrease, but also it is able to increase when the value of the regressor has become lower. Experiments are conducted for a task of image recognition using multilayer networks and the MNIST database. For networks of different structures, the proposed method allows reducing the number of training epochs significantly in comparison with the backpropagation method with a constant learning rate.