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The article developed a Methodology for the formation and selection of digital transformation programs of an industrial enterprise using machine learning algorithms. The method allows creating a set of valid alternative options for digital transformation programs for the production activity of an industrial enterprise by a set of workarounds for a multilayer graph model. The choice of the optimal program is carried out by assessing the weights of the workarounds of the graph by a set of Key Perfomance Inticators (KPIs). The method is based on the presentation of the structure of an industrial enterprise by weighted oriented graphs which determine the structure of a neural network, and its subsequent training on arrays of source information. Each hidden layer of the graph model determines any component of the production structure of the enterprise, and the neurons in them are the components of this structure. As a basic part of the digital transformation is determined a automated workstation and a cyber-physical system. The PyTorch library for the Python 3.8 programming language is used as the main tool for implementing the method.

Two mathematical models have been built to describe the behavior of an information system with a client-server architecture without and taking into account the ultimate reliability of the monitoring system and the restoration of the failed component of the system under consideration. The behavior of the information system in the presence of failures and the restoration of the performance of components is approximated by a Markov process and is described by a system of differential equations with variable coefficients. The solution of the obtained differential equations by numerical methods on computers allows the research of various characteristics of the reliability of information systems such as “client-server” in a wide range of changes in failure rates and restoration of system components.

The game task of confrontation of the attacked hardware-redundant dynamic system with an attacking enemy operating in conditions of incomplete information about the behavior of the attacked enemy in the process of conflict was posed and solved numerically and analytically. The attacking party aspires to increase the intensity of the failures of the components of the attacked system at the expense of its attack resources, up to its total failure. The attacked party, due to the corresponding strategy of redistribution of reserve blocks of the hardware-redundant dynamic system between the failed main blocks at the appropriate instants of time, strives to maximize the probability of failure-free operation of the attacked system at the end of the confrontation (game) with the attacking enemy. Behavior of the system under attack in the process of conflict is approximated by the Markov process, and the number of operable states is equal to the number of failed functional blocks that do not exceed the number of standby blocks. As a payment function in the game in question, the probability of failure-free operation of the attacked system is used by the time the game ends. The solution of the game is the vector of the system setup moments after the corresponding failures of the functional blocks and the set of reservation vectors corresponding to the instantaneous settings of the system being attacked, which maximizes the probability of system failure during the conflict. The differential game model is reduced to a multi-step matrix model with given probabilities of the states of the attacking enemy. Numerical algorithms for calculating the vector of reservation for the attacked system that maximizes the probability of its trouble-free operation by the end of the game and for solving the game problem in question are presented in a form convenient for implementation on a personal computer.