Currently, when modeling complex technological processes in cyber-physical systems, procedures for creating so-called "digital twins" (DT) have become widespread. DT are virtual copies of real objects which reflect their main properties at various stages of the life cycle. The use of digital twins allows real-time monitoring of the current state of the simulated system, and also provides additional opportunities for engineering and deeper customization of its components to improve the quality of products. The development of the "digital twin" technology is facilitated by the ongoing Fourth Industrial Revolution, which is characterized by the massive introduction of cyber-physical systems into production process. These systems are based on the use of the latest technologies for data processing and presentation and have a complex structure of information chain between its components. When creating digital twins of such systems elements, it is advisable to use programming languages, that allow visualization of simulated processes and provide a convenient and developed apparatus for working with complex mathematical dependencies. The Python programming language has similar characteristics. In the article, as an example of a cyber- physical system, a chemical-technological system based on a horizontal-grate machine is considered. This system is designed to implement the process of producing pellets from the apatite-nepheline ore mining wastes. The article describes various aspects of creating a digital twin of its elements that carry out the chemical-technological drying process in relation to a single pellet. The digital twin is implemented using the Python 3.7.5 programming language and provides the visualization of the process in the form of a three-dimensional interactive model. Visualization is done using the VPython library. The description of the digital twin software operation algorithm is given, as well as the type of the information system interface, the input and output information type, the results of modeling the investigated chemical-technological process. It is shown that the developed digital twin can be used in three versions: independently (Digital Twin Prototype), as an instance of a digital twin (Digital Twin Instance), and also as part of a digital twins set (Digital Twin Aggregate).

The article discusses the possibility of applying a precedent approach to improve the efficiency of control of thermophysical and chemical-energy-technological processes of processing ore raw materials. As an example, one of the variants of such processes is considered – heat treatment of pelletized phosphate raw materials. To form the knowledge base of an intelligent system, it is proposed to jointly use a compositional ontological model, which includes two ontologies, each of which is focused on describing one of the subject areas under consideration: thermophysical and chemical-energy-technological processes of heat treatment of pelletized phosphate ore processing plants. The use of this model makes it possible to take into account both the specific properties and characteristics of the processes under consideration, as well as unique tasks and management indicators, avoiding the need to form a generalized holistic ontology that would reflect these subject areas in a simplified form. The use of a compositional ontological model also makes it possible to store information not only in quantitative but also in qualitative form. To form solutions to provide support for the processes of managing the processing of ore raw materials, it is proposed to use a new modified case-based approach, which consists in the possibility of working with the proposed compositional ontological model in determining the closest solution to the current situation, as well as the formation of quantitative values of these decisions based on the information presented in linguistic form. It is possible to take into account the degree of significance of each of the ontologies when developing solutions for each individual current situation that arises when managing the processing of ore raw materials.

The effectiveness of design solutions largely depends on the promptness of processing a large amount of data from various sources, which determines the feasibility of using information decision support systems (IDSS) in the field of project management. The peculiarities of information processes in project management greatly complicate or even make it impossible to implement in practice methods for constructing analytical, as well as probabilistic and statistical dependencies between the characteristics of the modeled project management system and the indicators of its internal and external environment. In this regard, as an algorithmic support for IDSS for project management, it is promising to use precedent methods for analyzing information based on knowledge about similar situations previously observed in the practice of project management, and representing knowledge in the form of ontologies. Analysis of practical situations in the field of project management makes it possible to substantiate the expediency of organizing a monitoring procedure for the IDSS knowledge base, based on the results of which decisions on its adaptation are made. The article proposes the main ways of this adaptation: changing the structure and basic elements (first of all, concepts) of ontologies; clarification of the structure of the description of current situations and, therefore, precedents. The developed algorithm for monitoring the IDSS knowledge base on project management for the analysis and identification of typical situations of the feasibility of changing it is described. The algorithm is distinguished by the possibility of developing recommendations on the modification of ontologies based on a fuzzy classification of search results and using precedents relevant to current situations. A procedure is proposed for changing the structure of the description of precedents, taking into account the results of assessing the indices of the fuzzy correspondence of the characteristics of the existing precedents to the characteristics of the project being implemented. A description of a computer program that implements the proposed algorithm and its components, as well as the results of its application are given.

The relevance of the study is dictated by the introduction of digitalization in all spheres of human life, and timely protection of information and personal data of citizens in the first place. The objective of the study was the need to transform the methods and approaches of information protection during its transmission, creation and storage. Methodological arsenal of the study is presented by scientific methods of cognition of the studied phenomenon content, the structuring of its components and the system of generalization, and analysis of the causal relationship between the visualization functionality and information security of management decisions. The author analyzed the main virtualization technologies for digital business transformation and concluded that there is the need to improve the legal framework in this area. The significance of this article lies in the fact that the use of the virtualization method will increase the level of business security with minimal losses. Current GOST R 56938-2016 "Information protection when using virtualization technologies" does not fully reflect the issues of information protection in terms of its visualization, which leads to the need to improve the legal framework when using virtualization technologies for data protection. It is essential to pay special attention to cloud storage, collaboration and communication services, remote project management programs, cybersecurity solutions, and CRM systems. This is particularly relevant today during the emergence of virtual workplaces and transferring employees to remote work from home.

In recent years, simulation has been actively used to study socio-economic processes in order to test various management decisions (for analyzing risks, projects, regional processes, logistics, etc.). Today, three simulation systems (Actor Pilgrim, AnyLogic, GPSS World), each of which has its own areas of application, are the most widespread in Russia. So, the system Actor Pilgrim is most suitable for modeling socio- economic processes. The first version of this system was developed by a group led by Professor Alexander Anatolyevich Yemelyanov more than 35 years ago to solve experimental problems in the direction of "Flexible automated production". It was based on a new modeling paradigm, which was built on the actor-network theory. The transition to solving new problems, primarily in the economics, led to the need for its further system development through the implementation of temporal, financial and spatial dynamics. Currently, the system development is carried out through the construction of hybrid simulation models, which is associated with the introduction of various analysis methods. So, when modeling actual technical and economic processes (for example, import substitution of high- tech products), it is proposed to use artificial intelligence methods that allow you to get informed decisions in conditions of information uncertainty. Models that include fuzzy logic methods and swarm algorithms (in particular, bacterial optimization) have shown good results. For example, fuzzy logic methods have been used to assign "fair" priorities to option projects through a detailed analysis of the factors of the internal and external environment of enterprises that will implement them. Bacterial optimization algorithms have been used to search for "promising" areas for the implementation of the projects of import substitution of high-tech products. These swarm algorithms are distinguished by the ability to simultaneously study favorable and negative factors, i. e. allow taking into account various risk situations. The modern version of Actor Pilgrim is intended for systems analysts, economists-mathematicians and other professionals who are familiar with programming, but are not professional programmers.