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The aim of this research is to highlight the issues of building the models of control for automotion of the control process and, in particular, by using the artificial intelligence. The urgency of the problem is due to the passage of the economy from the fifth technological mode to the sixth one [1-5]. This passage is accompanied by the use of very complex automatic control systems, which are not limited only by automation of the executed algorithms. Management automation requires formalization of this process, construction and use of various management models. The latter requires the formalization and use of various management models that reflect various aspects of the management system. For simultaneous application of several fundamentally different models, an algebraic approach to modeling is proposed, which consists in distinguishing the following three components: 1) system of the basic models; 2) systems of standard transformations and standard combinations of models; 3) approximation mechanism intended to an approximate representation of the required model as the result of typical transformations and typical combinations of the basic models. The process plan is considered as the main activity model, we consider the strategy as the mechanism for creating the plan. Two ways of describing a strategy are proposed: a hierarchical model and an algebraic representation of a strategy. The study is a theoretical one. The methodological basis is the system analysis (A.A. Bogdanov) and the theory of modeling by Yu.B. Melnikov, in particular, the theory of adequacy, the theory of strategies, etc. Keywords: management model, algebraic approach to modeling, strategy of activity, purpose of activity

Education system is viewed as an important constituent of sustainable development of a society. The spread of information technology reduces the need for mastering the computing apparatus of mathematics. On the other hand, firstly, the role of mathematics is not limited at least to its computing apparatus, the other components of the mathematical apparatus (for example, conceptual, methodological, etc.) and other aspects of mathematics (historical, activity, education of “intellectual honesty”, the formation of specific types of thinking, for example, geometric, ampect, linked with modelling, etc.) are also significant issues; secondly, the use of a computing apparatus is actually the final stage of other types of mathematical and “near-mathematical” activities. The article identifies three factors that ensure the relevance of mathematical education for the sustainable development: 1) the system of teaching mathematics should form the ability to use the mathematical apparatus for solving problems of business, management, engineering, social development, etc. (five components of this factor are highlighted); 2) focus on working with educational material at the level of typical strategies and methodology, not limited to typical algorithms; 3) presentation of mathematics as a multidimensional cultural phenomenon, in which scientific, technical, aesthetic, historical and economic as well as historical and social aspects are distinguished (this in many cases requires the processing of the teaching methods constituents, in particular, curricula alongside with the educational and methodological support).

Large-scale changes associated with the digitalization of all industries require from the student to have both knowledge proficiency in the subject field and the formation of critical thinking, the ability to apply and update their knowledge, and the ability to apply knowledge to solve professional problems. Of particular importance in the learning process is the formation of a student’s system of goals, mastery of basic activity strategies. This requires flexible control mechanisms and monitoring to obtain a large amount of information about the current level of potential development of the student. The analysis shows the relevance of developing systems for supporting the adoption of pedagogical decisions in the context of mass education, based on a multi-aspect assessment of the results. The paper describes the author’s theory of adequacy based on the fact that the quality indicator of a model can be obtained by comparing the estimated model with a model accepted as a reference model. The mathematical basis is a clear definition of strategies, their analysis and improvement based on the algebraic approach, the application of which is reflected in the formation of three components: a system of basic elements; systems of standard transformations and standard combinations of elements; an approximation mechanism designed to represent the strategy as the result of applying standard transformations and typical combinations of basic elements. It is substantiated that the results for automated (automatic) decision-making can be obtained on the basis of continuous control and evaluation activities organized according to the developed methodology. The content of the decision-making system is described on the example of a mathematics course.