CONSTRUCTION OF DIFFERENTIAL MATHEMATICAL MODELS USED IN THE DEVELOPMENT OF A HYBRID INTELLECTUAL LEARNING ENVIRONMENT, TAKING INTO ACCOUNT DELAY AND CONTROL ACTIONS
The direction associated with the use of mathematical modeling and intelligent technologies in the development of methods and means of supporting educational processes is one of the relevant scientific areas. The issues of construction and analysis of mathematical models used in the development of a hybrid intelligent learning environment (GILE) are considered. When constructing and researching models, factors of delay, control actions are taken into account, and methods and algorithms of intelligent analysis are used, in particular, methods of neural network modeling. As part of the creation of GILE, it is proposed to build differential mathematical models with delayed feedback, as well as differential models with control actions. A continuous dynamic model is considered that describes the process of obtaining and assimilating knowledge, taking into account the use of assimilation coefficients, student motivation, the level of requirements and control actions in the system. A characteristic is given of a generalized model of the educational process, containing a knowledge base module and an interaction module based on artificial intelligence, in relation to the process of studying mathematics in the general education system. For the model of transferring tasks from teacher to student, taking into account the interaction with the GIOS and taking into account the time-delayed feedback, a number of qualitative properties have been studied. The described approach to the analysis of model properties makes it possible to take into account uncertainties and control actions in hybrid learning environments. Algorithms of artificial intelligence and parametric optimization, which imply effective numerical analysis and computational experiments aimed at assessing the process of obtaining the assimilation and control of knowledge in mathematics in the general education system, are characterized.