This paper analyzes digital technologies in the modern educational process, offers training and control services, formed with the help of the Learning Management System (LMS), which allows one to organize an active, creative and social training of modern specialists, in accordance with the program of "Digital economy of the Russian Federation". The paper analyzes modern learning technologies and existing services of digital platforms. The capabilities of digital platforms are demonstrated on the basis of LMS Blackboard. Training and control measures are offered which will allow forming and evaluating the specialists' competencies. The authors have developed a model "Business game" that is implemented based on the LMS Blackboard and with the help of software complex "SMARTlabwork". The results of the analysis of parameters of quality of performance of various training and control actions received by means of methods of the intellectual analysis (Data Mining) are presented. Essential signs of control measures and competence indicators are recommended.