Mathematical modeling of controlled development of scientific abilities

The structuring of scientific abilities and the mathematical model of their controlled development are proposed. This model uses the technique of differential equations and methods of optimal control theory and decision making under uncertainty. In the general case, the model is an optimal control problem to develop the abilities of a creative person on the basis of a seven-dimensional vector-valued criterion that reflects the obtained scientific qualification, the level of satisfaction got from the activity, the costs borne by society, etc. As much as 37 variables act as state coordinates that characterize the build-up of individual components of qualification with time and the time that is devoted by a person to the development of his abilities, while 72 variables act as controls; they define the consistency and intensity of the person's activity and the external support of this activity with respect to various elements of creative work in the field of science and technology. The use of the model allowed us to obtain a number of recommendations concerning the optimal control to develop the abilities of talented youths, in particular, an optimal methodological structure of research works that are carried out and a sliding scale for evaluating these works. These recommendations are implemented in the Highest-Quality Training Line at the Samara State Academy of Architecture and Construction (SSAAC) and in the Samara City "Personnel Potential" Target-Oriented Program.