Yasinsky V.V.

On the Approximate Solution of One Infinite-Dimensional Problem of Optimal Stabilization with Nonautonomous Perturbations in the Coefficients

This paper considers the optimal stabilization problem for solutions of parabolic inclusion in which nonautonomous perturbations act on the differential operator coefficients and multivalue interaction function. Such objects naturally occur in applied problems where medium characteristics change over time, and the interaction functions are discontinuous on a phase variable. Under general conditions on nonautonomous coefficients the solvability of the initial problem was proved.

Approximate Regulator for Evolutionary Inclusions subdifferential type

The article considers the problem of optimal stabilization for an evolution inclusion of subdifferential type with non-Lipschitz multi-valued interaction function of where – small parameter.

The Issue of Forecasting and Control of the Knowledge Evolution in Complex Training Systems

Relying on studies of systematic approach, we investigate the issue of forecasting and control for the model describing the knowledge evolution in complex training systems. We obtain the substantial mathematical results for the proposed nonlinear evolution equation. These results depend on conditions of parameters of a non-smooth function of the reaction system that ensures saving a fixed level of knowledge, the terms of the dissipation at this level, the existence of global attractor, and the ability to approximate the optimal control process of the evolution of educational knowledge.