FZZS-2024-0003
WP1 Results. Direct methods for identifying transient functions in modeling nonlinear dynamical systems based on Volterra integro-functional series arising in problems of radiophysics and telecommunications were proposed, the spectral theory of Volterra integro-functional equations of the second kind was constructed, the theory of bifurcation of solutions of integral equations with loads is proposed. The basement for constructing numerical methods for solving them in the linear case is constructed. A method for integrating rheological equations of non-Newtonian micropolar liquids is proposed. The analytical review of methods for recognizing the auroral oval on maps of the total electronic content of the ionosphere is compiled, and an author’s method for recognizing the boundary of the auroral oval in the area of the Northern Sea Route is proposed. A new approach to the study of optimal control problems in the space of non-negative quantities, the dynamics of which is determined by a non-local equilibrium law, is proposed. This approach is based on the transformation of the equilibrium law into an equation of continuity in the probability space. The main result is a version of the generalised Pontryagin maximum principle for the problem under consideration, which covers all known formulations of this type in the theory of midfield control.
As part of the ongoing cooperation with a newly established Sino-Russian Joint Research Center JCAEPS of Harbin Institute of Technology, the following results were obtained. To monitor temperature as a function of inductance and resistance, an approach to estimating the rotor temperature of an asynchronous motor in real time using a dynamic model with parameters has been developed. An online approach based on the theory of Ritta-Wu characteristic sets is proposed to evaluate the parameters of asynchronous generators with dual power for wind farms.
As part of the ongoing collaboration with Central South University (Professor Fang Liu’s group), a DC-DC converter control method and a dynamic model with parameters and singularities have been developed, ensuring high-quality regulation with large fluctuations in load currents through the use of differential gain and second derivative coefficients. The theoretical foundations have been laid for the development of control methods for DC-DC converters based on MPC (model prediction control) and weakly regular systems of Volterra integral equations.
The results are systematized and the monograph “Approximation and regularization methods for operator-functional equations” is presented for publication in the series “Advances in Mathematics for Applied Sciences” by the international publishing house World Scientific (Singapore), 2025.