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Registration Number

0217U004210, 0112U001673 , R & D reports

Title

Development of the mathematic interpretation methods for unknowncomplicated processes using the data of approximate measurements

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Head

Gubarev Vyacheslav, Доктор технічних наук

Registration Date

23-01-2017

Organization

Space Research Institute of National Academy of Sciences of Ukraine and State Space Agency of Ukraine

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The object of study: mathematical models of complex dynamic systems encounterd in high-tech fields. The purpose of the research: development of identification methods of mathematical models of complex dynamic systems and methods for constructing their approximate simplified mathematical models. Research methods: methods of solving inverse problems, identification of dynamical systems under parametric, structural uncertainty, and external disturbances, methods of linear algebra, optimization, stability theory. Results: A class of approximate mathematical models for dynamical systems with lump and distributed parameters was considered. The model complexity is consistent with the level of uncertainty of the measured information on the system where uncertainty is not assumed to possess helpful stochastic properties. A two-step frequency identification method for linear stationary models of dynamic systems has been developed. It was found that by varying the dimension of the model as a discrete regularization parameter of the problem, it is possible to ensure consistency between the existing uncertainty in the data and the accuracy of model parameters estimation. Within the framework of guaranteed approach to treatment of uncertainty it has developed a new method for solving overdetermined systems of linear equations. It has been shown a possibility of application of the method for solving the problem of spacecraft attitude determination, based on inaccurate data of measurement devices. The application of finite element Petrov-Galerkin method with quadratic weighting functions to the integration of the equations of magnetohydrodynamics with two space variables has been considered. Finite-dimensional model of the nonlinear system of ordinary differential equations has been built using the method. The method of selection of stabilizing parameters in the weight functions of the three-dimensional version of the Petrov-Galerkin method has been proposed. Solutions of state estimation problem for the physical processes described by partial differential equations based on the measurements of the processes in local areas has been obtaind.

Product Description

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Волосов Віктор Вікторович
Губарев Вячеслав Федорович
Компанієнко Лілія Григорівна
Максимюк Любов Володимирівна
Мельничук Сергій Вікторович
Сімаков Володимир Олександрович
Сальніков Микола Миколайович
Царук Ніна Петрівна
Шевченко Володимир Миколайович

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2020-04-02