Registration Number
0217U006666,
0116U002529
, R & D reports
Title
Development of new mathematical methods of system analysis and optimal solutions theory and ther applications
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Head
Nakonechnyi Oleksandr Grygorovych,
Registration Date
11-12-2017
Organization
Taras Shevchenko Kiev University
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The object of research: systems of equations of different types, stochastic equations, boundary problems, transport problems, uncertainty, mass service systems, random processes, balleans. New problems of parameters identification for special dynamic systems under uncertainty conditions are investigated. New results on the problems of guaranteed evaluation for Helmholtz equations are obtained. The problem of optimal control in the form of a reverse communication for a parabolic equation and with the energy criterion of quality is solved. The algorithm for estimating of unknown parameters based on matrix multiple regression is implemented. The descriptive complexity of subsets of groups is investigated. The application of convex programming method for solving a generalized Silvester operator equation in Hilbert spaces is proposed. New methods of transport problems solution with fuzzy parameters are offered. The problem of optimal behavior in two-stage games with randomness is investigated. The conditions, which guarantee a weak convergence of finite-dimensional distributions of normalized and centered random processes with immigration, are invented. The conditions of existence of the stationary regime for the model maintenance process are found, the approximate process and related functionals are constructed; they allow us to calculate the main parameters of the maintenance process for solving optimization problems. For the control problem, constructed for the transfer process, the normalized process is invented and the asymptotic normality in the form of Orshtein-Ulenbeck process is established. The methods and algorithms of statistical simulation of the generalized Wiener process are developed.5481
Product Description
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Іксанов О.М.
Григор'єва Н.М.
Доценко С.І.
Зінько Т.П.
Капустян О.А.
Коробко Т.В.
Лебєдєв Є.О.
Лосєва М.В.
Лукович О.В.
Мащенко С.О.
Нікітін А.В.
Назарага І.М.
Пашко А.О.
Подлипенко Ю.К.
Пономарьов В.Д.
Протасов І.В.
Протасова К.Д.
Самойленко І.В.
Усар І.Я.
Шестаков С.С.
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2020-04-02
