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Information × Registration Number 0222U003159, 0119U100338 , R & D reports Title Development of new mathematical methods for analysis and optimization of systems under uncertainty. popup.stage_title Head Nakonechnyi Oleksandr H, Доктор фізико-математичних наук Registration Date 19-02-2022 Organization Taras Shevchenko National University of Kyiv popup.description2 Object of research: systems described by boundary value problems for ordinary differential equations and equations in partial derivatives under uncertainty, evolutionary systems with rapidly oscillating coefficients, stochastic systems of different structure, asymptotic varieties. Purpose: development of new mathematical methods of analysis and optimization of systems in conditions of uncertainty. Research methods: modern methods of decision theory in conditions of uncertainty, new methods of system analysis and optimization of stochastic and deterministic systems, modern methods of group theory. New estimation methods have been developed, which allow for the first time to obtain representations for guaranteed a posteriori and a priori estimates of the states of systems described by impulse ordinary differential equations and equations of mathematical physics. Based on the theory of averaging, new methods for constructing optimal regulators for parabolic and hyperbolic equations with rapidly oscillating coefficients have been developed. For matrix regression problems under uncertainty, constructive algorithms for estimating unknown matrices have been obtained and found in practice. In the conditions of nonclassical Poisson and Levy approximation schemes, limit generators of impulse processes of perturbations and a dynamic control system with control for which there is a single equilibrium point are constructed. For such control the normalized process is built and its asymptotic normality is established. On the basis of the developed asymptotic approach the analysis of models of network structure for the decision of questions of cost, reliability, speed of functioning, structure and working loading of real networks is carried out. Algorithms of optimal resource management of modern telecommunication networks are built on the basis of fundamental theoretical results.  Product Description popup.authors Zinko Taras P. Kapustyan Olena A. Korobko Tetyana V. Kudin Hryhoriy І. Livinska Hanna V. Losyeva Mariya V. Nazaraga Inna M. Naumenko Yurii O. Pashko Anatolii O. Podlypenko Yurij K. Protasov Igor V. Protasova Kseniia D. Chikrii Arkadii O Shatyrko Andrii V. Shevchuk Yuliia M. popup.nrat_date 2022-03-09 Close