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Information × Registration Number 0225U002061, (0119U102317) , R & D reports Title Development and research of stochastic models of dynamic systems popup.stage_title Розробка та дослідження стохастичних моделей динамічних систем Head Kononov Yurii M., Доктор фізико-математичних наук Registration Date 18-02-2025 Organization Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine popup.description1 Create and explore new classes of stochastic models of dynamic systems with noise in operating modes and develop methods for analyzing these models to increase their efficiency and reliability of monitoring and control systems for real processes simulated by such systems. popup.description2  Object of Research: Stochastic models of dynamic systems. The aim of this research is to create and investigate new classes of stochastic models of dynamic systems affected by noise in operational modes and to develop methods for analyzing these models in order to improve the efficiency and reliability of monitoring and control systems for real processes modeled by such systems. Research Methods: Methods of analysis of stochastic differential equations and stochastic systems of agents in stochastic network environments. A new algorithm for estimating the parameters of arctangent regression is proposed. This algorithm is used to estimate the parameters of the Cauchy distribution. Necessary and sufficient conditions for the weak convergence of solutions of stochastic differential equations to the solutions of a boundary stochastic differential equation - under more general conditions on the coefficients of the stochastic equations than in other studies - are established. It is proven that uniformly exponentially stable dynamical equations on the semi-axis exhibit equivalent dynamics through C^m-conjugation. This result is derived both for random differential equations and for random dynamical systems with a uniformly exponentially stable linear part, where growth rates are not considered constant. Stochastic methods are applied to model the topological operating environment of an autonomous mobile agent. Based on the methods of simulated annealing, ant colony optimization, and biological evolution, algorithms for constructing markings of environmental regions - uniquely determining the agent's movement path between these regions - are developed and programmatically implemented. The obtained results are comparable to the best foreign analogues and can be used in financial mathematics and robotics. Product Description popup.authors Vasylieva Iryna H. Krykun Ivan H. Sapunov Serhii V. Senchenko Oleksii S. popup.nrat_date 2025-02-18 Close