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Registration Number

0221U105783, 0121U111617 , R & D reports

Title

Analytical methods and machine learning in control theory and decision-making in conditions of conflict and uncertainty

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Head

Norkin Volodymyr I., д.ф.-м.н.

Registration Date

30-08-2021

Organization

V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine

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Object of research: Problems of optimization of nonsmooth nonconvex and discontinuous functions under constraints, Markov fields with local interaction, conflict-controlled dynamic processes. Purpose: 1. To study the structure of critical points of smoothed functions and rate of convergence of the smoothing method. 2. To investigate asymptotic properties of the empirical means method for inhomogeneous discrete spatial models. 3. To investigate the group persecution problems on the basis of the solving functions apparatus. Results and novelty: 1. The a.s. convergence conditions of the sequential smoothing method on the class of Lipschitz functions are established. The convergence rate of this method in the case of nonsmooth convex functions under convex constraints is investigated. A method for recognizing objects as sets in a metric space using Hausdorff and Gromov-Hausdorff metrics has been developed. The finite convergence theorem of the learning for classification on the nearest neighbor principle for non-intersected compact classes in a metric space is proved. 2. Methods for estimating rate of convergence of the empirical means method for discrete stochastic optimization models with dependent nonstationary observations have been developed. The estimation methods are based on the theory of large deviations for stochastic systems for which the conditions of weak dependence are fulfilled. The exponential convergence rate of the proposed method for models of nonlinear and nonparametric regression in the presence of dependent observations is proved. 3. Methods have been developed to optimize the interaction of groups of controled objects in conflict conditions, taking into account the different information awareness of the participants. Different dynamics groups of opposing parties are considered. Based on the interval decomposition principle, problems of group and alternate convergence are investigated. The technique is extended on delayed and descriptor systems.

Product Description

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Bila Halyna
Bogdanov Olexandr V
Guro Dmytro A
Dunaievskyi Maksym S
Knopov Pavlo S
Kozyrev Anton Yu
Kurshakov Myhailo D
Norkin Volodymyr Ivanovych
Samosonok Oleksandr S
Chykriy Arkadiy O.

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2021-08-30