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Дифференциальные игры в задачах управления неопределенными объектами
M. :
URSS, 2023.
The book deals with controlled systems whose behavior is described by nonlinear differential in-clusions with uncertain initial conditions. The use of classical methods based on the assumption that all the characteristics of the system and perturbations are known is either associated with great computational difficulties or is not possible. There is a need to develop methods that would not require detailed knowledge of the entire state space of the system, its parameters and interaction with the environment. The approach proposed in the book for solving such problems is based on the application of the method of differential games. The development of this method for the syn-thesis of control systems expands the range of problems solved using the Pontryagin method and the dynamic programming method. The material of the book may be of interest both for specialists working in the field of controling various objects with incomplete information, and for undergrad-uate and graduate students of relevant specialties.
Дильмухаметова Алия Мидхатовна, Напалков В. В., Муллабаева А. У., Уфимский математический журнал 2010 Т. 2 № 1 С. 52–58
В данной статье введены обобщённые пространства Фока и рассмотрены основные свойства этих пространств. Найдена операция, сопряженная к операции умножения на переменную в обобщенном пространстве Фока. Также определены собственные функции сопряженного оператора. Изучены обобщенное преобразование Лапласа и задача построения базиса для введенных пространств. ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 855–862
Tasks related to the automation of medical data processing are becoming more urgent. Particular attention is paid to systems for monitoring and analyzing human physiological parameters. Such systems often use specialized sensors to capture biomedical images, such as infrared cameras. This article describes our study of the problem of segmenting the eye pupil and iris ...
Added: September 21, 2026
Aleksei Samarin, Nazarenko A., Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 844–854
Improving image quality is becoming an increasingly popular task, especially when working with mobile devices. One common approach to image enhancement is the use of convolutional neural networks. However, to achieve good results, such networks must be large enough, otherwise there is a risk of unwanted artifacts. In addition, large convolutional neural networks require significant ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Optical Memory and Neural Networks (Information Optics) 2024 Vol. 33 P. 424–434
This study explores the development of classifiers for microbial images, specifically focusing on streptococci captured via microscopy of live samples. Our approach uses AutoML-based techniques and automates the creation and analysis of feature spaces to produce optimal descriptors for classifying these microscopic images. This technique leverages interpretable taxonomic features based on the external geometric attributes ...
Added: September 21, 2026
Aleksei Samarin, Aleksei Toropov, Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1053–1060
This paper presents a novel approach to classification in biomedical imaging, specifically targeting polyp recognition in video endoscopy snapshots. Our method leverages specialized image descriptors to enhance the accuracy and robustness of polyp recognition. By employing these specialized descriptors, we address the challenges inherent in analyzing biomedical images from open datasets. Our approach not only ...
Added: September 21, 2026
Самарин А. В., Торопов А. Г., Савельев А. Г. et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1044–1052
This paper presents a study aimed at improving the detection quality of small-sized microorganisms under challenging microscopic conditions through the application of a lightweight combined image preprocessing model. We focused on the task of detecting diplococci in images obtained through dynamic sample microscopy. The proposed approach employs predefined filters for image preprocessing, combined with the ...
Added: September 21, 2026
Singapore: Springer Singapore, 2025.
Added: September 21, 2026
Aleksei Samarin, Nazarenko A., Kotenko E. et al., / Series arXiv "math". 2025. No. 2511.20141.
This paper presents a novel approach to neural network compression that addresses redundancy at both the filter and architectural levels through a unified framework grounded in information flow analysis. Building on the concept of tensor flow divergence, which quantifies how information is transformed across network layers, we develop a two-stage optimization process. The first stage ...
Added: September 21, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., «Doklady Mathematics» 2009 Т. 424 № 5 С. 591–593
В данной статье вводится определенный класс дифференциальных уравнений с переменными коэффициентами, который тесно связан с операцией умножения Адамара и операторами Данкла имеющими применение в математической физике. Показано, что уравнения этого класса могут быть сведены к уранвениям в обобщенных производных с постоянными коэффициентами. ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2025 Vol. 35 No. 2 P. 169–178
This study explores the incorporation of specialized self-attention mechanisms into deep learning architectures, with a particular emphasis on segmenting human iris and pupil regions in infrared images. In this work, we present some modified versions of nonlocal blocks designed to enhance self-attentive properties while addressing the distinct characteristics of infrared imaging data. By applying these customized ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Journal of Imaging 2025 Vol. 11 No. 10 Article 359
Timely identification and accurate delineation of ultra-early ischemic stroke lesions in non-contrast computed tomography (CT) scans of the human brain are of paramount importance for prompt medical intervention and improved patient outcomes. In this study, we propose a deep learning-driven methodology specifically designed for segmenting ultra-early ischemic regions, with a particular emphasis on both the ...
Added: September 21, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., «Doklady Mathematics» 2012 Т. 443 № 3 С. 293–295
В данной работе введены обобщенные частные производные, изучены дифференциальные уравнения в обобщенных частных производных с постоянными коэффициентами и доказан фундаментальный принцип Эйлера для таких уравнений. Устанавливлена связь с классом уравнений в обычных частных производных с переменными коэффициентами. ...
Added: September 21, 2026
Springer, Cham, 2025.
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Journal of Imaging 2025 Vol. 11 No. 6 P. 1–20
This study presents a unified low-parameter approach to multi-class classification of microorganisms (micrococci, diplococci, streptococci, and bacilli) based on automated machine learning. The method is designed to produce interpretable taxonomic descriptors through analysis of the external geometric characteristics of microorganisms, including cell shape, colony organization, and dynamic behavior in unfixed microscopic scenes. A key advantage ...
Added: September 21, 2026
Medvedev V., Annals of Global Analysis and Geometry 2026 Vol. 70 No. 2 P. 8–23
This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 323–334
In this paper, an improved approach for automatic wildlife detection in natural environments based on the integration of a neural network architecture with a two-stream attention mechanism and a novel preclassification step based on infrared data has been presented. The proposed method addresses one of the key challenges in environmental monitoring: the need for scalable ...
Added: September 19, 2026
Aleksei Samarin, Nazarenko A., Kotenko E. et al., Proceedings of the ACM on Management of Data, USA 2026 Vol. 4 No. 1 P. 1–28
Modern knowledge and large volumes of data are increasingly encoded within neural networks, making the task of simplifying their structures and reducing the number of parameters especially relevant, both to improve efficiency and to facilitate deployment in resource-constrained environments. This paper presents a novel approach to neural network compression that addresses redundancy at both the ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2025 Vol. 35 No. 2 P. 148–158
This paper describes our research on creating classifiers for microbial images (micrococci microscopy images) obtained from pictures of unfixed microscopic scenes. In our work, we propose an AutoML approach based on the automatic generation and analysis of the feature space for constructing the most optimal descriptors of microorganism images for subsequent classification. This makes it ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 302–312
The lack of annotated microscopic datasets remains a major obstacle to training robust deep learning models for microbial classification. In this paper, a novel data augmentation pipeline that uses visual–linguistic large-scale models to generate synthetic microscopic images of six different bacterial and nonbacterial classes has been proposed. Synthetic samples have gradually been added to the ...
Added: September 19, 2026
Afanasiev V., Гаража И. А., Труды Института системного анализа Российской академии наук 2025 Т. 75 № 3 С. 80–91
The problem of a zero-sum differential stabilization game with a quadratic performance functional is considered. The control plant, subject to uncontrollable disturbances, is described by a nonlinear ordinary differential
equation. It is known that the synthesis of optimal feedback controls leads to the need to solve a scalar Bellman-Isaacs partial differential equation at the system's operating speed. An algebraic ...
Added: September 29, 2025
Afanasiev V., Автоматика и телемеханика 2022 № 11 С. 103–120
We consider the problem of a zero-sum differential tracking game with a quadratic
performance functional in which the plant subjected to uncontrolled disturbances is described
by a nonlinear ordinary differential equation. The synthesis of optimal controls is known to
necessitate online solving a scalar Bellman–Isaacs partial differential equation that contains
information about the trajectory of the process to be ...
Added: June 19, 2023
Volkova O. N., Вологина Д. -., Korolev A. V., Математическая теория игр и ее приложения 2022 Т. 14 № 1 С. 21–48
Вводятся стохастические параметры в модели сетевых игр с производством и экстерналиями знаний, которая была сформулирована В. Матвеенко и А. Королевым и обобщает двухпериодную модель Ромера. Агенты различаются продуктивностью, имеющей детерминированную и винеровскую составляющие. Рассматривается динамика, которая возникает при объединении двух полных сетей. Получены явные выражения в форме броуновских случайных процессов. Проведен качественный анализ решения системы ...
Added: May 11, 2022
Korolev A. V., Математическая теория игр и ее приложения 2021 № 1 С. 102–129
In this paper, stochastic parameters are introduced into the network games model with production and knowledges externalities. This model was formulated by V. Matveenko and A. Korolev and generalized two-period Romer model. Agents' productivities have deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle which ...
Added: May 15, 2021
Afanasiev V., Semion A., Проблемы управления 2021 № 1 С. 24–35
A differential game of several players is considered as follows. One player (attacker) penetrates some space, and several other players (pursuers) appear simultaneously to intercept the attacker. Upon detecting the pursuers, the attacker tries to evade them. The dynamics of each player are described by a time-invariant linear system of a general type with scalar ...
Added: April 6, 2021