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Алгоритм коррекции навигационного комплекса на основе дифференциального игрового подхода
Авиакосмическое приборостроение. 2025. № 9. С. 37–45.
The problem of a zero-sum differential stabilization game with a quadratic performance functional is considered. The navigation system of an aircraft, including a platform inertial navigation system with structural correction using a control algorithm, is investigated. Errors of the navigation system, subject to the influence of uncontrolled disturbances, are described by a nonlinear ordinary differential equation. It is known that the synthesis of optimal feedback controls leads to the need to solve the scalar Bellman-Isaacs partial differential equation at the pace of system operation. To solve this equation, a method for equivalent transformation of the original nonlinear equation of the plant into a model with a linear structure, but with state-dependent parameters is proposed. This allows one to rewrite the Bellman equation as a Riccati equation with state-dependent parameters. An algorithm for solving this equation is proposed. The performance of the developed algorithm was tested using a flight experiment.
Keywords: уравнение Риккати с параметрами, зависящими от состоянияdifferential gamesбортовой навигационный комплексуравнение Беллмана-Айзексарасширенная линеаризацияextended linearization methodRiccati equation with state-dependent parametersBellman equationsДифференциальные игрыonboard navigation system
Flamarion M. V., Pelinovsky E., Wave Motion 2027 Vol. 148 Article 103867
We consider the interaction of two solitary waves in the modified Benjamin–Bona–Mahony
(mBBM) equation in a regime where a small parameter measures the departure from the classical
modified Korteweg–de Vries (mKdV) equation. A regular perturbation method is used to
analyze the modification of the two-soliton wave field induced by the weak non-integrability of
the mBBM equation. We show that, ...
Added: October 23, 2026
Бецофен С. Я., Осинцев О. Е., Кабанова Ю. А. et al., Вестник Московского авиационного института 2016 Т. 23 № 4 С. 181–188
Методами рентгеноструктурного анализа и механических испытаний на растяжение исследованы особенности формирования анизотропии механических свойств, текстуры и фазового состава тонколистовых сплавов Al–4,3Cu–1,4Li–0,4Mg и Al–1,8Li–1,8Cu–0,9Mg. Установлен различный тип анизотропии прочностных свойств сплавов: нормальный (прочность в долевом направлении выше, чем в поперечном) для сплава Al–4,3Cu–1,4Li–0,4Mg и обратный для сплава Al–1,8Li–1,8Cu–0,9Mg. Показано, что на анизотропию прочностных свойств влияет не ...
Added: October 21, 2026
Lev Pyatko, Sergey Aksenov, Regular and Chaotic Dynamics 2026 Vol. 31 No. 5 P. 794–813
In the circular restricted three-body problem, families of periodic and quasi-periodic orbits exist in the vicinity of the libration points and are of significant interest for practical applications. This work presents a neural network-based algorithm for orbit construction and station-keeping, applicable to both periodic and quasi-periodic orbits near collinear libration points. The method employs a ...
Added: October 19, 2026
Vorontsova T., М.: Академия, 2025.
The textbook has been prepared in accordance with the requirements of the federal state educational standards for secondary vocational education and is intended for studying the professional modules “Information Security in Information and Telecommunication Systems and Networks Using Software and Hardware‑Software Tools, Including Cryptographic Protection Tools” and “Information Security in Automated Systems Using Software and ...
Added: October 19, 2026
Naumov A., Рубцов А. С., Samsonov S. et al., Успехи математических наук 2026 Т. 81 № 4 (490) С. 161–162
Краткое сообщение рассматривает Моментные оценки для стохастической аппроксимации ...
Added: October 17, 2026
Roman Avdeev, Yulia Zaitseva, Mediterranean Journal of Mathematics 2026 Vol. 23 No. 7 Article 224
We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...
Added: October 17, 2026
Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51
An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...
Added: October 16, 2026
Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309
We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...
Added: October 16, 2026
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592
Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...
Added: October 14, 2026
Gusein-Zade S., Campillo A., Delgado F., Mathematische Zeitschrift 2026 Vol. 314 No. 1 P. 1–22
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coefficients in $\K$. We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a (discrete, rank one) valuation on it. ...
Added: October 13, 2026
Mishuris G., Meylan M. H., Pelinovsky E., Journal of Fluid Mechanics 2026 Vol. 1045 Article A4
In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of ...
Added: October 12, 2026
Gusein-Zade S., М.: МЦНМО, 2026.
Книга содержит курс лекций по дифференциальной геометрии и топологии, читавшихся автором на механико-математическом факультете МГУ в разные годы. В дополнениях приводятся некоторые сюжеты (связности в расслоениях, теорема Фробениуса, производные Ли и др.), которые были включены в курс в отдельные годы либо содержались в аналогичных курсах лекций в Независимом московском университете.
Для студентов математических и физических специальностей. ...
Added: October 12, 2026
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
М.: Юрайт, 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
Khalifeh K., Afanasiev V., Мехатроника, автоматизация, управление 2026 № 8 С. 1–18
Theoretically, this work belongs to a fairly broad class of articles and books devoted to solving
control problems for dynamic objects with constraints on control actions and the Bolza functional.
The necessary conditions for the existence of optimal controls for a terminal differential game are
described by a two-point boundary value problem and the condition for choosing the ...
Added: May 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., М.: ЛЕНАНД, 2023.
Valery Nikolaevich Afanasyev
Differential Games in Control Problems of Uncertain Objects
This book examines uncertain control systems whose behavior is described by nonlinear differential inclusions with fuzzy initial conditions. The application of classical methods, based on the assumption that all system characteristics and disturbances are known, is either computationally difficult or impossible. This necessitates the development of ...
Added: September 24, 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
Afanasiev V., Ladjal B., Автоматизация. Современные технологии 2022 Т. 76 № 07 С. 308–314
The implementation of synthesized controls for a nonlinear plant represented by a mathematical model with state dependent parameters encounters the problem of finding solutions to the Riccati equation parameterized by the current
the state of the object. To solve this problem, the article proposes a method of suboptimal controls with quasi-stationary values of parameters, called the ...
Added: June 7, 2023
N. M. Galieva, A. V. Korolev, Ougolnitsky G. A., Dynamic Games and Applications 2023 P. 1–34
The discrete- and continuous-time network models of opinions control and resource allocation in marketing are considered. Three cases of interaction of economic agents are studied: independent behavior, cooperation, and hierarchical control by the resource-owning Principal. The corresponding dynamic games are analytically solved. The agents’ payoffs in these cases are compared. Two concepts, “enough resources” and ...
Added: March 14, 2023
Shnourkoff P. V., Информатика и ее применения 2021 Т. 15 № 4 С. 33–40
The work is devoted to the creation of a stochastic dynamic model of optimal control with discrete time within the framework of a one-sector economic system. The basis is a classical deterministic dynamic model of the economic system in which one universal product is produced. This product is divided into investment and consumer components. System management consists in ...
Added: February 2, 2023