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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
Spiridonov V. P., Belousov N. M., Sarkissian G. A., Analysis and Mathematical Physics 2026 Vol. 16 Article 96
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...
Added: August 4, 2026
Gayfullin S., Kikteva V., Results in Mathematics 2026 Vol. 81 No. 5 Article 146
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal horospherical varieties, horospherical varieties with an action of a semisimple group, and non-normal toric varieties. ...
Added: August 3, 2026
Lunts V., Функциональный анализ и его приложения 2026 Т. 60 № 3 С. 127–129
Доказано, что канонические полуортогональные разложения производной категории диаграммной схемы индуцируют аналогичные разложения подкатегории совершенных комплексов. ...
Added: August 3, 2026
Belomestny D., Gasnikov A., Gladin E. et al., Russian Mathematical Surveys 2026 Vol. 81 No. 4(490) P. 3–90
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates ...
Added: August 3, 2026
A. Radomskii, Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...
Added: July 31, 2026
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560
Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...
Added: July 29, 2026
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.
As part of a demonstration ...
Added: July 28, 2026
Metlov K., Andrei B. Bogatyrëv, Annalen der Physik 2026 Vol. 538 No. 6 Article e70234
Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing
interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications.
Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and
reason about. Here we build analytical representation for such ...
Added: July 28, 2026
Menovshchikov A., Ukhlov A., Rendiconti del Circolo Matematico di Palermo 2026 Vol. 75 Article 91
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These embeddings give the solvability of the Neumann spectral problem in this setting and provide estimates for the corresponding weighted Neumann eigenvalues. ...
Added: July 27, 2026
Menovshchikov A., Journal of Mathematical Sciences 2026 Vol. 298 P. 608–618
We study the set of (p, q)-eigenvalues of the p-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains. ...
Added: July 27, 2026
Edward R. Rzaev, Aleksandr Y. Romanov, Andrey M. Sukhov, IEEE Access 2026 Vol. 14 P. 2169–3536
This work presents a hierarchy of strictly local fault-tolerant routing algorithms for 3D mesh networks-on-chip, culminating in an algorithm that combines a live-neighbor selection rule with a bounded single-hop rollback mechanism. The proposed algorithms operate exclusively on immediate neighbor information, maintain O(1) per hop complexity, and require no global topology knowledge, additional virtual channels, or ...
Added: July 23, 2026
Balakin S., Лунёв Д. О., Стеняева Д. А., Космическая техника и технологии 2026 Т. 1(52) № 1 С. 88–98
The paper discusses the experience of developing and using several generations of level
measuring systems, including those used for refueling launch vehicles and upper stages produced
by RSC Energia being the leading organization in development of level measuring systems
for dielectric propellant components. The first generation of level measuring systems based on digital
extreme measurement bridges with close inductive ...
Added: July 20, 2026
Singapore: Springer, 2024.
Included in the following conference series:
INdAM: INdAM Meeting: Kolmogorov Operators and their Applications Workshop
Conference proceedings info: INdAM 2022
Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields.
This volume collects a selection of the talks given at the Cortona meeting by ...
Added: July 17, 2026
Veretennikov A., Pascucci A., Rondelli A., Stochastic Processes and their Applications 2026 Vol. 199 Article 104978
We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural conditions, we also establish results concerning both weak and strong well-posedness. ...
Added: July 17, 2026
Veretennikov A., Ляппиева А. А., Теория вероятностей и ее применения 2026 Т. 71 № 2 С. 295–304
Установлен новый результат о сильной единственности для многомерного СДУ с невырожденной диффузией и частично нерегулярным сносом. Его можно рассматривать как комбинированный вариант на темы Ямада и Ватанабэ (1971), Звонкина (1974) и первого автора настоящей статьи (1980). ...
Added: July 17, 2026
Veretennikov A., Нуриева А. И., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 525 С. 24–30
Предложено новое достаточное условие в задаче о центральной предельной теореме в схеме серий для неоднородных цепей Маркова, с возможностью того, что минимум эргодического коэффициента Маркова–Добрушина может быть ближе к нулю, чем в основном условии Добрушина. ...
Added: July 17, 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