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SPIRAL-LIKE SOLUTIONS IN OPTIMAL CONTROL PROBLEMS WITH CONTROL IN A DISK
P. 25–26.
Ronzhina M., Manita L.
For some class of small-dimensional optimal control problems we found a family of extremals in the form of logarithmic spirals. These extremals reach the singular surface in a finite time, while the control performs an infinite number of rotations around the circle.
Parfenyev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 No. 1 Article 015104
Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a floating drone or active particle -- that is advected by a two-dimensional flow, self-propels at a fixed speed smaller than or comparable to the characteristic flow velocity, ...
Added: July 17, 2026
Optimal Control for Stochastic Multi-agent Systems With the Use of Parallel Hybrid Genetic Algorithm
Akopov A. S., Beklaryan A., , in: Numerical Computations: Theory and Algorithms. 4th International Conference, NUMTA 2023, Pizzo Calabro, Italy, June 14–20, 2023, Revised Selected Papers, Part IVol. 14476.: Springer Publishing Company, 2025. P. 273–280.
In modern times, stochastic large-scale multi-agent systems (MAS) aimed at supporting socio-economic planning are being developed. There is a well known problem of a high computational complexity task of an optimal control for multiple agents’ behaviour in models of random interactions. In particular, agents (such as sellers and buyers) should make individualised decisions on establishing ...
Added: November 23, 2025
Afanasiev V., Автоматика и телемеханика 2025 № 10 С. 3–20
The optimal control of a system’s final state is a fundamental problem that constitutes the core of many optimization tasks. Such problems involve describing the dynamic object, specifying constraints on controls and states, and defining a quality functional, typically a Bolza functional. The necessary optimality conditions for synthesizing the corresponding controls are written as a canonical Euler–Lagrange system with specified ...
Added: September 24, 2025
Delev A., Semakov S., , in: 2025 8th International Conference on Artificial Intelligence and Big Data (ICAIBD).: IEEE, 2025. P. 318–322.
Profit is one of the most important economic indicators of a company’s performance, and for every company it is necessary to allocate resources in such a way as to obtain the maximum possible profit. The profit maximization problem is usually a dynamic optimization problem. This article discusses an approach to solving the production expansion problem ...
Added: August 25, 2025
Ронжина М. И., Manita L., Дифференциальные уравнения 2024 Т. 60 № 11 С. 1531–1540
We study a neighbourhood of a singular second-order extremal in optimal control problems that are affine in control in a disk. We consider the case in which the Hamiltonian system has dimension 8 and is a small (in the sense of the action of the Fuller group) perturbation of the Hamiltonian system of the generalized ...
Added: February 6, 2025
Ронжина М. И., Manita L., Итоги науки и техники. Современная математика и ее приложения. Тематические обзоры 2024 Т. 233 С. 75–88
We study a neighborhood of singular second-order extremals in optimal control problems that are affine in a two-dimensional control in a disk. We study the stabilization problem for a linear system of second-order differential equations for which the origin is a singular second-order extremal. This problem can be considered as a perturbation of an analog ...
Added: June 27, 2024
-, 2024.
This collection of articles contains materials of the talks presented at the International Conference «Systems Analysis: Modeling and Control» in memory of Academician A.V. Kryazhimskiy, Moscow, January 23–24, 2024. ...
Added: June 24, 2024
Aksiotis V., Voskoboynikov A., Ossadtchi A. et al., , in: 2023 Fifth International Conference Neurotechnologies and Neurointerfaces (CNN) 18-20 Sept. 2023.: IEEE, 2023. P. 4–7.
Decision-making is a complex and prolonged process. In this study, we present an adaptive algorithm designed to explicitly estimate the duration of perceptual decision-making in the Random Dot Motion Task. The algorithm effectively disentangles the duration of the preparation period for the subject's decision on the direction of movement of the dots from the period ...
Added: November 9, 2023
Pleiades Publishing, Ltd. (Плеадес Паблишинг, Лтд), 2023.
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas:
mathematics
mathematical physics
computer science
control theory, and computers
It publishes brief ...
Added: June 9, 2023
T. A. Alexeeva, Kuznetsov N. V., Lobachev M. et al., IFAC-PapersOnLine 2022 Vol. 55 No. 40 P. 157–162
One of the central tasks of macroeconomic analysis is forecasting and control of economic agents’ expectations for key macroeconomic indicators such as inflation, gross domestic product (GDP), prices and others, etc., so that to achieve maximum level of their welfare through monetary and fiscal policy. This problem is solved within the framework of the optimal ...
Added: April 8, 2023
Manita L., Ronzhina M., , in: Дифференциальные уравнения и оптимальное управление: Материалы Международной конференции, посвященной 100-летию со дня рождения академика Евгения Фроловича Мищенко, Москва, 7–9 июня 2022 г.: M.: Steklov Mathematical Institute, 2022. P. 90–92.
we show that in a control problem of a rocket there are spiral like extremals that attain the singular point (on the singular surface of the second order) in finite time, wherein the corresponding controls perform an infinite number of rotations along the circle S1. ...
Added: January 31, 2023
Gubar E., Taynitskiy V., Fedyanin D. et al., Computation 2022 Vol. 10 No. 2 Article 31
In the current study, we define a hierarchical epidemic model that helps to describe the
propagation of a pathogen in a clustered human population. The estimation of a novel coronavirus
spreading worldwide leads to the idea of the hierarchical structure of the epidemic process. Thus,
the propagation process is divided into three possible levels: a city, a country, ...
Added: October 4, 2022
Belomestny Denis, Iosipoi L., Paris Q. et al., Bernoulli: a journal of mathematical statistics and probability 2022 Vol. 28 No. 2 P. 1382–1407
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some restrictions imposed on the functional class fast convergence rates can be achieved including the optimal non-parametric rates for expressive classes in the ...
Added: April 17, 2022
Alexeeva T., Kuznetsov N., Mokaev T. et al., IFAC-PapersOnLine 2021 Vol. 54 No. 17 P. 26–31
Irregular fluctuations in economy lead to unpredictable effects and disrupt its stable functioning. Various tools could be used to stabilize irregular dynamics in economic models. For example, to introduce control into the model as an external function, as well as to take into account the internal characteristics of economic agents in the economy under consideration, ...
Added: February 5, 2022
Vadim Azhmyakov, Oxford: Elsevier, 2019.
A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems proposes a unified approach to effective and numerically tractable relaxation schemes for optimal control problems of hybrid and switched systems. The book gives an overview of the existing (conventional and newly developed) relaxation techniques associated with the conventional systems described by ordinary differential equations. ...
Added: October 30, 2021
Azhmyakov V., Verriest E. I., Guzman Trujillo L. A. et al., IFAC-PapersOnLine 2018 Vol. 51 No. 25 P. 18–23
Our contribution deals with a class of Optimal Control Problems (OCPs) of dynamic systems with randomly varying time delays. We study the minimax-type OCPs associated with a family of delayed differential equations. The presented minimax dynamic optimization has a natural interpretation as a robustness (in optimization) with respect to the possible delays in control system ...
Added: October 30, 2021
Foroozandeh Z., Shamsi M., Azhmyakov V. et al., Mathematical Methods in the Applied Sciences 2017 Vol. 40 No. 5 P. 1783–1793
This paper presents a direct method based on Legendre–Radau pseudospectral method for efficient and accurate solution of a class of singular optimal control problems. In this scheme, based on a priori knowledge of control, the problem is transformed to a multidomain formulation, in which the switching points appear as unknown parameters. Then, by utilizing Legendre-Radau ...
Added: October 30, 2021
Azhmyakov V., Trujillo L. A., Italian Journal of Pure and Applied Mathematics 2017 Vol. 2017 No. 37 P. 219–237
This paper deals with a constrained LQ-type optimal control problem (OCP) in the presence of fixed levels input restrictions. We consider control processes governed by linear differential equations with a priori known control switching structure. The set of admissible inputs reflects some important natural engineering applications and moreover, can also be interpreted as a result ...
Added: October 30, 2021