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Economic Equilibrium with Random Transactions
P. 284–289.
Zhukova A., Pospelov I. G.
This paper presents the advances in modelling the system of agents under the conditions of random transactions between them. We face certain challenges in this project which we would like to highlight in this presentation. The agents in the modelled system are a large number of consumers, a large number of producers and the bank as the intermediary. Consumers take loans from the bank to spend on consumption goods and producers borrow to make investment at random moments of time. The moments of time the agents deal form the Poisson flow. We present the approach to agents' optimal control problems by the Lagrange method instead of dynamic programming. This enables us obtaining the expressions for the optimal feedback control which appear to be linear in state variables. The solution to the optimal control problems are obtained using asymptotic methods assuming large frequency of transactions. Using the linearity of the agents' optimal control, we may aggregate description of agents, stock-flow consistent on the average. Instead of an ensemble of independent random transactions by agents, the description of the aggregate dynamics is deterministic. The system of equations for the aggregate dynamics is reduced to one equation. There are two cases of this equation, depending on the description of the bank. The equation has a specific form, its numerical analysis is challenging. We provide numerical results and discuss further directions of research. © 2020 IEEE.
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
Ronzhina M., Manita L., , in: Systems Analysis: Modeling and Control: Materials of the International Conference in memory of Academician A.V. Kryazhimskiy, Moscow, January 23–24, 2024. Abstracts.: -, 2024. P. 25–26.
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. ...
Added: October 8, 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
Ilia Nikitin, Belan S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 109 No. 5 Article 054117
Optimization of the mean completion time of random processes by restart is a subject of active theoretical research in statistical physics and has long found practical application in computer science. Meanwhile, one of the key issues remains largely unsolved: how to construct a restart strategy for a process whose detailed statistics are unknown to ensure ...
Added: November 4, 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
Springer, 2022.
Presents the latest research in the field of reliability engineering applications. Signposts areas for useful future research. A Useful reference to engineers, researchers and advanced students in reliability engineering ...
Added: December 16, 2022
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
Dutta S., Applied Soft Computing Journal 2018 Vol. 62 P. 867 –891
This paper is concerned with portfolio selection problem using a fuzzy stochastic price scenario. In this scenario, a ratio factor (k) is calculated from the historical data to generated the future price of the stocks of Bombay Stock Exchange. The ratio factor k of different stocks are treated as a fuzzy numbers, which in turn gives future ...
Added: January 11, 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
Zhukova A., Pospelov I. G., , in: 2020 7th International Conference on Control, Decision and Information Technologies (CoDIT).: IEEE, 2020. P. 1111–1116.
This paper presents the approach to modelling the system of agents making transactions at random time. The two main ideas are, to obtain the agents' optimal control in the form of synthesis (feedback) and, secondly, to make the aggregate dynamics stock-flow consistent on the average, not strictly at any moment of time. We present a ...
Added: June 17, 2021
Zhukova A., Pospelov I. G., , in: Numerical Computations: Theory and Algorithms. Third International Conference, NUMTA 2019, Crotone, Italy, June 15–21, 2019, Revised Selected Papers* 2.: Switzerland: Springer, 2020. P. 255–267.
This work is dedicated to modelling economic dynamics with random time scale. We propose a solution in the form a continuous time model where interactions of agents are random exchanges of finite portions of products and money at random points in time. In this framework, the economic agent determines the volume, but not the moments ...
Added: June 16, 2021
Ronzhina M., Manita L., Journal of Physics: Conference Series 2021 Vol. 1740 P. 1–5
We study singularities of optimal solutions in a problem of controlling the Timoshenko beam vibrations. The Timoshenko beam vibrations are described by a system of two coupled hyperbolic equations. Controls are introduced as external bounded forces. We consider the problem of minimizing the mean square deviation of the Timoshenko beam from the equilibrium position. For ...
Added: April 5, 2021
Afanasiev V., Presnova A., Automation and Remote Control 2021 Vol. 82 No. 2 P. 245–263
We state an optimal control problem for a class of dynamical systems whose nonlinear objects can be represented as objects with linear structure and state-dependent parameters. The linearity of the structure of the transformed nonlinear system and the quadratic performance functional allow one to move from the need to search for solutions of the Hamilton–Jacobi ...
Added: January 27, 2021