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Suboptimal Control of Nonlinear Object:Problem of Keeping Tabs on Reference Trajectory
P. 1505–1509.
An optimal control problem is formulated for a class of nonlinear systems which can be presented by system with linear structure and state-depended coefficients (SDC). The system being under the influence of uncontrollable disturbance is supposed. The linearity of the transformed system structure and the quadratic functional make it possible to pass over from the Hamilton–Jacoby–Bellman equation (HJB) to the state dependent Riccati equation (SDRE) upon the control synthesis. In thus paper the optimal control problem by nonlinear system in a task of Keeping Tabs on Reference Trajectory we decide in a key of differential game. The presented example illustrates the application of the proposed control method.
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
Chertopolokhov V., Mukhamedov A., Bugriy G. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...
Added: May 22, 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
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., Куприянов А. О., Неусыпин К. А., 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 ...
Added: November 1, 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
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 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
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
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
-, 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
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., М.: Издательская группа 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 ...
Added: June 19, 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