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Оптимальное управление нелинейным объектом, линеаризуемым обратной связью по состоянию
С. 104–117.
Mathematical models of nonlinear systems of a certain class allow them represented as linear systems with nonlinear state feedback. In other words, let make the appropriate coordinate transformation of the original dynamic model. Such a transformation, using Lyapunov functions, a number of studies used to determine the parameters of regulators to ensure the asymptotic stability properties of the nonlinear system, ie guaranteeing bounded trajectories emanating from the initial states of the system. For linear systems, there is a powerful and convenient mathematical apparatus allows the synthesis of optimal controls, but this unit is not applicable or partially applicable for nonlinear systems. Unlike prior work in this paper for nonlinear systems linearizable feedback as in the synthesis of optimal control problems with quadratic performance applied the method based on the use of the Riccati equation with parameters depending on the state.
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
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
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., 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
Киреенков А. А., AIP Conference Proceedings 2022 Vol. 2611 Article 100001
Main goal of the Symposium: "Mathematical Models and Investigations Methods for Nonlinear Systems of Different Nature"is providing a possibility for the exchange of new ideas and results between research groups in the field of mathematical models and their implementation for the investigation for nonlinear systems of the different nature. This Symposium is logical continuation of ...
Added: May 24, 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
Afanasiev V., М.: Красанд/URSS, 2020.
This book has been prepared on the basis of lectures on control theory given by the author for a number of years to students of the Department of Applied Mathematics of the National Research University Higher School of Economics and the Faculty of Physics Moscow State University named after M. V. Lomonosov. The content of the ...
Added: August 27, 2022
Volkova O. N., Вологина Д. -., Korolev A. V., Математическая теория игр и ее приложения 2022 Т. 14 № 1 С. 21–48
Вводятся стохастические параметры в модели сетевых игр с производством и экстерналиями знаний, которая была сформулирована В. Матвеенко и А. Королевым и обобщает двухпериодную модель Ромера. Агенты различаются продуктивностью, имеющей детерминированную и винеровскую составляющие. Рассматривается динамика, которая возникает при объединении двух полных сетей. Получены явные выражения в форме броуновских случайных процессов. Проведен качественный анализ решения системы ...
Added: May 11, 2022
Korolev A. V., , in: Frontiers of Dynamic Games: Game Theory and Management, St. Petersburg, 2020.: Cham: Birkhäuser, 2021. P. 167–187.
Added: April 5, 2022
Cham: Birkhäuser, 2021.
This book features contributions from the GTM 2020 International Meeting on Game Theory held virtually from St. Petersburg, Russia, including presentations by plenary speakers. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management. ...
Added: April 5, 2022
Botkin N. D., Golubev A., Turova V. L., IFAC-PapersOnLine 2019 Vol. 52 No. 16 P. 706–711
The problem of aircraft take-off under windshear conditions is considered as a differential game. A simplified five-dimensional nonlinear model of aircraft dynamics, assuming the flight in a vertical plane, is used. The overloads, differences between the projections of the thrust and drag, respectively lift, forces are considered as control variables. The corresponding technically relevant control, ...
Added: November 18, 2021
Petrosyan L., Yeung D., Pankratova Y., , in: Mathematical Optimization Theory and Operations Research: Recent Trends: 20th International Conference, MOTOR 2021, Irkutsk, Russia, July 5–10, 2021, Revised Selected Papers.: Cham: Springer, 2021. P. 403–416.
A class of cooperative differential games on networks is considered. It is supposed that players have the possibility to cut connections with neighbors at each time instant of the game. This gives the possibility to compute the values of a characteristic function for each coalition as a joint payoff of players from this coalition without ...
Added: November 1, 2021
Bonilla M., Azhmyakov V., Malable M., IFAC-PapersOnLine 2017 Vol. 50 No. 1 P. 10822–10827
This paper discusses a novel implementable approach to an exact linearization procedure based on the implicit systems techniques. The formal procedure we propose includes a specific “splitting” of the nonlinear state representation in two parts that involve a basic rectangular representation and an auxiliary nonlinear algebraic equation. The proposed linear implicit systems description makes it ...
Added: October 30, 2021
Blas L. A., Bonilla M., Malable M. et al., IFAC-PapersOnLine 2017 Vol. 50 No. 1 P. 922–927
In this paper, a structural feedback linearization technique is proposed. This is a quite simple and effective linear control scheme based on failure detection techniques. Our proposed linear control approach is intended to reject the nonlinearities, which are treated as failure signals affecting the systems dynamics. The proposed control methodology is illustrated via the attitude ...
Added: October 30, 2021