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Mathematical models and investigations methods for nonlinear systems of different nature
AIP Conference Proceedings. 2022. Vol. 2611. Article 100001.
Киреенков А. А.
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 the Symposium "Mathematical Models and Investigations Methods of Strongly Nonlinear Systems"[1] which was held within the framework of the previous 15th International Conference of Computational Methods in Sciences and Engineering (ICCMSE - 2020) [2].
Keywords: nonlinear systems
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 ...
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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 ...
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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
Azhmyakov V., Martinez J. C., Poznyak A., Optimal Control Applications and Methods 2016 Vol. 37 No. 5 P. 1035–1055
This paper is devoted to general optimal control problems (OCPs) associated with a family of nonlinear continuous-time switched systems in the presence of some specific control constraints. The stepwise (fixed-level type) control restrictions we consider constitute a common class of admissible controls in many real-world engineering systems. Moreover, these control restrictions can also be interpreted ...
Added: October 30, 2021
Presnova A., Автоматизация. Современные технологии 2018 Т. 72 № 12 С. 563–569
The problem of searching for optimal control of nonlinear systems is indicated. Using the algorithmic method proposed in this paper, suboptimal control of a nonlinear object is constructed. The necessary assumptions are made for using the method of extended linearization. The example demonstrates the work of an algorithmic method for synthesizing suboptimal controls, and compares ...
Added: October 2, 2018
Presnova A., Качество. Инновации. Образование 2016 № 5 С. 33–41
Built parametric suboptimal control of supply of drugs using the method of algorithmic design in the problem of stabilization of the cells of the immune system in patients with the HIV. A mathematical model describing the dynamics of HIV in the human body represents a nonlinear system of differential equations. In this paper uses the ...
Added: May 25, 2016
Kapalin V. I., Шаповалова Н. Е., Промышленные АСУ и контроллеры 2012 № 10 С. 14–17
An algorithm for the design of linear regulators for nonlinear control objects is suggested. The algorithm is based on interpolation technique and state-space method. An example of the suggested design method in MATLAB is given ...
Added: November 29, 2015
Afanasiev V., Проблемы управления 2015 № 3 С. 12–19
The problem of optimal control for a class of nonlinear objects with uncontrolled bounded disturbances is formulated in the key differential game. For problems with a quadratic quality functional task of searching for the optimal control reduces the need to find solutions to the scalar partial differential equation Hamilton-Jacobi-Isaacs. Finding solutions to this equation in ...
Added: March 28, 2015
Afanasiev V., М.: Либроком/URSS, 2015.
Сложность большого количества современных систем управления зачастую не позволяет получить заранее полное описание процессов, протекающих внутри системы, и ее взаимодействия со средой. Как правило, реальные системы описываются нелинейными дифференциальными уравнениями и достаточно часто математические модели систем управления учитывают лишь допустимые области изменения параметров и характеристик отдельных элементов без конкретизации самих этих параметров и характеристик. Указанные ...
Added: October 29, 2014
Afanasiev V., В кн.: Проблемы устойчивости и управления: сборник научных статей, посвященный 80-летию академика Владимира Мефодьевича Матросова.: М.: Физматлит, 2013. 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 ...
Added: March 7, 2014
Afanasiev V., Окунькова Е. В., Мехатроника, автоматизация, управление 2013 № 5(146) С. 2–5
The task of designing the control actions for a heavy water reactor under uncertainty changes its parameters considered in the key differential game. The possibility of representing nonlinear dynamics of the object in the form of a system with parameters depending on the state (State Dependent Coefficients) and quadratic functional qualities allow you to go ...
Added: September 21, 2013
Afanasiev V., Orlov P., Известия РАН. Теория и системы управления 2011 Т. 50 № 3 С. 13–22
An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation (diffeomorphism) transforming the original system into a system with a linear main part and a nonlinear feedback. In this case the coordinate transformation significantly changes the form of original quadratic functional. The penalty matrices become dependent ...
Added: April 13, 2012
Afanasiev V., Известия РАН. Теория и системы управления 2011 Т. 9 № 1 С. 24–31
Quite many engineering problems, problems from ecology, medicine, and social sciences are characterized by the presence of factors bringing uncertainty into the corresponding control systems. Additional difficulties for control action construction arise in the case when the objects are described by nonlinear highorder evolutionary equations. An important subset of these objects consists of the object ...
Added: April 13, 2012
Afanasiev V., Автоматика и телемеханика 2011 № 4 С. 43–56
The theoretical fundamentals for solving the linear quadratic problems may be some times used to design the optimal control actions for the nonlinear systems. The method relying on the Riccati equation with state-dependent coefficients is promising and rapidly developing tools for design of the nonlinear controllers. The set of possible suboptimal solutions is generated by ...
Added: April 13, 2012