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Estimation of Reachability Sets for Large-Scale Uncertain Systems: from Theory to Computation
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Daryin A., Куржанский А. Б.
In press
The estimation of reachability sets for systems of high dimensions is a challenging issue due to its high computational complexity. For linear systems, an efficient way of calculating such estimates is to find their set-valued approximations provided by ellipsoidal calculus. The present paper deals with various aspects of such approach as applied to systems of high dimensions with unknown but bounded input disturbances. We present an innovative technique based on parallel computation that involves on-line mixing of ellipsoidal tubes found in parallel. This improves robustness of the ellipsoidal estimates. Finally discussed is an implementation of the algorithm intended for supercomputer clusters.
In book
Maui: Institute of Electrical and Electronics Engineers, 2012.
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., 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
Sukhov A., Romanov A., Глушак Е. В., Ученые записки Казанского университета. Серия: Физико-математические науки 2023 Т. 165 № 3 С. 282–293
The article discusses routing methods in two-dimensional circulant graphs (each vertex is connected to four neighboring ones). The unique group of symmetries of the circulant graph makes it possible to use it as a topology for high performance computing devices, including networks-on-chip and cluster supercomputers. It is shown that the minimum number of transitions along ...
Added: January 5, 2024
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
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
Kostenetskiy P., Chulkevich R., Kozyrev V., Journal of Physics: Conference Series 2021 Vol. 1740 Article 012050
The National Research University Higher School of Economics launched its HPC cluster and created a new division named the Supercomputer Simulation Unit. Now the university HPC cluster occupies seventh place in rating the most powerful computers of the CIS TOP50. The HPC cluster uses to solve machine learning problems, population genomics, hydrodynamics, atomistic and continuous ...
Added: February 25, 2021
Afanasiev V., Semion A., Автоматизация. Современные технологии 2020 Т. 74 № 4 С. 170–175
Во многих современных приложениях теории автоматического управления проявляется эффект запаздывания, заключающийся в том, что состояние объекта начинают изменяться только через некоторое время, после изменения входного воздействия. Так, например, при заражении клетки ВИЧ существует инкубационный период, длительность которого необходимо учитывать при лечении [1]. В подобных условиях регуляторы, синтезированные без учета запаздываний, могут оказаться недостаточно эффективными для ...
Added: June 11, 2020
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
Guskova N. V., Наука. Мысль 2016 № 1-2 С. 13–21
В статье рассмотрен вопрос использования синергетического подхода к процессу иноязычной подготовки студентов в ВУЗе. Синергетика характеризуется как новая научная парадигма для образования и лингводидактики, как новая научная идеологии, которая выводится из знания законов эволюции, самоорганизации и самоуправления сложных систем. Существенной характеристикой синергетического подхода к образованию является формирование учащимися своих собственных знаний, развитие своих новых возможностей, ...
Added: January 31, 2017
Saakian D., Yakushkina T., Hu C., Scientific Reports 2016 Vol. 6
We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase ...
Added: September 16, 2016
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
Аладышев О. С., Дикарев Н. И., Овсянников А. П. et al., Известия высших учебных заведений. Электроника 2004 № 1 С. 13–17
Supercomputer: Application Scope and High Performance Requirements
Aladyshev O.S., Dikarev N.I., Ovsyannikov A.P., Telegin P.N., Shabanov B.M.
Supercomputer development trends for the recent years and their power requirements have been analyzed. ...
Added: August 20, 2015
М.: КомКнига, 2006.
В настоящем сборнике публикуются последние достижения в области математического моделирования, управления неоднородными и неопределенными системами, системного анализа, принятия решений, интеллектуальных воспринимающих систем, информатизации общества. Издается на русском и английском языках. ...
Added: April 27, 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