mireabulletinRussian Technological JournalRussian Technological Journal2782-32102500-316XRTU MIREA10.32362/2500-316X-2023-11-5-94-10mireabulletin-767Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕMATHEMATICAL MODELINGОб адаптивной идентификации систем с несколькими нелинейностямиOn adaptive identification of systems having multiple nonlinearitieshttps://orcid.org/0000-0002-3706-7431КарабутовН. Н.KarabutovN. N.

Карабутов Николай Николаевич, д.т.н., профессор, кафедра проблем управления Института искусственного интеллекта; Лауреат Государственной премии в области науки и техники

119454, Москва, пр-т Вернадского, д. 78

Scopus Author ID 6603372930

ResearcherID P-5683-2015

Nikolay N. Karabutov, Dr. Sci. (Eng.), Professor, Department of Problems Control, Institute of Artificial Intelligence; Laureate of the Russian Federation State Prize in Science and Technology

78, Vernadskogo pr., Moscow, 119454

Scopus Author ID 6603372930

ResearcherID P-5683-2015

 

karabutov@mirea.ruМИРЭА – Российский технологический университетРоссияMIREA – Russian Technological UniversityRussian Federation20230610202311594105Copyright © Карабутов Н.Н., 20232023Карабутов Н.Н.Karabutov N.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.rtj-mirea.ru/jour/article/view/767Цели

Цели. Задача идентификации систем с несколькими нелинейностями является актуальной. Решение этой задачи зависит от наличия обратных связей, способов соединения нелинейных звеньев, свойств сигналов. Специфика нелинейных систем накладывает отпечаток на методы синтеза систем управления. В условиях полной априорной определенности обычно применяют линеаризацию систем. Если существует априорная неопределенность, то задача синтеза системы идентификации обеспечения усложняется. Целью настоящей работы является разработка подхода к идентификации нелинейных динамических систем с несколькими нелинейностями. Для решения проблемы применяется подход, основанный на декомпозиции системы на ряд подсистем и разработке метода адаптивной идентификации, использующего только доступную информацию о системе и измерениях. Необходимо оценить частотные свойства сигналов, которые должны гарантировать оценку параметров системы и обеспечивать структурную идентифицируемость нелинейностей в системе; оценить работоспособность синтезированной адаптивной системы.

Методы

Методы. Применяются метод адаптивной идентификации системы, неявное идентификационное представление, S-синхронизация нелинейной системы, метод векторных функций Ляпунова.

Результаты

Результаты. Введено условие постоянства возбуждения переменных состояния с учетом S-синхронизируемости нелинейной части системы. Дано обобщение условия постоянства возбуждения. Предложен способ декомпозиции системы в выходном пространстве. Получены адаптивные алгоритмы на основе второго метода Ляпунова. Доказана ограниченность траекторий адаптивной системы в параметрическом и координатном пространствах на основе векторных функций Ляпунова. Получены условия, гарантирующие экспоненциальную устойчивость траекторий системы. Рассмотрены системы генерации автоколебаний и нелинейной коррекции нелинейной системы.

Выводы

Выводы. Результаты моделирования подтвердили возможность применения предлагаемого подхода для решения задач адаптивной идентификации с учетом оценки структурной идентифицируемости (S-синхронизируемости) нелинейной части системы. Исследовано влияние структуры и связей системы на качество получаемых параметрических оценок. Предлагаемые методы могут использоваться при разработке систем идентификации и управления сложными динамическими системами.

Objectives

Objectives. The solution to the relevant problem of identifying systems with multiple nonlinearities depends on such factors as feedback, ways of connecting nonlinear links, and signal properties. The specifics of nonlinear systems affect control systems design methods. As a rule, the basis for the development of a mathematical model involves the linearization of a system. Under conditions of uncertainty, the identification problem becomes even more relevant. Therefore, the present work sets out to develop an approach to the identification of nonlinear dynamical systems under conditions of uncertainty. In order to obtain a solution to the problem, an adaptive identification method is developed by decomposing the system into subsystems.

Methods

Methods. Methods applied include the adaptive identification method, implicit identified representation, S-synchronization of a nonlinear system, and the Lyapunov vector function method.

Results

Results. A generalization of the excitation constancy condition based on fulfilling the S-synchronizability for a nonlinear system is proposed along with a method for decomposing the system in the output space. Adaptive algorithms are obtained on the basis of the second Lyapunov method. The boundedness of the adaptive system trajectories in parametric and coordinate spaces is demonstrated. Approaches for self-oscillation generation and nonlinear correction of a nonlinear system are considered along with obtained exponential stability conditions for the adaptive system.

Conclusions

Conclusions. Simulation results confirm the possibility of applying the proposed approach to solving the problems of adaptive identification while taking the estimation of the structural identifiability (S-synchronization) of the system nonlinear part into account. The influence of the structure and relations of the system on the quality of the obtained parametric estimates is investigated. The proposed methods can be used in developing identification and control systems for complex dynamic systems.

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The authors declare that there are no conflicts of interest present.