ipolytechiPolytech JournaliPolytech Journal2782-40042782-6341Irkutsk National Research Technical University10.21285/1814-3520-2021-6-753-761ipolytech-549Research ArticleЭНЕРГЕТИКАPOWER ENGINEERINGНовый критерий асимптотической устойчивости нейронных сетей Хопфилда с переменным запаздываниемA new criterion of asymptotic stability for Hopfield neural networks with time-varying delayhttps://orcid.org/0000-0002-7390-0400ГоВэйжуGuoWeiru

Вэйжу Го, аспирант, Школа автоматизации

410083, г. Чанша, зд. Миньчжу, Китайская Народная Республика

Weiru Guo, PhD student, School of Automation

Changsha 410083, Minzhu Building, People’s Republic of China

weiruguo@csu.edu.cnhttps://orcid.org/0000-0003-0750-8344ЛюФанLiuFang

Фан Лю, профессор, Школа автоматизации

410083, г. Чанша, зд. Миньчжу, Китайская Народная Республика

Fang Liu, full professor, School of Automation

Changsha 410083, Minzhu Building, People’s Republic of China

csuliufang@csu.edu.cnЦентральный Южный университетКитайCentral South UniversityChina202111012022256753761Copyright © Го В., Лю Ф., 20222022Го В., Лю Ф.Guo W., Liu F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ipolytech.elpub.ru/jour/article/view/549

Цель – анализ устойчивости нейронных сетей Хопфилда с изменяющейся во времени задержкой. Для того чтобы система могла работать в устойчивом состоянии, важно гарантировать устойчивость нейронных сетей Хопфилда с изменяющейся во времени задержкой. Метод функционала Ляпунова-Красовского является основным методом исследования устойчивости систем с временной задержкой. На основе данного метода в работе анализируется устойчивость нейронных сетей Хопфилда с изменяющейся во времени задержкой. Известно, что из-за таких факторов, как время связи, ограниченная скорость переключения различных активных устройств, в различных технических системах часто возникают временные задержки, которые существенно ухудшают раб оту системы, что может в свою очередь приводить к полной потере устойчивости. В связи с этим в работе был построен функционал Ляпунова-Красовского типа «delay-product», что позволяет использовать больше информации о временной задержке и уменьшать консерватизм метода. Затем было использовано обобщенное инте гральное неравенство на основе свободной матрицы. Сформулирован новый критерий асимптотической устойчивости нейронных сетей Хопфилда с изменяющейся во времени задержкой, который обладает меньшим консерватизмом. Проиллюстрирована эффективность предложенного метода. Таким образом, в работе сформулирован и обоснован критерий асимптотической устойчивости для нейронных сетей Хопфилда с изменяющейся во времени задержкой. При этом расширенный функционал Ляпунова-Красовского строится на основе запаздывания и квадратичного мультипликативного функционала, а производная функционала определяется матричным интегральным неравенством со свободными весами. Эффективность метода иллюстрируется на модельном примере.

The objective of this paper is to analyze the stability of Hopfield neural networks with time-varying delay. For the system to operate in a steady state, it is important to guarantee the stability of Hopfield neural networks with time-varying delay. The Lyapunov-Krasovsky functional method is the main method for investigating the stability of time-delayed systems. On the basis of this method, the stability of Hopfield neural networks with time-varying delay is ana-lysed. It is known that due to such factors as communication time, limited switching speed of various active devices, time delays often arise in various technical systems, which significantly degrade the performance of the system, which can in turn lead to a complete loss of stability. In this regard, a Lyapunov-Krasovsky type delay-product functional was con-structed in the paper, which allows more information about the time delay and reduces the conservatism of the method. Then a generalized integral inequality based on the free matrix was used. A new criterion for asymptotic stability of Hop-field neural networks with time-varying delay, which has less conservatism, was formulated. The effectiveness of the proposed method is illustrated. Thus an asymptotic stability criterion for Hopfield neural networks with time-varying delay was formulated and justified. The expanded Lyapunov-Krasovsky functional is constructed on the basis of delay and quadratic multiplicative functional, and the derivative of the functional is defined by a matrix integral inequality with free weights. The effectiveness of the method is illustrated by a model example.

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