Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations
In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2018-08-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13167 |
| _version_ | 1811275749005459456 |
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| author | Yujiao Liu Xiaoxiao Wan Enli Wu Xinsong Yang Fuad E. Alsaadi Tasawar Hayat |
| author_facet | Yujiao Liu Xiaoxiao Wan Enli Wu Xinsong Yang Fuad E. Alsaadi Tasawar Hayat |
| author_sort | Yujiao Liu |
| collection | DOAJ |
| description | In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results. |
| first_indexed | 2024-04-12T23:43:30Z |
| format | Article |
| id | doaj.art-28d0f481f08a4c458b140e6873214df0 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-04-12T23:43:30Z |
| publishDate | 2018-08-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-28d0f481f08a4c458b140e6873214df02022-12-22T03:11:55ZengVilnius University PressNonlinear Analysis1392-51132335-89632018-08-0123410.15388/NA.2018.4.4Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activationsYujiao Liu0Xiaoxiao Wan1Enli Wu2Xinsong Yang3Fuad E. Alsaadi4Tasawar Hayat5Mianyang Teachers’ College, ChinaChongqing Normal University, ChinaSichuan University of Science and Engineering, ChinaChongqing Normal University, ChinaKing Abdulaziz University, Saudi ArabiaKing Abdulaziz University; Quaid-I-Azam UniversityIn this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results.http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13167neural networksdiscontinuous activationfinite-time synchronizationMarkovian switchingproportional delays |
| spellingShingle | Yujiao Liu Xiaoxiao Wan Enli Wu Xinsong Yang Fuad E. Alsaadi Tasawar Hayat Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations Nonlinear Analysis neural networks discontinuous activation finite-time synchronization Markovian switching proportional delays |
| title | Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations |
| title_full | Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations |
| title_fullStr | Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations |
| title_full_unstemmed | Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations |
| title_short | Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations |
| title_sort | finite time synchronization of markovian neural networks with proportional delays and discontinuous activations |
| topic | neural networks discontinuous activation finite-time synchronization Markovian switching proportional delays |
| url | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13167 |
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