FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH*

doi:10.1007/s10473-023-0325-y

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1439-1461.doi: 10.1007/s10473-023-0325-y

FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH^*

Wanlu WEI, Cheng HU^†, Juan YU, Haijun JIANG

College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China

收稿日期:2022-02-04 修回日期:2022-08-25 出版日期:2023-06-25 发布日期:2023-06-06
通讯作者: ^† Cheng HU, E-mail: hucheng@xju.edu.cn
作者简介:Wanlu WEI, E-mail: wwl15744@163.com; Juan YU, E-mail: yujuanseesea@163.com; Haijun JIANG, E-mail: jianghai@xju.edu.cn
基金资助:
National Natural Science Foundation of China (61963033, 61866036, 62163035), the Key Project of Natural Science Foundation of Xinjiang (2021D01D10), the Xinjiang Key Laboratory of Applied Mathematics (XJDX1401) and the Special Project for Local Science and Technology Development Guided by the Central Government (ZYYD2022A05).

FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH^*

Wanlu WEI, Cheng HU^†, Juan YU, Haijun JIANG

College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China

Received:2022-02-04 Revised:2022-08-25 Online:2023-06-25 Published:2023-06-06
Contact: ^† Cheng HU, E-mail: hucheng@xju.edu.cn
About author:Wanlu WEI, E-mail: wwl15744@163.com; Juan YU, E-mail: yujuanseesea@163.com; Haijun JIANG, E-mail: jianghai@xju.edu.cn
Supported by:
National Natural Science Foundation of China (61963033, 61866036, 62163035), the Key Project of Natural Science Foundation of Xinjiang (2021D01D10), the Xinjiang Key Laboratory of Applied Mathematics (XJDX1401) and the Special Project for Local Science and Technology Development Guided by the Central Government (ZYYD2022A05).

摘要/Abstract

摘要： The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical results.

关键词: fixed-time synchronization, preassigned-time synchronization, quaternion-valued neural networks, discontinuous activation, direct analysis method

Abstract: The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical results.

Key words: fixed-time synchronization, preassigned-time synchronization, quaternion-valued neural networks, discontinuous activation, direct analysis method

Wanlu WEI, Cheng HU, Juan YU, Haijun JIANG. FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH^*[J]. 数学物理学报(英文版), 2023, 43(3): 1439-1461.

Wanlu WEI, Cheng HU, Juan YU, Haijun JIANG. FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1439-1461.

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FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH^*

FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH^*

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