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fixed-time synchronization of delayed Cohen-Grossberg neural networks based on a novel sliding mode

NEURAL NETWORKS 2020年 128卷 1-12页

作者： Xiao, Jian Zeng, Zhigang Wu, Ailong Wen, Shiping Jiangsu Univ Sch Elect & Informat Engn Zhenjiang 212013 Jiangsu Peoples R China Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan 430074 Peoples R China Hubei Normal Univ Coll Math & Stat Huangshi 435002 Hubei Peoples R China Univ Technol Sydney Fac Engn Informat Technol Ctr Artificial Intelligence Ultimo NSW 2007 Australia

This paper has discussed fixed-time synchronization of discontinuous Cohen-Grossberg neural networks with time-varying delays and matched disturbances based on sliding mode control technology. First, a novel sliding-mode surface is established. And, the dynamics on the sliding-mode surface can be achieved in the fixed time by employing the Gudermannian function. Then, considering the effect of delay, two different control schemes are introduced to ensure the fixed time reachability of the sliding mode. In addition, some useful criteria are given out for fixed-time synchronization of neural networks, and the setting time is formulated in a straightforward way. Finally, some examples and simulations are presented to verify the validity of the proposed results. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Cohen-Grossberg neural networks fixed-time synchronization Sliding-mode surface Discontinuous activations

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fixed-time synchronization of hybrid coupled networks with time-varying delays

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CHAOS SOLITONS & FRACTALS 2018年 108卷 49-56页

作者： Chen, Chuan Li, Lixiang Peng, Haipeng Kurths, Jurgen Yang, Yixian Beijing Univ Posts & Telecommun Informat Secur Ctr State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China Potsdam Inst Climate Impact Res D-14473 Potsdam Germany State Key Lab Publ Big Data Guiyang 550025 Guizhou Peoples R China

In this paper, we study the fixed-time synchronization of hybrid coupled networks, which have only one transmittal delay in the delayed coupling terms. The settling time of fixed-time synchronization can be adjusted to some desired values in advance regardless of the initial conditions. By constructing suitable Lyapunov functions and designing delay-dependent feedback controllers, we derive several novel synchronization criteria, which guarantee the considered hybrid coupled networks can achieve fixed-time synchronization. Two numerical examples are given to show the effectiveness of our results. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： fixed-time synchronization Hybrid coupled networks Delay-dependent feedback controllers

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fixed-time synchronization for coupled delayed neural networks with discontinuous or continuous activations

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NEUROCOMPUTING 2018年 314卷 143-153页

作者： Lu, Hui He, Wangli Han, Qing-Long Peng, Chen Shanghai Univ Sch Mechatron Engn & Automat Shanghai 200072 Peoples R China East China Univ Sci & Technol Minist Educ Key Lab Adv Control & Optimizat Chem Proc Shanghai 200237 Peoples R China Swinburne Univ Technol Sch Software & Elect Engn Melbourne Vic 3122 Australia

This paper is concerned with fixed-time synchronization of coupled delayed neural networks with discontinuous or continuous activation functions. Two discontinuous control protocols under undirected or directed topologies are proposed to guarantee that coupled delayed neural networks achieve synchronization with a desired trajectory in fixed time, respectively. Several sufficient criteria for fixed-time synchronization are obtained. Furthermore, an upper bound of the settling time is theoretically estimated, which is independent on initial conditions. Finally, two numerical examples are given to illustrate the effectiveness of the synchronization criteria. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Neural networks time-delays fixed-time synchronization Continuous activations Discontinuous activations

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fixed-time synchronization and energy cost estimation of delayed coupled neural networks

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2024年第6期34卷 4064-4078页

作者： Xu, Zhenyu Zhu, Song Luo, Weiwei Liu, Xiaoyang Wen, Shiping China Univ Min & Technol Sch Math Xuzhou Jiangsu Peoples R China Jiangsu Ctr Appl Math CUMT Xuzhou 221116 Jiangsu Peoples R China Jiangsu Normal Univ Sch Comp Sci & Technol Xuzhou Jiangsu Peoples R China Univ Technol Sydney Australian AI Inst Sydney NSW Australia Univ Technol Sydney Fac Engn & Informat Technol Sydney NSW Australia China Univ Min & Technol Sch Math Xuzhou 221116 Jiangsu Peoples R China

This article concentrates on the fixed-time synchronization (FTS) and energy cost (EC) problems of delayed coupled neural networks (NNs). A switching controller is proposed and some sufficient conditions are advanced to ensure FTS of delayed coupled NNs based on the comparison theorem. Following that, the required EC is estimated during the control process. The main results of FTS and EC for considered NNs are obtained based on the Lyapunov functions in the sense of vector 1-norm, 2-norm, and infinity$$ \infty $$-norm, respectively. Under the same controller parameters, this article shows that the minimum estimation of settling time and EC are sometimes not in one norm sense. Finally, numerical examples are given to show the effectiveness of theoretical results.

关键词： coupled neural networks energy cost fixed-time synchronization time delay

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fixed-time synchronization for competitive neural networks with Gaussian-wavelet-type activation functions and discrete delays

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2020年第1-2期64卷 103-118页

作者： Zhou, Jie Bao, Haibo Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China

In this article, the fixed-time synchronization for competitive neural networks (CNNs) with Gaussian-wavelet-type activation functions and discrete delays is investigated. Firstly, in terms of Lyapunov stability theory and inequality technique, simple synchronization conditions are obtained by designing some feedback controllers. Secondly, the activation functions adopted in CNNs are Gaussian-wavelet-type activation functions for the first time, which have great preponderance in network optimization and storage capacity. Furthermore, the settling time with upper bound of the system to achieve fixed-time synchronization can be explicitly evaluated, which is irrelevant to the initial value of the system. Finally, the theoretical results which we derived are attested to be indeed feasible in terms of two numerical simulations.

关键词： fixed-time synchronization Competitive neural networks Gaussian-wavelet-type activation functions Discrete delays

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fixed-time synchronization of Memristive Fuzzy BAM Cellular Neural Networks With time-Varying Delays Based on Feedback Controllers

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IEEE ACCESS 2018年 6卷 12085-12102页

作者： Zheng, Mingwen Li, Lixiang Peng, Haipeng Xiao, Jinghua Yang, Yixian Zhang, Yanping Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China Shandong Univ Technol Sch Math & Stat Zibo 255000 Peoples R China Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Informat Secur Ctr Beijing 100876 Peoples R China

This paper mainly investigates the fixed-time synchronization problem of memristive fuzzy bidirectional associative memory (BAM) cellular neural networks (MFBAMCNNs) with time-varying delays. MFBAMCNNs are formulated by virtue of differential inclusion and set-valued map theories. By utilizing the definition of fixed-time synchronization and some inequality techniques, some novel criteria for easy verification are derived to ensure the fixed-time synchronization of the drive-response MFBAMCNNs based on the Lyapunov stability theory and nonlinear feedback controllers. The results of the main theorem can be easily extended to the fuzzy BAM cellular neural networks without memristor and the memristive BAM cellular neural networks without fuzzy logic. In addition, the settling time of fixed-time synchronization, which does not depend on the initial values, can be simply calculated. At last, two numerical examples are presented to verify the effectiveness of main results.

关键词： fixed-time synchronization memristor MFBAMCNNs Lyapunov function nonlinear feedback controller

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fixed-time synchronization of coupled memristor-based neural networks with time-varying delays

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NEURAL NETWORKS 2019年 116卷 101-109页

作者： Yang, Chao Huang, Lihong Cai, Zuowei Changsha Univ Dept Math & Comp Sci Changsha 410022 Hunan Peoples R China Changsha Univ Sci & Technol Sch Math & Stat Changsha 410114 Hunan Peoples R China Hunan Womens Univ Dept Informat Technol Changsha 410002 Hunan Peoples R China

This paper investigates the fixed-time synchronization of Memristor-based neural networks with time-delayed and coupled. In view of the retarded differential inclusions theory, drive-response concept, the authors give some sufficient conditions to ensure the fixed-time synchronization issue of Memristor-based neural networks. Two novel state-feedback controllers and adaptive controller are designed such that the system can realize fixed-time complete synchronization by means of inequality technique and non-smooth analysis theory. It is worth to point out that, without desiring values of the initial conditions or under the linear growth condition of the controller, the settling time of fixed-time synchronization is estimated. Finally, an example is given to further illustrate the benefits of the proposed switched control approach. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： fixed-time synchronization Differential inclusion Memristor-based neural networks Coupled

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fixed-time synchronization of delayed memristive neural networks with impulsive effects via novel fixed-time stability theorem

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NEURAL NETWORKS 2023年第1期163卷 75-85页

作者： Wang, Dongshu Li, Luke Huaqiao Univ Sch Math Sci Quanzhou 362021 Peoples R China

In this study, the fixed-time synchronization (FXTS) of delayed memristive neural networks (MNNs) with hybrid impulsive effects is explored. To investigate the FXTS mechanism, we first propose a novel theorem about the fixed-time stability (FTS) of impulsive dynamical systems, where the coefficients are extended to functions and the derivatives of Lyapunov function (LF) are allowed to be indefinite. After that, we obtain some new sufficient conditions for achieving FXTS of the system within a settling-time using three different controllers. At last, to verify the correctness and effectiveness of our results, a numerical simulation was conducted. Significantly, the impulse strength studied in this paper can take different values at different points, so it can be regarded as a time-varying function, unlike those in previous studies (the impulse strength takes the same value at different points). Hence, the mechanisms in this article are of more practical applicability. (c) 2023 Elsevier Ltd. All rights reserved.

关键词： Memristive neural networks fixed-time stability fixed-time synchronization time-varying impulse strength Hybrid impulsive effects

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fixed-time synchronization for quaternion-valued memristor-based neural networks with mixed delays

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NEURAL NETWORKS 2023年第1期165卷 274-289页

作者： Zhang, Yanlin Yang, Liqiao Kou, Kit Ian Liu, Yang Univ Macau Fac Sci & Technol Dept Math Macau 999078 Peoples R China Zhejiang Normal Univ Coll Math & Comp Sci Jinhua 321004 Peoples R China

In this paper, the fixed-time synchronization (FXTSYN) of unilateral coefficients quaternion-valued memristor-based neural networks (UCQVMNNs) with mixed delays is investigated. A direct analytical approach is suggested to obtain FXTSYN of UCQVMNNs utilizing one-norm smoothness in place of decomposition. When dealing with drive-response system discontinuity issues, use the set-valued map and the differential inclusion theorem. To accomplish the control objective, innovative nonlinear controllers and the Lyapunov functions are designed. Furthermore, some criteria of FXTSYN for UCQVMNNs are given using inequality techniques and the novel FXTSYN theory. And the accurate settling time is obtained explicitly. Finally, in order to show that the obtained theoretical results are accurate, useful, and applicable, numerical simulations are presented at the conclusion.& COPY;2023 Elsevier Ltd. All rights reserved.

关键词： fixed-time synchronization Nonlinear controllers Unilateral coefficients Quaternion-valued Memristor-based neural networks

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fixed-time synchronization of Fractional-order Hopfield Neural Networks

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2022年第11期20卷 3584-3591页

作者： Mei, Xu Ding, Yucai Southwest Univ Sci & Technol Sch Sci Mianyang 621010 Sichuan Peoples R China

This paper investigates the fixed-time synchronization of fractional-order Hopfield neural networks (FHNNs). The aim of this paper is to design a state-feedback controller to make the synchronization error convergent to zero within bounded time. Based on the Lyapunov function and fractional calculus theory, we derived some criteria of synchronization for delay-free FHNNs and delayed FHNNs, respectively. At the same time, the upper bound of settling time for synchronization are given. Numerical simulations demonstrate the effectiveness of the theoretical analysis.

关键词： Feedback controller fixed-time synchronization fractional order Hopfield neural networks

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