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Wu X, Tu Z, Peng T, Wang D. Global attractive set for quaternion-valued neural networks with neutral items. Sci Rep 2024; 14:17975. [PMID: 39095525 PMCID: PMC11297258 DOI: 10.1038/s41598-024-68763-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2024] [Accepted: 07/27/2024] [Indexed: 08/04/2024] Open
Abstract
This paper investigated the global attractive set for quaternion-valued neural networks (QVNNs) with leakage delay, time-varying delay, and neutral items. Based on various basic conditions of activation function, the global attractive set and global exponential attractive set of QVNNs are given combined with novel analytical techniques and Lyapunov theory. The QVNNs are studied by a direct method, without any decomposition. The time delay can be non-differential, which makes the results more pragmatic. Restrictions on the activation function of the neutral item are relaxed. The neutral activation function can be bounded or unbounded, which makes the results more practical. Two simulation examples are given to verify the validity of the theory results.
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Affiliation(s)
- Xili Wu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China
| | - Zhengwen Tu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China.
| | - Tao Peng
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China
| | - Dandan Wang
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China
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2
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Shu J, Wu B, Xiong L. Robust H∞ control of uncertain time-delay Markovian jump quaternion-valued neural networks subject to partially known transition probabilities: direct quaternion method. Cogn Neurodyn 2023; 17:767-787. [PMID: 37265648 PMCID: PMC10229530 DOI: 10.1007/s11571-022-09846-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Revised: 06/16/2022] [Accepted: 07/06/2022] [Indexed: 11/03/2022] Open
Abstract
This paper addresses the issue of robust stochastic stabilization and H ∞ control of uncertain time-delay Markovian jump quaternion-valued neural networks (MJQVNNs) subject to partially known transition probabilities. First, the direct quaternion method is proposed to analyse the MJQVNNs, which is different from some conventional methods in that the former is without any decomposition for systems. After that, in order to estimate the upper bound of the derivative of the constructed Lyapunov-Krasovskii functional (LKF) more accurately, the real-valued convex inequality is extended to quaternion domain. Then, by designed the mode-dependent state feedback controllers, the robust stochastic stabilization conditions of MJQVNNs are given for the admissible uncertainties, and reduce the influence of input disturbance on the controlled output to a specified performance level. Lastly, two numerical examples are given to illustrate the effectiveness of the proposed method.
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Affiliation(s)
- Jinlong Shu
- School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119 China
| | - Baowei Wu
- School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119 China
| | - Lianglin Xiong
- School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, 650500 China
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3
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Wei R, Cao J, Alsaadi FE. Fixed/Prescribed-Time Bipartite Synchronization of Coupled Quaternion-Valued neural Networks with Competitive Interactions. Neural Process Lett 2023. [DOI: 10.1007/s11063-023-11225-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
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4
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Xiao J, Zhong S, Wen S. Unified Analysis on the Global Dissipativity and Stability of Fractional-Order Multidimension-Valued Memristive Neural Networks With Time Delay. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:5656-5665. [PMID: 33950847 DOI: 10.1109/tnnls.2021.3071183] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.
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5
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Fixed-time passivity of coupled quaternion-valued neural networks with multiple delayed couplings. Soft comput 2022. [DOI: 10.1007/s00500-022-07500-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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6
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Fixed-Time Control for Memristor-Based Quaternion-Valued Neural Networks with Discontinuous Activation Functions. Cognit Comput 2022. [DOI: 10.1007/s12559-022-10057-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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7
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Zhang T, Jian J. Quantized intermittent control tactics for exponential synchronization of quaternion-valued memristive delayed neural networks. ISA TRANSACTIONS 2022; 126:288-299. [PMID: 34330433 DOI: 10.1016/j.isatra.2021.07.029] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2020] [Revised: 07/17/2021] [Accepted: 07/17/2021] [Indexed: 06/13/2023]
Abstract
This article studies the global exponential synchronization (GES) of quaternion-valued memristive delayed neural networks (QVMDNNs) by quantized intermittent control (QIC). Without decomposing the original systems into usual real-valued or complex-valued ones, the discussed system is directly processed in both cases of the differential inclusion theory. Based on two QIC strategies and applying Lyapunov functional method and inequality techniques, several new delay-dependent criteria in the form of real-valued algebraic inequalities are directly derived to assure the GES of the concerned system. Compared to the traditional feedback control, the QIC strategy can reduce the control expenses and shorten time to achieve the GES. Ultimately, two examples are given to validate the effectiveness and advantages of the proposed outcomes.
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Affiliation(s)
- Tingting Zhang
- College of Science, China Three Gorges University, Yichang, Hubei, 443002, China.
| | - Jigui Jian
- College of Science, China Three Gorges University, Yichang, Hubei, 443002, China.
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8
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Aouiti C, Touati F. Global Dissipativity of Quaternion-Valued Fuzzy Cellular Fractional-Order Neural Networks With Time Delays. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10893-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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9
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Li R, Cao J. Passivity and Dissipativity of Fractional-Order Quaternion-Valued Fuzzy Memristive Neural Networks: Nonlinear Scalarization Approach. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:2821-2832. [PMID: 33055054 DOI: 10.1109/tcyb.2020.3025439] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In this article, the problem of passivity and dissipativity analysis is investigated for a class of fractional-order quaternion-valued fuzzy memristive neural networks. Based on the famous nonlinear scalarizing function, a nonlinear scalarization method is developed, which can be employed to compare the "size" of two different quaternions. In this way, the convex closure proposed by the quaternion-valued connection weights is meaningful. By constructing proper Lyapunov functional, several improved passivity criteria and dissipativity conclusions are established, which can be checked efficiently by utilizing some standard mathematical calculations. Finally, the obtained results are validated by simulation examples.
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10
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Lagrange Stability of BAM Quaternion-Valued Inertial Neural Networks via Auxiliary Function-Based Integral Inequalities. Neural Process Lett 2022. [DOI: 10.1007/s11063-021-10685-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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11
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Synchronization in Fixed Time for Reaction–Diffusion Quaternion-Valued NNs with Nonlinear Interconnected Protocol and Its Application. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10579-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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12
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Synchronization in Quaternion-Valued Neural Networks with Delay and Stochastic Impulses. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10653-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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13
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Liu W, Huang J, Yao Q. Stability analysis for quaternion-valued inertial memristor-based neural networks with time delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.03.106] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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14
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Xiao J, Cao J, Cheng J, Wen S, Zhang R, Zhong S. Novel Inequalities to Global Mittag-Leffler Synchronization and Stability Analysis of Fractional-Order Quaternion-Valued Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:3700-3709. [PMID: 32997634 DOI: 10.1109/tnnls.2020.3015952] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article is concerned with the problem of the global Mittag-Leffler synchronization and stability for fractional-order quaternion-valued neural networks (FOQVNNs). The systems of FOQVNNs, which contain either general activation functions or linear threshold ones, are successfully established. Meanwhile, two distinct methods, such as separation and nonseparation, have been employed to solve the transformation of the studied systems of FOQVNNs, which dissatisfy the commutativity of quaternion multiplication. Moreover, two novel inequalities are deduced based on the general parameters. Compared with the existing inequalities, the new inequalities have their unique superiorities because they can make full use of the additional parameters. Due to the Lyapunov theory, two novel Lyapunov-Krasovskii functionals (LKFs) can be easily constructed. The novelty of LKFs comes from a wider range of parameters, which can be involved in the construction of LKFs. Furthermore, mainly based on the new inequalities and LKFs, more multiple and more flexible criteria are efficiently obtained for the discussed problem. Finally, four numerical examples are given to demonstrate the related effectiveness and availability of the derived criteria.
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15
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Global Exponential Dissipativity of Impulsive Recurrent Neural Networks with Multi-proportional Delays. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10451-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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16
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Xiao J, Zhong S, Wen S. Improved approach to the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks based on new inequalities. Neural Netw 2020; 133:87-100. [PMID: 33152567 DOI: 10.1016/j.neunet.2020.10.008] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Revised: 09/13/2020] [Accepted: 10/15/2020] [Indexed: 11/17/2022]
Abstract
This paper studies the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks (FOMVBAMNNs) with general activation functions (AFs). First, the unified model is established for the researched systems of FOMVBAMNNs which can be turned into the corresponding multidimension-valued systems as long as the state variables, the connection weights and the AFs of the neural networks are valued to be real, complex, or quaternion. Then, without any decomposition, the criteria in unified form are derived by constructing the new Lyapunov-Krasovskii functionals (LKFs) in vector form, combining two new inequalities and considering the easy controllers. It is worth mentioning that the obtained criteria have many advantages in higher flexibility, more diversity, smaller computation, and lower conservatism. Finally, a simulation example is provided to illustrate the availability and improvements of the acquired results.
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Affiliation(s)
- Jianying Xiao
- School of Sciences, Southwest Petroleum University, Chengdu, 610050, PR China.
| | - Shouming Zhong
- School of Mathematical Sciences, University of Electronic Science and Technology, Chengdu, 611731, PR China.
| | - Shiping Wen
- Centre for Artificial Intelligence, Faculty of Engineering Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia.
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17
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Popa CA. Dissipativity of impulsive matrix-valued neural networks with leakage delay and mixed delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.042] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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18
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19
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Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks. Inf Sci (N Y) 2020. [DOI: 10.1016/j.ins.2020.03.101] [Citation(s) in RCA: 54] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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20
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Chen X, Lin D, Lan W. Global dissipativity of delayed discrete-time inertial neural networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.01.073] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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21
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Li HL, Jiang H, Cao J. Global synchronization of fractional-order quaternion-valued neural networks with leakage and discrete delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.12.018] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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22
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Xiao J, Wen S, Yang X, Zhong S. New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality. Neural Netw 2020; 122:320-337. [DOI: 10.1016/j.neunet.2019.10.017] [Citation(s) in RCA: 66] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Revised: 09/10/2019] [Accepted: 10/28/2019] [Indexed: 11/16/2022]
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23
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Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10154-1] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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24
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Synchronization Control of Quaternion-Valued Neural Networks with Parameter Uncertainties. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10153-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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25
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Li Y, Meng X. Almost Automorphic Solutions in Distribution Sense of Quaternion-Valued Stochastic Recurrent Neural Networks with Mixed Time-Varying Delays. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10151-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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26
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Xiao J, Zhong S. Synchronization and stability of delayed fractional-order memristive quaternion-valued neural networks with parameter uncertainties. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.06.044] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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27
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Wei R, Cao J. Synchronization control of quaternion-valued memristive neural networks with and without event-triggered scheme. Cogn Neurodyn 2019; 13:489-502. [PMID: 31565093 DOI: 10.1007/s11571-019-09545-w] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2019] [Revised: 05/29/2019] [Accepted: 06/19/2019] [Indexed: 11/29/2022] Open
Abstract
In this paper, the real-valued memristive neural networks (MNNs) are extended to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established. The problem of master-slave synchronization of this type of networks is investigated in this paper. Two types of controllers are designed: the traditional feedback controller and the event-triggered controller. Corresponding synchronization criteria are then derived based on Lyapunov method. Moreover, it is demonstrated that Zeno behavior can be avoided in case of the event-triggered strategy proposed in this work. Finally, corresponding simulation examples are proposed to demonstrate the correctness of the proposed results derived in this work.
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Affiliation(s)
- Ruoyu Wei
- Research Center for Complex Systems and Network Sciences, and School of Mathematics, Southeast University, Nanjing, 210096 China
| | - Jinde Cao
- Research Center for Complex Systems and Network Sciences, and School of Mathematics, Southeast University, Nanjing, 210096 China
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28
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Li HL, Hu C, Cao J, Jiang H, Alsaedi A. Quasi-projective and complete synchronization of fractional-order complex-valued neural networks with time delays. Neural Netw 2019; 118:102-109. [DOI: 10.1016/j.neunet.2019.06.008] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Revised: 06/10/2019] [Accepted: 06/14/2019] [Indexed: 10/26/2022]
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29
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Li R, Gao X, Cao J, Zhang K. Dissipativity and exponential state estimation for quaternion-valued memristive neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.07.036] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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30
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Huang C, Nie X, Zhao X, Song Q, Tu Z, Xiao M, Cao J. Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw 2019; 117:67-93. [DOI: 10.1016/j.neunet.2019.05.002] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2019] [Revised: 05/04/2019] [Accepted: 05/06/2019] [Indexed: 11/16/2022]
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31
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Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks. Neural Netw 2019; 117:307-327. [DOI: 10.1016/j.neunet.2019.05.015] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2018] [Revised: 03/22/2019] [Accepted: 05/20/2019] [Indexed: 11/17/2022]
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32
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Li Y, Shen S. Almost automorphic solution of quaternion-valued BAM neural networks with time-varying delays on time scales1. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-181118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Yongkun Li
- Department of Mathematics, Yunnan University, Kunming, Yunnan, People’s Republic of China
| | - Shiping Shen
- Department of Mathematics, Yunnan University, Kunming, Yunnan, People’s Republic of China
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33
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Liu J, Jian J. Global dissipativity of a class of quaternion-valued BAM neural networks with time delay. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.03.026] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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34
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Fixed-time synchronization of quaternion-valued memristive neural networks with time delays. Neural Netw 2019; 113:1-10. [DOI: 10.1016/j.neunet.2019.01.014] [Citation(s) in RCA: 68] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2018] [Revised: 12/01/2018] [Accepted: 01/23/2019] [Indexed: 11/21/2022]
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35
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Design of Plant Protection UAV Variable Spray System Based on Neural Networks. SENSORS 2019; 19:s19051112. [PMID: 30841563 PMCID: PMC6427117 DOI: 10.3390/s19051112] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/26/2019] [Revised: 02/19/2019] [Accepted: 03/02/2019] [Indexed: 11/16/2022]
Abstract
Recently, unmanned aerial vehicles (UAVs) have rapidly emerged as a new technology in the fields of plant protection and pest control in China. Based on existing variable spray research, a plant protection UAV variable spray system integrating neural network based decision making is designed. Using the existing data on plant protection UAV operations, combined with artificial neural network (ANN) technology, an error back propagation (BP) neural network model between the factors affecting droplet deposition is trained. The factors affecting droplet deposition include ambient temperature, ambient humidity, wind speed, flight speed, flight altitude, propeller pitch, nozzles pitch and prescription value. Subsequently, the BP neural network model is combined with variable rate spray control for plant protection UAVs, and real-time information is collected by multi-sensor. The deposition rate is determined by the neural network model, and the flow rate of the spray system is regulated according to the predicted deposition amount. The amount of droplet deposition can meet the prescription requirement. The results show that the training variance of the ANN is 0.003, and thus, the model is stable and reliable. The outdoor tests show that the error between the predicted droplet deposition and actual droplet deposition is less than 20%. The ratio of droplet deposition to prescription value in each unit is approximately equal, and a variable spray operation under different conditions is realized.
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36
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Song Q, Chen X. Multistability Analysis of Quaternion-Valued Neural Networks With Time Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:5430-5440. [PMID: 29994739 DOI: 10.1109/tnnls.2018.2801297] [Citation(s) in RCA: 69] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper addresses the multistability issue for quaternion-valued neural networks (QVNNs) with time delays. By using the inequality technique, sufficient conditions are proposed for the boundedness and the global attractivity of delayed QVNNs. Based on the geometrical properties of the activation functions, several criteria are obtained to ensure the existence of equilibrium points, of which are locally stable. Two numerical examples are provided to illustrate the effectiveness of the obtained results.
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37
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Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw 2018; 105:88-103. [DOI: 10.1016/j.neunet.2018.04.015] [Citation(s) in RCA: 89] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2017] [Revised: 02/12/2018] [Accepted: 04/20/2018] [Indexed: 11/15/2022]
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38
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Li Y, Qin J, Li B. Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9867-8] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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39
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40
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Existence and global exponential stability of periodic solutions for quaternion-valued cellular neural networks with time-varying delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.02.077] [Citation(s) in RCA: 48] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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41
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42
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Popa CA, Kaslik E. Multistability and multiperiodicity in impulsive hybrid quaternion-valued neural networks with mixed delays. Neural Netw 2018; 99:1-18. [DOI: 10.1016/j.neunet.2017.12.006] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2017] [Revised: 10/25/2017] [Accepted: 12/12/2017] [Indexed: 10/18/2022]
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43
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Huang C, Cao J. Impact of leakage delay on bifurcation in high-order fractional BAM neural networks. Neural Netw 2017; 98:223-235. [PMID: 29274499 DOI: 10.1016/j.neunet.2017.11.020] [Citation(s) in RCA: 71] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Revised: 11/20/2017] [Accepted: 11/28/2017] [Indexed: 10/18/2022]
Abstract
The effects of leakage delay on the dynamics of neural networks with integer-order have lately been received considerable attention. It has been confirmed that fractional neural networks more appropriately uncover the dynamical properties of neural networks, but the results of fractional neural networks with leakage delay are relatively few. This paper primarily concentrates on the issue of bifurcation for high-order fractional bidirectional associative memory(BAM) neural networks involving leakage delay. The first attempt is made to tackle the stability and bifurcation of high-order fractional BAM neural networks with time delay in leakage terms in this paper. The conditions for the appearance of bifurcation for the proposed systems with leakage delay are firstly established by adopting time delay as a bifurcation parameter. Then, the bifurcation criteria of such system without leakage delay are successfully acquired. Comparative analysis wondrously detects that the stability performance of the proposed high-order fractional neural networks is critically weakened by leakage delay, they cannot be overlooked. Numerical examples are ultimately exhibited to attest the efficiency of the theoretical results.
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Affiliation(s)
- Chengdai Huang
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China.
| | - Jinde Cao
- School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210996, China; School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China
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Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field. Neural Netw 2017; 94:55-66. [DOI: 10.1016/j.neunet.2017.06.014] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2017] [Revised: 05/26/2017] [Accepted: 06/26/2017] [Indexed: 11/23/2022]
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