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Thakur GK, Garg SK, Singh T, Ali MS, Arora TK. Non-fragile synchronization of BAM neural networks with randomly occurring controller gain fluctuation. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:7302-7315. [PMID: 37161153 DOI: 10.3934/mbe.2023317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
In this research, a non-fragile synchronization of bidirectional association memory (BAM) delayed neural networks is taken into consideration. The controller gain fluctuation seems in a very random manner, that obeys sure Bernoulli distributed noise sequences. Delay dependent criteria are derived to confirm the asymptotic stability of the BAM delayed neural networks. The non-fragile controller are often obtained by determination a collection of linear matrix inequalities (LMIs). A simulation example is used to demonstrate the efficiency of the developed control.
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Affiliation(s)
- Ganesh Kumar Thakur
- Department of Applied sciences, ABES Engineering College, Ghaziabad, UP-201007, India
| | - Sudesh Kumar Garg
- Department of Applied Science, G L BAJAJ Institute of Technology and Management, Greater Noida, Uttar Pradesh, India
| | - Tej Singh
- Department of Applied sciences, ABES Engineering College, Ghaziabad, UP-201007, India
| | - M Syed Ali
- Department of Mathematics, Thiruvalluvar University, Vellore-632115, Tamilndau, Inida
| | - Tarun Kumar Arora
- Department of Applied sciences, ABES Engineering College, Ghaziabad, UP-201007, India
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2
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Stability of Memristor-based Fractional-order Neural Networks with Mixed Time-delay and Impulsive. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11061-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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3
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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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4
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Controller design for finite-time and fixed-time stabilization of fractional-order memristive complex-valued BAM neural networks with uncertain parameters and time-varying delays. Neural Netw 2020; 130:60-74. [DOI: 10.1016/j.neunet.2020.06.021] [Citation(s) in RCA: 48] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2020] [Revised: 06/04/2020] [Accepted: 06/28/2020] [Indexed: 11/19/2022]
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5
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Nagamani G, Rajan GS, Zhu Q. Exponential State Estimation for Memristor-Based Discrete-Time BAM Neural Networks With Additive Delay Components. IEEE TRANSACTIONS ON CYBERNETICS 2020; 50:4281-4292. [PMID: 30908249 DOI: 10.1109/tcyb.2019.2902864] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This paper focuses on the dynamical behavior for a class of memristor-based bidirectional associative memory neural networks (BAMNNs) with additive time-varying delays in discrete-time case. The necessity of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is exponentially stable with a prescribed decay rate. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and utilizing Cauchy-Schwartz-based summation inequality, the delay-dependent sufficient conditions for the existence of the desired estimator are derived in the absence of uncertainties which are further extended to available uncertain parameters of the prescribed memristor-based BAMNNs in terms of linear matrix inequalities (LMIs). By solving the proposed LMI conditions the estimation gain matrices are obtained. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed results.
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6
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Liu H, Ma L, Wang Z, Liu Y, Alsaadi FE. An overview of stability analysis and state estimation for memristive neural networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.01.066] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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7
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Gao D, Li J. Global Asymptotic Stability of Periodic Solutions for Neutral-Type BAM Neural Networks with Delays. Neural Process Lett 2020. [DOI: 10.1007/s11063-019-10092-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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8
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Pershin YV, Di Ventra M. On the validity of memristor modeling in the neural network literature. Neural Netw 2019; 121:52-56. [PMID: 31536899 DOI: 10.1016/j.neunet.2019.08.026] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Revised: 08/13/2019] [Accepted: 08/22/2019] [Indexed: 10/26/2022]
Abstract
An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks.
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Affiliation(s)
- Yuriy V Pershin
- Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208, USA.
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9
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Abdurahman A, Jiang H. Nonlinear control scheme for general decay projective synchronization of delayed memristor-based BAM neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.05.015] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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10
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Stability property of impulsive inertial neural networks with unbounded time delay and saturating actuators. Neural Comput Appl 2019. [DOI: 10.1007/s00521-019-04115-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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11
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Li B, Zhao Y, Shi G. A novel design of memristor-based bidirectional associative memory circuits using Verilog-AMS. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.11.050] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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12
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Hou P, Hu J, Gao J, Zhu P. Stability Analysis for Memristor-Based Complex-Valued Neural Networks with Time Delays. ENTROPY (BASEL, SWITZERLAND) 2019; 21:e21020120. [PMID: 33266836 PMCID: PMC7514603 DOI: 10.3390/e21020120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2018] [Revised: 01/19/2019] [Accepted: 01/21/2019] [Indexed: 06/12/2023]
Abstract
In this paper, the problem of stability analysis for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is investigated extensively. This paper focuses on the exponential stability of the MCVNNs with time-varying delays. By means of the Brouwer's fixed-point theorem and M-matrix, the existence, uniqueness, and exponential stability of the equilibrium point for MCVNNs are studied, and several sufficient conditions are obtained. In particular, these results can be applied to general MCVNNs whether the activation functions could be explicitly described by dividing into two parts of the real parts and imaginary parts or not. Two numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Ping Hou
- School of Management, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
| | - Jun Hu
- School of Management Science and Engineering, Central University of Finance and Economics, Beijing 100080, China
| | - Jie Gao
- School of Sciences, Southwest Petroleum University, Chengdu 610500, China
| | - Peican Zhu
- School of Computer Science, Northwestern Polytechnical University, Xi’an 710072, China
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13
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Liu W, Jiang M, Yan M. Stability analysis of memristor-based time-delay fractional-order neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.09.073] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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14
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Wang P, Wang G, Su H. The existence and exponential stability of periodic solution for coupled systems on networks without strong connectedness. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.06.036] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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15
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Li XM, Chen Y, Li JY. Finite-time state estimation for delayed periodic neural networks over multiple-packet transmission. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.05.059] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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16
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The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control. PLoS One 2018; 13:e0204002. [PMID: 30248118 PMCID: PMC6152966 DOI: 10.1371/journal.pone.0204002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Accepted: 08/31/2018] [Indexed: 11/19/2022] Open
Abstract
In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.
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17
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Global asymptotical stability for a class of non-autonomous impulsive inertial neural networks with unbounded time-varying delay. Neural Comput Appl 2018. [DOI: 10.1007/s00521-018-3498-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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18
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Wang C, Rathinasamy S. Double almost periodicity for high-order Hopfield neural networks with slight vibration in time variables. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.12.008] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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19
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Wang F, Chen Y, Liu M. pth moment exponential stability of stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays. Neural Netw 2018; 98:192-202. [DOI: 10.1016/j.neunet.2017.11.007] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2017] [Revised: 09/18/2017] [Accepted: 11/07/2017] [Indexed: 11/30/2022]
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20
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Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhang Y, Zhao H. Globally fixed-time synchronization of coupled neutral-type neural network with mixed time-varying delays. PLoS One 2018; 13:e0191473. [PMID: 29370248 PMCID: PMC5784957 DOI: 10.1371/journal.pone.0191473] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Accepted: 01/07/2018] [Indexed: 11/18/2022] Open
Abstract
This paper mainly studies the globally fixed-time synchronization of a class of coupled neutral-type neural networks with mixed time-varying delays via discontinuous feedback controllers. Compared with the traditional neutral-type neural network model, the model in this paper is more general. A class of general discontinuous feedback controllers are designed. With the help of the definition of fixed-time synchronization, the upper right-hand derivative and a defined simple Lyapunov function, some easily verifiable and extensible synchronization criteria are derived to guarantee the fixed-time synchronization between the drive and response systems. Finally, two numerical simulations are given to verify the correctness of the results.
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Affiliation(s)
- Mingwen Zheng
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
- School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
| | - Lixiang Li
- Information Security Center, State Key Laboratory of Networking and Switching Technology, National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Haipeng Peng
- Information Security Center, State Key Laboratory of Networking and Switching Technology, National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Jinghua Xiao
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Yixian Yang
- Information Security Center, State Key Laboratory of Networking and Switching Technology, National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Yanping Zhang
- School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
| | - Hui Zhao
- Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan 250022, China
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21
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Global Dissipativity of Inertial Neural Networks with Proportional Delay via New Generalized Halanay Inequalities. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9788-6] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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22
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Fu Q, Cai J, Zhong S, Yu Y. Dissipativity and passivity analysis for memristor-based neural networks with leakage and two additive time-varying delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.09.014] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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23
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Wang P, Chen Z, Li W. Graph-theoretic approach to exponential synchronization of discrete-time stochastic coupled systems with time-varying delay. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.08.069] [Citation(s) in RCA: 10] [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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24
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Exponential input-to-state stability for complex-valued memristor-based BAM neural networks with multiple time-varying delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.10.038] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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25
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$$H_{\infty }$$
H
∞
state estimation for discrete-time stochastic memristive BAM neural networks with mixed time-delays. INT J MACH LEARN CYB 2017. [DOI: 10.1007/s13042-017-0769-2] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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26
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Sliding Surface in Consensus Problem of Multi-Agent Rigid Manipulators with Neural Network Controller. ENERGIES 2017. [DOI: 10.3390/en10122127] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
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27
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Almost automorphic solution for neutral type high-order Hopfield BAM neural networks with time-varying leakage delays on time scales. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.05.089] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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28
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Chen C, Li L, Peng H, Yang Y. Fixed-time synchronization of memristor-based BAM neural networks with time-varying discrete delay. Neural Netw 2017; 96:47-54. [DOI: 10.1016/j.neunet.2017.08.012] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Revised: 08/03/2017] [Accepted: 08/25/2017] [Indexed: 10/18/2022]
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29
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30
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Li H, Li C, Huang T. Periodicity and stability for variable-time impulsive neural networks. Neural Netw 2017; 94:24-33. [DOI: 10.1016/j.neunet.2017.06.006] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2017] [Revised: 04/27/2017] [Accepted: 06/09/2017] [Indexed: 10/19/2022]
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31
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32
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Global stability analysis for discrete-time coupled systems with both time delay and multiple dispersal and its application. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.013] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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33
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Kazemy A. Global synchronization of neural networks with hybrid coupling: a delay interval segmentation approach. Neural Comput Appl 2016. [DOI: 10.1007/s00521-016-2661-5] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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