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Man J, Zeng Z, Xiao Q, Zhang H. Exponential Stabilization of Semi-Markov Reaction-Diffusion Memristive NNs via Event-Based Spatially Pointwise-Piecewise Switching Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024; 35:2655-2666. [PMID: 35853063 DOI: 10.1109/tnnls.2022.3190694] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
This article considers both the semi-Markov jumping phenomenon and spatial distribution characteristics when investigating the exponential stabilization of memristive neural networks (MNNs). The introduction of the semi-Markov jumping parameters relaxes the restriction on the sojourn time of Markovian MNNs. To increase the operability while ensuring control effect, a novel event-based spatially pointwise-piecewise switching control scheme is presented under a unified spatial division criterion, in which the pointwise and piecewise control can switch according to the preset event condition for the applicability to different control requirements. Moreover, by constructing a semi-Markov Lyapunov functional and utilizing the properties of the considered cumulative distribution function, the final exponential stabilization criterion and two related corollaries are obtained. Finally, simulation results illustrate the effectiveness and superiority of the proposed control strategy.
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Wei A, Wang K, Wang E, Tong T. Finite-time stabilization for semi-Markov reaction–diffusion memristive NNs: A boundary pinning control scheme. Knowl Based Syst 2023. [DOI: 10.1016/j.knosys.2023.110409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
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3
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Wu X, Liu S, Wang H. Pinning synchronization of stochastic neutral memristive neural networks with reaction–diffusion terms. Neural Netw 2023; 157:1-10. [DOI: 10.1016/j.neunet.2022.09.032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2022] [Revised: 08/19/2022] [Accepted: 09/27/2022] [Indexed: 11/06/2022]
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4
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Song X, Man J, Song S, Ahn CK. Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:2952-2964. [PMID: 32735537 DOI: 10.1109/tnnls.2020.3009081] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.
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Ren F, Jiang M, Xu H, Fang X. New finite-time synchronization of memristive Cohen–Grossberg neural network with reaction–diffusion term based on time-varying delay. Neural Comput Appl 2021. [DOI: 10.1007/s00521-020-05259-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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6
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Li L, Xu R, Gan Q, Lin J. Synchronization of neural networks with memristor-resistor bridge synapses and Lévy noise. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.12.041] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Guo Z, Wang S, Wang J. Global Exponential Synchronization of Coupled Delayed Memristive Neural Networks With Reaction-Diffusion Terms via Distributed Pinning Controls. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:105-116. [PMID: 32191900 DOI: 10.1109/tnnls.2020.2977099] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article presents new theoretical results on global exponential synchronization of nonlinear coupled delayed memristive neural networks with reaction-diffusion terms and Dirichlet boundary conditions. First, a state-dependent memristive neural network model is introduced in terms of coupled partial differential equations. Next, two control schemes are introduced: distributed state feedback pinning control and distributed impulsive pinning control. A salient feature of these two pinning control schemes is that only partial information on the neighbors of pinned nodes is needed. By utilizing the Lyapunov stability theorem and Divergence theorem, sufficient criteria are derived to ascertain the global exponential synchronization of coupled neural networks via the two pining control schemes. Finally, two illustrative examples are elaborated to substantiate the theoretical results and demonstrate the advantages and disadvantages of the two control schemes.
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Ren F, Jiang M, Xu H, Li M. Quasi fixed-time synchronization of memristive Cohen-Grossberg neural networks with reaction-diffusion. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.07.071] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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9
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Cao Y, Cao Y, Guo Z, Huang T, Wen S. Global exponential synchronization of delayed memristive neural networks with reaction–diffusion terms. Neural Netw 2020; 123:70-81. [DOI: 10.1016/j.neunet.2019.11.008] [Citation(s) in RCA: 40] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Revised: 11/09/2019] [Accepted: 11/12/2019] [Indexed: 10/25/2022]
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Wang S, Guo Z, Wen S, Huang T. Global synchronization of coupled delayed memristive reaction–diffusion neural networks. Neural Netw 2020; 123:362-371. [DOI: 10.1016/j.neunet.2019.12.016] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 11/18/2019] [Accepted: 12/14/2019] [Indexed: 11/16/2022]
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Finite-time nonfragile time-varying proportional retarded synchronization for Markovian Inertial Memristive NNs with reaction-diffusion items. Neural Netw 2019; 123:317-330. [PMID: 31896463 DOI: 10.1016/j.neunet.2019.12.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Revised: 10/23/2019] [Accepted: 12/10/2019] [Indexed: 11/22/2022]
Abstract
The issue of synchronization for a class of inertial memristive neural networks over a finite-time interval is investigated in this paper. Specifically, reaction-diffusion items and Markovian jump parameters are both considered in the system model, meanwhile, a novel nonfragile time-varying proportional retarded control strategy is proposed. First, a befitting variable substitution is invoked to transform the original second-order differential system into a first-order one so that the corresponding synchronization error system that is represented by a first-order differential form is established. Second, by utilizing the integral inequality technique, reciprocally convex combination approach and free-weighting matrix method, a less conservative synchronization criterion in terms of linear matrix inequalities is obtained. Finally, three simulations are exploited to illustrate the feasibility, practicability and superiority of the designed controller so that the acquired theoretical results are supported.
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Ding S, Wang Z, Zhang H. Quasi-Synchronization of Delayed Memristive Neural Networks via Region-Partitioning-Dependent Intermittent Control. IEEE TRANSACTIONS ON CYBERNETICS 2019; 49:4066-4077. [PMID: 30106704 DOI: 10.1109/tcyb.2018.2856907] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper aims at investigating the master-slave quasi-synchronization of delayed memristive neural networks (MNNs) by proposing a region-partitioning-dependent intermittent control. The proposed method is described by three partitions of non-negative real region and an auxiliary positive definite function. Whether the control input is imposed on the slave system or not is decided by the dynamical relationships among the three subregions and the auxiliary function. From these ingredients, several succinct criteria with the associated co-design procedure are presented such that the synchronization error converges to a predetermined level. The proposed intermittent control scheme is also applied to the event-triggered control, and an intermittent event-triggered mechanism is devised to investigate the quasi-synchronization of MNNs correspondingly. Such mechanism eliminates the events in rest time, and then it reduces the amount of samplings. Finally, two illustrative examples are presented to verify the effectiveness of our theoretical results.
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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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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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Memory-based State Estimation of T–S Fuzzy Markov Jump Delayed Neural Networks with Reaction–Diffusion Terms. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10026-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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16
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Exponential Synchronization of Stochastic Memristive Neural Networks with Time-Varying Delays. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-09989-5] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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17
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Passivity analysis of delayed reaction–diffusion memristor-based neural networks. Neural Netw 2019; 109:159-167. [DOI: 10.1016/j.neunet.2018.10.004] [Citation(s) in RCA: 77] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Revised: 09/25/2018] [Accepted: 10/09/2018] [Indexed: 11/21/2022]
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18
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Wei H, Chen C, Tu Z, Li N. New results on passivity analysis of memristive neural networks with time-varying delays and reaction–diffusion term. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.10.035] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Li R, Cao J. Finite-Time Stability Analysis for Markovian Jump Memristive Neural Networks With Partly Unknown Transition Probabilities. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:2924-2935. [PMID: 28114080 DOI: 10.1109/tnnls.2016.2609148] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper is concerned with the finite-time stochastically stability (FTSS) analysis of Markovian jump memristive neural networks with partly unknown transition probabilities. In the neural networks, there exist a group of modes determined by Markov chain, and thus, the Markovian jump was taken into consideration and the concept of FTSS is first introduced for the memristive model. By introducing a Markov switching Lyapunov functional and stochastic analysis theory, an FTSS test procedure is proposed, from which we can conclude that the settling time function is a stochastic variable and its expectation is finite. The system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases. More importantly, a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point; compared with the fixed point Theorem that has been widely used in the existing results, this method is more easy to implement. Besides, the delay interval was divided into four subintervals, which make full use of the information of the subsystems upper bounds of the time-varying delays. Finally, the effectiveness and superiority of the proposed method is demonstrated by two simulation examples.
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Sampled-data state estimation for delayed memristive neural networks with reaction-diffusion terms: Hardy–Poincarè inequality. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.05.060] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Yang Z, Luo B, Liu D, Li Y. Pinning synchronization of memristor-based neural networks with time-varying delays. Neural Netw 2017; 93:143-151. [DOI: 10.1016/j.neunet.2017.05.003] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Revised: 04/13/2017] [Accepted: 05/03/2017] [Indexed: 11/17/2022]
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22
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Li R, Cao J. Finite-Time and Fixed-Time Stabilization Control of Delayed Memristive Neural Networks: Robust Analysis Technique. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9689-0] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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23
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Extended dissipative analysis for memristive neural networks with two additive time-varying delay components. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.07.054] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Wei H, Li R, Chen C, Tu Z. Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays. Neural Process Lett 2016. [DOI: 10.1007/s11063-016-9531-0] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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25
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Li R, Cao J, Tu Z. Passivity analysis of memristive neural networks with probabilistic time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.01.035] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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