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Chen L, Li B, Zhang R, Luo J, Wen C, Zhong S. State estimation for memristive neural networks with mixed time-varying delays via multiple integral equality. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.06.044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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2
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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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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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4
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Wang L, Zeng Z, Ge MF, Hu J. Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays. Neural Netw 2018; 105:65-74. [DOI: 10.1016/j.neunet.2018.04.014] [Citation(s) in RCA: 59] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Revised: 04/08/2018] [Accepted: 04/20/2018] [Indexed: 12/01/2022]
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5
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Wang J, Jiang H, Ma T, Hu C. Delay-dependent dynamical analysis of complex-valued memristive neural networks: Continuous-time and discrete-time cases. Neural Netw 2018; 101:33-46. [DOI: 10.1016/j.neunet.2018.01.015] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2017] [Revised: 12/21/2017] [Accepted: 01/30/2018] [Indexed: 11/29/2022]
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Wan L, Wu A. Multistability in Mittag-Leffler sense of fractional-order neural networks with piecewise constant arguments. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.01.049] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Wan P, Jian J. Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays. ISA TRANSACTIONS 2018; 74:88-98. [PMID: 29455890 DOI: 10.1016/j.isatra.2018.02.002] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Revised: 12/18/2017] [Accepted: 02/04/2018] [Indexed: 06/08/2023]
Abstract
This paper focuses on delay-dependent passivity analysis for a class of memristive impulsive inertial neural networks with time-varying delays. By choosing proper variable transformation, the memristive inertial neural networks can be rewritten as first-order differential equations. The memristive model presented here is regarded as a switching system rather than employing the theory of differential inclusion and set-value map. Based on matrix inequality and Lyapunov-Krasovskii functional method, several delay-dependent passivity conditions are obtained to ascertain the passivity of the addressed networks. In addition, the results obtained here contain those on the passivity for the addressed networks without impulse effects as special cases and can also be generalized to other neural networks with more complex pulse interference. Finally, one numerical example is presented to show the validity of the obtained results.
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Affiliation(s)
- Peng Wan
- 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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Finite-time stability for memristor based switched neural networks with time-varying delays via average dwell time approach. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.10.003] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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9
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Wang J, Liu F, Qin S. Global exponential stability of uncertain memristor-based recurrent neural networks with mixed time delays. INT J MACH LEARN CYB 2017. [DOI: 10.1007/s13042-017-0759-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Wang L, Shen Y, Zhang G. Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:2648-2659. [PMID: 28113640 DOI: 10.1109/tnnls.2016.2598598] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.
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Affiliation(s)
- Leimin Wang
- School of Automation, China University of Geosciences, Wuhan, China
| | - Yi Shen
- School of Automation, Huazhong University of Science and Technology, Wuhan, China
| | - Guodong Zhang
- College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, China
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Wen S, Zeng Z, Chen MZQ, Huang T. Synchronization of Switched Neural Networks With Communication Delays via the Event-Triggered Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:2334-2343. [PMID: 27429449 DOI: 10.1109/tnnls.2016.2580609] [Citation(s) in RCA: 68] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper addresses the issue of synchronization of switched delayed neural networks with communication delays via event-triggered control. For synchronizing coupled switched neural networks, we propose a novel event-triggered control law which could greatly reduce the number of control updates for synchronization tasks of coupled switched neural networks involving embedded microprocessors with limited on-board resources. The control signals are driven by properly defined events, which depend on the measurement errors and current-sampled states. By using a delay system method, a novel model of synchronization error system with delays is proposed with the communication delays and event-triggered control in the unified framework for coupled switched neural networks. The criteria are derived for the event-triggered synchronization analysis and control synthesis of switched neural networks via the Lyapunov-Krasovskii functional method and free weighting matrix approach. A numerical example is elaborated on to illustrate the effectiveness of the derived results.
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Wang X, She K, Zhong S, Cheng J. Exponential synchronization of memristor-based neural networks with time-varying delay and stochastic perturbation. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.02.059] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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13
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Liu D, Zhu S, Chang W. Input-to-state stability of memristor-based complex-valued neural networks with time delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.09.075] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Wang Z, Ding S, Huang Z, Zhang H. Exponential Stability and Stabilization of Delayed Memristive Neural Networks Based on Quadratic Convex Combination Method. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2016; 27:2337-2350. [PMID: 26513808 DOI: 10.1109/tnnls.2015.2485259] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper is concerned with the exponential stability and stabilization of memristive neural networks (MNNs) with delays. First, we present some generalized double-integral inequalities, which include some existing inequalities as their special cases. Second, combining with quadratic convex combination method, these double-integral inequalities are employed to formulate a delay-dependent stability condition for MNNs with delays. Third, a state-dependent switching control law is obtained for MNNs with delays based on the proposed stability conditions. The desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples.
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Han X, Wu H, Fang B. Adaptive exponential synchronization of memristive neural networks with mixed time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.11.103] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Anbuvithya R, Mathiyalagan K, Sakthivel R, Prakash P. Passivity of memristor-based BAM neural networks with different memductance and uncertain delays. Cogn Neurodyn 2016; 10:339-51. [PMID: 27468321 DOI: 10.1007/s11571-016-9385-1] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2015] [Accepted: 04/13/2016] [Indexed: 11/30/2022] Open
Abstract
This paper addresses the passivity problem for a class of memristor-based bidirectional associate memory (BAM) neural networks with uncertain time-varying delays. In particular, the proposed memristive BAM neural networks is formulated with two different types of memductance functions. By constructing proper Lyapunov-Krasovskii functional and using differential inclusions theory, a new set of sufficient condition is obtained in terms of linear matrix inequalities which guarantee the passivity criteria for the considered neural networks. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.
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Affiliation(s)
- R Anbuvithya
- Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620 015 India
| | - K Mathiyalagan
- Department of Mathematics, Anna University-Regional Centre, Coimbatore, 641 047 India
| | - R Sakthivel
- Department of Mathematics, Sri Ramakrishna Institute of Technology, Coimbatore, 641 010 Tamil Nadu India ; Department of Mathematics, Sungkyunkwan University, Suwon, 440-746 The Republic of Korea
| | - P Prakash
- Department of Mathematics, Periyar University, Salem, 636 011 India
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Finite-time robust stabilization of uncertain delayed neural networks with discontinuous activations via delayed feedback control. Neural Netw 2016; 76:46-54. [DOI: 10.1016/j.neunet.2016.01.005] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2015] [Revised: 12/17/2015] [Accepted: 01/13/2016] [Indexed: 11/18/2022]
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Wu A, Zeng Z, Song X. Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.11.055] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Mathiyalagan K, Anbuvithya R, Sakthivel R, Park JH, Prakash P. Non-fragile H∞ synchronization of memristor-based neural networks using passivity theory. Neural Netw 2016; 74:85-100. [DOI: 10.1016/j.neunet.2015.11.005] [Citation(s) in RCA: 110] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2015] [Revised: 10/20/2015] [Accepted: 11/06/2015] [Indexed: 11/16/2022]
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A new delay-independent condition for global robust stability of neural networks with time delays. Neural Netw 2015; 66:131-7. [DOI: 10.1016/j.neunet.2015.03.004] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2015] [Revised: 02/15/2015] [Accepted: 03/03/2015] [Indexed: 11/17/2022]
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