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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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2
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Intermittent Control Based Exponential Synchronization of Inertial Neural Networks with Mixed Delays. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10574-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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3
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Fei K, Jiang M, Zhang Y. Global dissipativity and finite-time synchronization of mixed time-varying delayed memristor-based neural networks with discontinuous activations. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-191397] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In this paper, the matters of dissipativity and finite time synchronization for memristor-based neural networks (MNNs) with mixed time-varying discontinuities are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. Then, the global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, some novel sufficient conditions are introduced to guarantee the finite-time synchronization of the drive-response MNNs based on a simple Lyapunov function and two different feedback controllers. Finally, several numerical examples are given to verify the validity of the theoretical results.
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Affiliation(s)
- Kaifang Fei
- Institute of Nonlinear Complex Systems, China Three Gorges University, YiChang, Hubei, China
- Three Gorges Mathematical Research Center, China Three Gorges University, China
| | - Minghui Jiang
- Institute of Nonlinear Complex Systems, China Three Gorges University, YiChang, Hubei, China
- Three Gorges Mathematical Research Center, China Three Gorges University, China
| | - Yadan Zhang
- Institute of Nonlinear Complex Systems, China Three Gorges University, YiChang, Hubei, China
- Three Gorges Mathematical Research Center, China Three Gorges University, China
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Wang L, Wu J, Wang X. Finite-Time Stabilization of Memristive Neural Networks with Time Delays. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10390-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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5
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Finite-time synchronization of memristor neural networks via interval matrix method. Neural Netw 2020; 127:7-18. [PMID: 32305714 DOI: 10.1016/j.neunet.2020.04.003] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Revised: 03/17/2020] [Accepted: 04/02/2020] [Indexed: 11/23/2022]
Abstract
In this paper, the finite-time synchronization problems of two types of driven-response memristor neural networks (MNNs) without time-delay and with time-varying delays are investigated via interval matrix method, respectively. Based on interval matrix transformation, the driven-response MNNs are transformed into a kind of system with interval parameters, which is different from the previous research approaches. Several sufficient conditions in terms of linear matrix inequalities (LMIs) are driven to guarantee finite-time synchronization for MNNs. Correspondingly, two types of nonlinear feedback controllers are designed. Meanwhile, the upper-bounded of the settling time functions are estimated. Finally, two numerical examples with simulations are given to illustrate the correctness of the theoretical results and the effectiveness of the proposed controllers.
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Bao H, Park JH, Cao J. Non-fragile state estimation for fractional-order delayed memristive BAM neural networks. NEURAL NETWORKS : THE OFFICIAL JOURNAL OF THE INTERNATIONAL NEURAL NETWORK SOCIETY 2019. [PMID: 31446237 DOI: 10.1016/j.amc.2018.08.031] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
This paper deals with the non-fragile state estimation problem for a class of fractional-order memristive BAM neural networks (FMBAMNNs) with and without time delays for the first time. By means of a novel transformation and interval matrix approach, non-fragile estimators are designed and parameter mismatch problem is averted. Sufficient criteria are established to ascertain the error system is asymptotically stable based on fractional-order Lyapunov functionals and linear matrix inequalities (LMIs). Two examples are put forward to show the effectiveness of the obtained results.
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Affiliation(s)
- Haibo Bao
- School of Mathematics and Statistics, Southwest University, Chongqing 400715, China.
| | - Ju H Park
- Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan 38541, Republic of Korea.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China.
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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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Zhou L. Delay-dependent and delay-independent passivity of a class of recurrent neural networks with impulse and multi-proportional delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.04.076] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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9
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Exponential synchronization of memristor-based recurrent neural networks with multi-proportional delays. Neural Comput Appl 2018. [DOI: 10.1007/s00521-018-3569-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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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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11
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New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays. Neural Netw 2018; 97:183-191. [DOI: 10.1016/j.neunet.2017.10.003] [Citation(s) in RCA: 106] [Impact Index Per Article: 17.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2017] [Revised: 08/05/2017] [Accepted: 10/12/2017] [Indexed: 11/17/2022]
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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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Su L, Zhou L. Passivity of memristor-based recurrent neural networks with multi-proportional delays. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.05.064] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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14
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Li R, Cao J, Alsaedi A, Hayat T. Non-fragile state observation for delayed memristive neural networks: Continuous-time case and discrete-time case. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.03.039] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Li N, Cao J, Alsaedi A, Alsaadi F. Lag Synchronization Criteria for Memristor-Based Coupled Neural Networks via Parameter Mismatches Analysis Approach. Neural Comput 2017; 29:1721-1744. [DOI: 10.1162/neco_a_00918] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
This letter focuses on lag synchronization control analysis for memristor-based coupled neural networks with parameter mismatches. Due to the parameter mismatches, lag complete synchronization in general cannot be achieved. First, based on the [Formula: see text]-measure method, generalized Halanay inequality, together with control algorithms, some sufficient conditions are obtained to ensure that coupled memristor-based neural networks are in a state of lag synchronization with an error. Moreover, the error level is estimated. Second, we show that memristor-based coupled neural networks with parameter mismatches can reach lag complete synchronization under a discontinuous controller. Finally, two examples are given to illustrate the effectiveness of the proposed criteria and well support theoretical results.
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Affiliation(s)
- Ning Li
- College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, Henan, China
| | - Jinde Cao
- School of Mathematics, and Research Center for Complex Systems and Network Sciences Southeast University, Nanjing 210096, China, and Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Ahmed Alsaedi
- Nonlinear Analysis and Applied Mathematics Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Fuad Alsaadi
- Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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Wang Z, Xu Y, Lu R, Peng H. Finite-Time State Estimation for Coupled Markovian Neural Networks With Sensor Nonlinearities. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:630-638. [PMID: 26552097 DOI: 10.1109/tnnls.2015.2490168] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper investigates the issue of finite-time state estimation for coupled Markovian neural networks subject to sensor nonlinearities, where the Markov chain with partially unknown transition probabilities is considered. A Luenberger-type state estimator is proposed based on incomplete measurements, and the estimation error system is derived by using the Kronecker product. By using the Lyapunov method, sufficient conditions are established, which guarantee that the estimation error system is stochastically finite-time bounded and stochastically finite-time stable, respectively. Then, the estimator gains are obtained via solving a set of coupled linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed new design method.
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17
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Improved exponential convergence result for generalized neural networks including interval time-varying delayed signals. Neural Netw 2017; 86:10-17. [DOI: 10.1016/j.neunet.2016.10.009] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Revised: 09/06/2016] [Accepted: 10/27/2016] [Indexed: 11/23/2022]
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18
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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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19
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Huang C, Cao J, Cao J. Stability analysis of switched cellular neural networks: A mode-dependent average dwell time approach. Neural Netw 2016; 82:84-99. [DOI: 10.1016/j.neunet.2016.07.009] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Revised: 06/07/2016] [Accepted: 07/18/2016] [Indexed: 11/29/2022]
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Radhika T, Nagamani G. Dissipativity analysis of stochastic memristor-based recurrent neural networks with discrete and distributed time-varying delays. NETWORK (BRISTOL, ENGLAND) 2016; 27:237-267. [PMID: 27385193 DOI: 10.1080/0954898x.2016.1196834] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this paper, based on the knowledge of memristor-based recurrent neural networks (MRNNs), the model of the stochastic MRNNs with discrete and distributed delays is established. In real nervous systems and in the implementation of very large-scale integration (VLSI) circuits, noise is unavoidable, which leads to the stochastic model of the MRNNs. In this model, the delay interval is decomposed into two subintervals by using the tuning parameter α such that 0 < α < 1. By constructing proper Lyapunov-Krasovskii functional and employing direct delay decomposition technique, several sufficient conditions are given to guarantee the dissipativity and passivity of the stochastic MRNNs with discrete and distributed delays in the sense of Filippov solutions. Using the stochastic analysis theory and Itô's formula for stochastic differential equations, we establish sufficient conditions for dissipativity criterion. The dissipativity and passivity conditions are presented in terms of linear matrix inequalities, which can be easily solved by using Matlab Tools. Finally, three numerical examples with simulations are presented to demonstrate the effectiveness of the theoretical results.
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Affiliation(s)
- Thirunavukkarasu Radhika
- a Department of Mathematics , Gandhigram Rural Institute - Deemed University , Gandhigram , Tamil Nadu , India
| | - Gnaneswaran Nagamani
- a Department of Mathematics , Gandhigram Rural Institute - Deemed University , Gandhigram , Tamil Nadu , India
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21
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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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22
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Syed Ali M, Saravanakumar R, Cao J. New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.07.101] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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23
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Jiang P, Zeng Z, Chen J. Almost periodic solutions for a memristor-based neural networks with leakage, time-varying and distributed delays. Neural Netw 2015; 68:34-45. [DOI: 10.1016/j.neunet.2015.04.005] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2014] [Revised: 02/10/2015] [Accepted: 04/14/2015] [Indexed: 11/28/2022]
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