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Ding Z, Yang L, Ye Y, Li S, Huang Z. Passivity and passification of fractional-order memristive neural networks with time delays. ISA TRANSACTIONS 2023; 137:314-322. [PMID: 36746695 DOI: 10.1016/j.isatra.2023.01.034] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Revised: 12/23/2022] [Accepted: 01/27/2023] [Indexed: 06/04/2023]
Abstract
A class of fractional-order memristive neural networks (FMNNs) with time delays is studied. At first, the original network system is converted to fractional-order uncertain one to simplify the analysis by a variable transformation. Successively, some new LMIs-based passivity criteria are derived by differential inclusions, set-valued maps, inequality techniques and linear matrix inequality approach. Furthermore, a feedback control protocol is designed to solve the passification problem for the considered system, whose feedback control effect on different neurons can be changed artificially, which can be better applied to neural networks. The obtained results include some existing ones as special cases. A numerical example is proposed to illustrate the theoretical results.
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Affiliation(s)
- Zhixia Ding
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Le Yang
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Yanyan Ye
- School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Sai Li
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
| | - Zixin Huang
- School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
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2
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Synchronization analysis and parameters identification of uncertain delayed fractional-order BAM neural networks. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07791-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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3
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Extended analysis on the global Mittag-Leffler synchronization problem for fractional-order octonion-valued BAM neural networks. Neural Netw 2022; 154:491-507. [DOI: 10.1016/j.neunet.2022.07.031] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2022] [Revised: 06/16/2022] [Accepted: 07/26/2022] [Indexed: 11/22/2022]
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4
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Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities. MATHEMATICS 2022. [DOI: 10.3390/math10050835] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for the considered drive-response systems. The inequalities in our paper, applied to obtaining the maximum-valued and designing the novel controllers, are different from those in existing papers.
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5
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Quasi-Synchronization and Complete Synchronization of Fractional-Order Fuzzy BAM Neural Networks Via Nonlinear Control. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10769-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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6
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Sakthivel R, S.A K, Wang C, S K. Finite-time reliable sampled-data control for fractional-order memristive neural networks with quantisation. J EXP THEOR ARTIF IN 2022. [DOI: 10.1080/0952813x.2021.1960626] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- R. Sakthivel
- Department of Applied Mathematics, Bharathiar University, Coimbatore, India
| | - Karthick S.A
- Department of Mathematics, Anna University Regional Campus, Coimbatore, India
| | - Chao Wang
- Department of Mathematics, Yunnan University, Kunming, Yunnan, China
| | - Kanakalakshmi S
- Department of Mathematics, Anna University Regional Campus, Coimbatore, India
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7
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Improved Results on Finite-Time Passivity and Synchronization Problem for Fractional-Order Memristor-Based Competitive Neural Networks: Interval Matrix Approach. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6010036] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This research paper deals with the passivity and synchronization problem of fractional-order memristor-based competitive neural networks (FOMBCNNs) for the first time. Since the FOMBCNNs’ parameters are state-dependent, FOMBCNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, the conventional robust control scheme cannot guarantee the synchronization of FOMBCNNs. Under the framework of the Filippov solution, the drive and response FOMBCNNs are first transformed into systems with interval parameters. Then, the new sufficient criteria are obtained by linear matrix inequalities (LMIs) to ensure the passivity in finite-time criteria for FOMBCNNs with mismatched switching jumps. Further, a feedback control law is designed to ensure the finite-time synchronization of FOMBCNNs. Finally, three numerical cases are given to illustrate the usefulness of our passivity and synchronization results.
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Viera-Martin E, Gómez-Aguilar JF, Solís-Pérez JE, Hernández-Pérez JA, Escobar-Jiménez RF. Artificial neural networks: a practical review of applications involving fractional calculus. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2022; 231:2059-2095. [PMID: 35194484 PMCID: PMC8853315 DOI: 10.1140/epjs/s11734-022-00455-3] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2021] [Accepted: 01/13/2022] [Indexed: 05/13/2023]
Abstract
In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.
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Affiliation(s)
- E. Viera-Martin
- Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos Mexico
| | - J. F. Gómez-Aguilar
- CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos Mexico
| | - J. E. Solís-Pérez
- Escuela Nacional de Estudios Superiores Unidad Juriquilla, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, Juriquilla La Mesa, C.P. 76230 Juriquilla, Querétaro Mexico
| | - J. A. Hernández-Pérez
- Universidad Autónoma del Estado de Morelos/Centro de Investigación en Ingeniería y Ciencias Aplicadas, Av. Universidad No. 1001, Col Chamilpa, C.P. 62209 Cuernavaca, Morelos Mexico
| | - R. F. Escobar-Jiménez
- Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos Mexico
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9
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New criteria on the finite-time stability of fractional-order BAM neural networks with time delay. Neural Comput Appl 2021. [DOI: 10.1007/s00521-021-06605-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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10
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Shi J, Zeng Z. Design of In-Situ Learning Bidirectional Associative Memory Neural Network Circuit With Memristor Synapse. IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2021. [DOI: 10.1109/tetci.2020.3005703] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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11
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Zhang L, Zhong J, Lu J. Intermittent control for finite-time synchronization of fractional-order complex networks. Neural Netw 2021; 144:11-20. [PMID: 34438324 DOI: 10.1016/j.neunet.2021.08.004] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Revised: 07/05/2021] [Accepted: 08/02/2021] [Indexed: 11/17/2022]
Abstract
This paper is concerned with the finite-time synchronization problem for fractional-order complex dynamical networks (FCDNs) with intermittent control. Using the definition of Caputo's fractional derivative and the properties of Beta function, the Caputo fractional-order derivative of the power function is evaluated. A general fractional-order intermittent differential inequality is obtained with fewer additional constraints. Then, the criteria are established for the finite-time convergence of FCDNs under intermittent feedback control, intermittent adaptive control and intermittent pinning control indicate that the setting time is related to order of FCDNs and initial conditions. Finally, these theoretical results are illustrated by numerical examples.
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Affiliation(s)
- Lingzhong Zhang
- School of Electrical Engineering and Automation, Changshu Institute of Technology, Changshu 215500, China
| | - Jie Zhong
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China.
| | - Jianquan Lu
- School of Mathematics, Southeast University, Nanjing 210096, China
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12
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singh A, Rai JN. Stability of Fractional Order Fuzzy Cellular Neural Networks with Distributed Delays via Hybrid Feedback Controllers. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10460-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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13
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Memristor-based BAM circuit implementation for image associative memory and filling-in. Neural Comput Appl 2021. [DOI: 10.1007/s00521-020-05538-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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14
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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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15
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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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16
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Zhang L, Yang Y. Bipartite Synchronization Analysis of Fractional Order Coupled Neural Networks with Hybrid Control. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10332-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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17
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Wang W, Jia X, Wang Z, Luo X, Li L, Kurths J, Yuan M. Fixed-time synchronization of fractional order memristive MAM neural networks by sliding mode control. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.043] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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18
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Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays. MATHEMATICS 2020. [DOI: 10.3390/math8071146] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.
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19
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Bipartite finite time synchronization for general Caputo fractional-order impulsive coupled networks. Neural Comput Appl 2020. [DOI: 10.1007/s00521-020-05135-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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20
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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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21
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Synchronization with general decay rate for memristor-based BAM neural networks with distributed delays and discontinuous activation functions. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.12.124] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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22
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Zhang L, Yang Y. Finite time impulsive synchronization of fractional order memristive BAM neural networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.12.056] [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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23
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Wang Y, Arumugam A, Liu Y, Alsaadi FE. Finite-time event-triggered non-fragile state estimation for discrete-time delayed neural networks with randomly occurring sensor nonlinearity and energy constraints. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.12.038] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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24
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Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays. Neural Process Lett 2020. [DOI: 10.1007/s11063-020-10206-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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25
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Quantized synchronization of memristive neural networks with time-varying delays via super-twisting algorithm. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.11.003] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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26
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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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27
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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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28
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Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays. MATHEMATICS 2019. [DOI: 10.3390/math7080759] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This sequel is concerned with the analysis of projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks (FOMBNNs) with mixed time delays via hybrid controller. Firstly, a new type of hybrid control scheme, which is the combination of open loop control and adaptive state feedback control is designed to guarantee the global projective lag synchronization of the addressed FOMBNNs model. Secondly, by using a Lyapunov–Krasovskii functional and Barbalet’s lemma, a new brand of sufficient criterion is proposed to ensure the projective lag synchronization of the FOMBNNs model considered. Moreover, as special cases by using a hybrid control scheme, some sufficient conditions are derived to ensure the global projective synchronization, global complete synchronization and global anti-synchronization for the FOMBNNs model considered. Finally, numerical simulations are provided to check the accuracy and validity of our obtained synchronization results.
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29
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Chen C, Li L, Peng H, Yang Y, Mi L, Wang L. A new fixed-time stability theorem and its application to the synchronization control of memristive neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.03.040] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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30
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Ding Z, Zeng Z, Zhang H, Wang L, Wang L. New results on passivity of fractional-order uncertain neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.03.042] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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31
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Li X, Zhang W, Fang JA, Li H. Finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.02.051] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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32
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Hu T, He Z, Zhang X, Zhong S. Global synchronization of time-invariant uncertainty fractional-order neural networks with time delay. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.02.020] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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33
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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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34
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Li HL, Cao J, Jiang H, Alsaedi A. Finite-time synchronization of fractional-order complex networks via hybrid feedback control. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.09.021] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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35
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Pratap A, Raja R, Cao J, Rajchakit G, Alsaadi FE. Further synchronization in finite time analysis for time-varying delayed fractional order memristive competitive neural networks with leakage delay. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.08.016] [Citation(s) in RCA: 52] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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36
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Zhang R, Park JH, Zeng D, Liu Y, Zhong S. A new method for exponential synchronization of memristive recurrent neural networks. Inf Sci (N Y) 2018. [DOI: 10.1016/j.ins.2018.07.038] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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37
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Switching event-triggered network-synchronization for chaotic systems with different dimensions. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.05.039] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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38
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Auxiliary function-based integral inequality approach to robust passivity analysis of neural networks with interval time-varying delay. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.04.026] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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39
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Exponential stability criterion of high-order BAM neural networks with delays and impulse via fixed point approach. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.02.081] [Citation(s) in RCA: 8] [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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40
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Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. Neural Netw 2018; 103:128-141. [PMID: 29677558 DOI: 10.1016/j.neunet.2018.03.012] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Revised: 01/28/2018] [Accepted: 03/16/2018] [Indexed: 11/23/2022]
Abstract
Fractional order system is playing an increasingly important role in terms of both theory and applications. In this paper we investigate the global existence of Filippov solutions and the robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. By means of growth conditions, differential inclusions and generalized Gronwall inequality, a sufficient condition for the existence of Filippov solution is obtained. Then, sufficient criteria are given for the robust generalized Mittag-Leffler synchronization between discontinuous activation function of impulsive fractional order neural network systems with (or without) parameter uncertainties, via a delayed feedback controller and M-Matrix theory. Finally, four numerical simulations demonstrate the effectiveness of our main results.
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41
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Yuan M, Luo X, Wang W, Li L, Peng H. Pinning Synchronization of Coupled Memristive Recurrent Neural Networks with Mixed Time-Varying Delays and Perturbations. Neural Process Lett 2018. [DOI: 10.1007/s11063-018-9811-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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42
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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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43
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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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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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45
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Exponential dissipativity criteria for generalized BAM neural networks with variable delays. Neural Comput Appl 2017. [DOI: 10.1007/s00521-017-3224-0] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Sowmiya C, Raja R, Cao J, Rajchakit G, Alsaedi A. Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay. ADVANCES IN DIFFERENCE EQUATIONS 2017; 2017:318. [PMID: 29071005 PMCID: PMC5635139 DOI: 10.1186/s13662-017-1378-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 09/25/2017] [Indexed: 06/07/2023]
Abstract
This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen's inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.
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Affiliation(s)
- C Sowmiya
- Department of Mathematics, Alagappa University, Karaikudi, 630 004 India
| | - R Raja
- Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004 India
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing, 210096 China
| | - G Rajchakit
- Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand
| | - Ahmed Alsaedi
- Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589 Saudi Arabia
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47
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Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays. Neural Netw 2017; 94:46-54. [DOI: 10.1016/j.neunet.2017.06.011] [Citation(s) in RCA: 64] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2016] [Revised: 05/17/2017] [Accepted: 06/22/2017] [Indexed: 11/16/2022]
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Chen C, Li L, Peng H, Yang Y. Finite time synchronization of memristor-based Cohen-Grossberg neural networks with mixed delays. PLoS One 2017; 12:e0185007. [PMID: 28931066 PMCID: PMC5607209 DOI: 10.1371/journal.pone.0185007] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2017] [Accepted: 09/04/2017] [Indexed: 11/18/2022] Open
Abstract
Finite time synchronization, which means synchronization can be achieved in a settling time, is desirable in some practical applications. However, most of the published results on finite time synchronization don't include delays or only include discrete delays. In view of the fact that distributed delays inevitably exist in neural networks, this paper aims to investigate the finite time synchronization of memristor-based Cohen-Grossberg neural networks (MCGNNs) with both discrete delay and distributed delay (mixed delays). By means of a simple feedback controller and novel finite time synchronization analysis methods, several new criteria are derived to ensure the finite time synchronization of MCGNNs with mixed delays. The obtained criteria are very concise and easy to verify. Numerical simulations are presented to demonstrate the effectiveness of our theoretical results.
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Affiliation(s)
- Chuan Chen
- Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Lixiang Li
- Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Haipeng Peng
- Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Yixian Yang
- Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
- State Key Laboratory of Public Big Data, Guizhou 550025, China
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50
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Ding X, Cao J, Zhao X, Alsaadi FE. Mittag-Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes. Proc Math Phys Eng Sci 2017; 473:20170322. [PMID: 28878565 DOI: 10.1098/rspa.2017.0322] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Accepted: 06/30/2017] [Indexed: 11/12/2022] Open
Abstract
This paper is concerned with the drive-response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques. Numerical simulations are presented to validate the proposed methodologies.
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Affiliation(s)
- Xiaoshuai Ding
- School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, People's Republic of China.,School of Education, Xizang Minzu University, Xianyang 712082, People's Republic of China
| | - Jinde Cao
- School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, People's Republic of China.,Department of Mathematics, Faculty of Science, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Xuan Zhao
- School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, People's Republic of China
| | - Fuad E Alsaadi
- Electrical and Computer Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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