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Zhang H, Zeng Z. Adaptive Synchronization of Reaction-Diffusion Neural Networks With Nondifferentiable Delay via State Coupling and Spatial Coupling. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:7555-7566. [PMID: 35100127 DOI: 10.1109/tnnls.2022.3144222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.
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Sheng Y, Zeng Z, Huang T. Finite-Time Stabilization of Competitive Neural Networks With Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:11325-11334. [PMID: 34133310 DOI: 10.1109/tcyb.2021.3082153] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article investigates finite-time stabilization of competitive neural networks with discrete time-varying delays (DCNNs). By virtue of comparison strategies and inequality techniques, finite-time stabilization of the underlying DCNNs is analyzed by designing a discontinuous state feedback controller, which simplifies the controller design and proof processes of some existing results. Meanwhile, global exponential stabilization of the DCNNs is provided under a continuous state feedback controller. In addition, global exponential stability of the DCNNs is shown as an M-matrix, which contains some published outcomes as special cases. Finally, three examples are given to illuminate the validity of the theories.
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3
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Yang W, Wang YW, Morarescu IC, Liu XK, Huang Y. Fixed-Time Synchronization of Competitive Neural Networks With Multiple Time Scales. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:4133-4138. [PMID: 33556017 DOI: 10.1109/tnnls.2021.3052868] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this brief, we investigate the fixed-time synchronization of competitive neural networks with multiple time scales. These neural networks play an important role in visual processing, pattern recognition, neural computing, and so on. Our main contribution is the design of a novel synchronizing controller, which does not depend on the ratio between the fast and slow time scales. This feature makes the controller easy to implement since it is designed through well-posed algebraic conditions (i.e., even when the ratio between the time scales goes to 0, the controller gain is well defined and does not go to infinity). Last but not least, the closed-loop dynamics is characterized by a high convergence speed with a settling time which is upper bounded, and the bound is independent of the initial conditions. A numerical simulation illustrates our results and emphasizes their effectiveness.
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Lag Synchronization of Noisy and Nonnoisy Multiple Neurobiological Coupled FitzHugh–Nagumo Networks with and without Delayed Coupling. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022; 2022:5644875. [PMID: 35694576 PMCID: PMC9184196 DOI: 10.1155/2022/5644875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Revised: 04/15/2022] [Accepted: 04/26/2022] [Indexed: 11/21/2022]
Abstract
This paper presents a methodology for synchronizing noisy and nonnoisy multiple coupled neurobiological FitzHugh–Nagumo (FHN) drive and slave neural networks with and without delayed coupling, under external electrical stimulation (EES), external disturbance, and variable parameters for each state of both FHN networks. Each network of neurons was configured by considering all aspects of real neurons communications in the brain, i.e., synapse and gap junctions. Novel adaptive control laws were developed and proposed that guarantee the synchronization of FHN neural networks in different configurations. The Lyapunov stability theory was utilized to analytically derive the sufficient conditions that ensure the synchronization of the FHN networks. The effectiveness and robustness of the proposed control laws were shown through different numerical simulations.
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Li M, Yang X, Li X. Delayed Impulsive Control for Lag Synchronization of Delayed Neural Networks Involving Partial Unmeasurable States. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; PP:783-791. [PMID: 35648880 DOI: 10.1109/tnnls.2022.3177234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
In the framework of impulsive control, this article deals with the lag synchronization problem of neural networks involving partially unmeasurable states, where the time delay in impulses is fully addressed. Since the complexity of external environment and uncertainty of networks, which may lead to a result that the information of partial states is unmeasurable, the key problem for lag synchronization control is how to utilize the information of measurable states to design suitable impulsive control. By using linear matrix inequality (LMI) and transition matrix method coupled with dimension expansion technique, some sufficient conditions are derived to guarantee lag synchronization, where the requirement for information of all states is needless. Moreover, our proposed conditions not only allow the existence of unmeasurable states but also reduce the restrictions on the number of measurable states, which shows the generality of our results and wide-application in practice. Finally, two illustrative examples and their numerical simulations are presented to demonstrate the effectiveness of main results.
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Wang L, Zhang CK. Exponential Synchronization of Memristor-Based Competitive Neural Networks With Reaction-Diffusions and Infinite Distributed Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; PP:745-758. [PMID: 35622804 DOI: 10.1109/tnnls.2022.3176887] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Taking into account the infinite distributed delays and reaction-diffusions, this article investigates the global exponential synchronization problem of a class of memristor-based competitive neural networks (MCNNs) with different time scales. Based on the Lyapunov-Krasovskii functional and inequality approach, an adaptive control approach is proposed to ensure the exponential synchronization of the addressed drive-response networks. The closed-loop system is a discontinuous and delayed partial differential system in a cascade form, involving the spatial diffusion, the infinite distributed delays, the parametric adaptive law, the state-dependent switching parameters, and the variable structure controllers. By combining the theories of nonsmooth analysis, partial differential equation (PDE) and adaptive control, we present a new analytical method for rigorously deriving the synchronization of the states of the complex system. The derived m-norm (m ≥ 2)-based synchronization criteria are easily verified and the theoretical results are easily extended to memristor-based neural networks (NNs) without different time scales and reaction-diffusions. Finally, numerical simulations are presented to verify the effectiveness of the theoretical results.
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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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8
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Liu X, Yang C, Zhu S. Inverse optimal synchronization control of competitive neural networks with constant time delays. Neural Comput Appl 2022. [DOI: 10.1007/s00521-021-06358-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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9
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Synchronization of Fractional Order Uncertain BAM Competitive Neural Networks. FRACTAL AND FRACTIONAL 2021. [DOI: 10.3390/fractalfract6010014] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Krasovskii functional, novel sufficient conditions are obtained to achieve global asymptotic stability of fractional order uncertain BAM competitive neural networks. This novel approach is based on the linear matrix inequality (LMI) technique and the derived conditions are easy to verify via the LMI toolbox. Moreover, numerical examples are presented to show the feasibility and effectiveness of the theoretical results.
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10
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Zhang F, Huang T, Wu Q, Zeng Z. Multistability of delayed fractional-order competitive neural networks. Neural Netw 2021; 140:325-335. [PMID: 33895556 DOI: 10.1016/j.neunet.2021.03.036] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Revised: 02/27/2021] [Accepted: 03/24/2021] [Indexed: 10/21/2022]
Abstract
This paper is concerned with the multistability of fractional-order competitive neural networks (FCNNs) with time-varying delays. Based on the division of state space, the equilibrium points (EPs) of FCNNs are given. Several sufficient conditions and criteria are proposed to ascertain the multiple O(t-α)-stability of delayed FCNNs. The O(t-α)-stability is the extension of Mittag-Leffler stability of fractional-order neural networks, which contains monostability and multistability. Moreover, the attraction basins of the stable EPs of FCNNs are estimated, which shows the attraction basins of the stable EPs can be larger than the divided subsets. These conditions and criteria supplement and improve the previous results. Finally, the results are illustrated by the simulation examples.
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Affiliation(s)
- Fanghai Zhang
- School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, China.
| | - Tingwen Huang
- Science Program, Texas A&M University at Qatar, Doha, Qatar.
| | - Qiujie Wu
- School of Internet, Anhui University, Hefei, China.
| | - Zhigang Zeng
- School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, China.
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11
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Rajchakit G, Chanthorn P, Niezabitowski M, Raja R, Baleanu D, Pratap A. Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.07.036] [Citation(s) in RCA: 44] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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12
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Shi J, Zeng Z. Global exponential stabilization and lag synchronization control of inertial neural networks with time delays. Neural Netw 2020; 126:11-20. [PMID: 32172041 DOI: 10.1016/j.neunet.2020.03.006] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Revised: 03/03/2020] [Accepted: 03/05/2020] [Indexed: 11/25/2022]
Abstract
The global exponential stabilization and lag synchronization control of delayed inertial neural networks (INNs) are investigated. By constructing nonnegative function and employing inequality techniques, several new results about exponential stabilization and exponential lag synchronization are derived via adaptive control. And the theoretical outcomes are developed directly from the INNs themselves without variable substitution. In addition, the synchronization results are also applied to image encryption and decryption. Finally, an example is presented to illustrate the validity of the derived results.
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Affiliation(s)
- Jichen Shi
- School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China
| | - Zhigang Zeng
- School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China.
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13
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Fixed-time synchronization of competitive neural networks with proportional delays and impulsive effect. Neural Comput Appl 2019. [DOI: 10.1007/s00521-019-04654-3] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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14
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Zhao X, Zhou J, Lu JA. Pinning Synchronization of Multiplex Delayed Networks With Stochastic Perturbations. IEEE TRANSACTIONS ON CYBERNETICS 2019; 49:4262-4270. [PMID: 30130248 DOI: 10.1109/tcyb.2018.2861822] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
As the monoplex network has its limitations in describing the real world, a new framework called the multiplex network is put forward and has received much attention in recent years. This paper focuses on synchronization of the multiplex network with multiple delays and stochastic perturbations. Due to the complexity, pinning control of the multiplex network is of particular interest. Based on the LaSalle-type invariance principle for stochastic differential delay equations and the Lyapunov stability theory, some control schemes and synchronization criteria are obtained. It is concluded that under some mild conditions, one can determine which nodes should be pinned in a multiplex network. In addition, it is found that the number of pinned nodes increases with the varying interval of noise and time delay, and decreases with the varying interval of intralayer coupling strength. Some two-layer and three-layer networks are employed to validate the effectiveness of the proposed algorithm.
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Chen H, Shi P, Lim CC. Cluster Synchronization for Neutral Stochastic Delay Networks via Intermittent Adaptive Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2019; 30:3246-3259. [PMID: 30794189 DOI: 10.1109/tnnls.2018.2890269] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This paper studies the problem of cluster synchronization at exponential rates in both the mean square and almost sure senses for neutral stochastic coupled neural networks with time-varying delay via a periodically intermittent pinning adaptive control strategy. The network topology can be symmetric or asymmetric, with each network node being described by neutral stochastic delayed neural networks. When considering the exponential stabilization in the mean square sense for neutral stochastic delay system, the delay integral inequality approach is used to circumvent the obstacle arising from the coexistence of random disturbance, neutral item, and time-varying delay. The almost surely exponential stabilization is also analyzed with the nonnegative semimartingale convergence theorem. Sufficient criteria on cluster synchronization at exponential rates in both the mean square and almost sure senses of the underlying networks under the designed control scheme are derived. The effectiveness of the obtained theoretical results is illustrated by two examples.
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16
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Gong S, Guo Z, Wen S, Huang T. Synchronization control for memristive high-order competitive neural networks with time-varying delay. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.06.049] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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17
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Lian HH, Xiao SP, Wang Z, Zhang XH, Xiao HQ. Further results on sampled-data synchronization control for chaotic neural networks with actuator saturation. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.08.090] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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18
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Duan L, Zhang M, Zhao Q. Finite-time synchronization of delayed competitive neural networks with different time scales. JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2019. [DOI: 10.1080/02522667.2018.1453670] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Lian Duan
- School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Anhui 232001, China
- School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China
| | - Mengmeng Zhang
- School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Anhui 232001, China
| | - Qianjin Zhao
- School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, Anhui 232001, China
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19
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Nonlinear optimal control for the synchronization of biological neurons under time-delays. Cogn Neurodyn 2018; 13:89-103. [PMID: 30728873 DOI: 10.1007/s11571-018-9510-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2018] [Revised: 08/26/2018] [Accepted: 10/01/2018] [Indexed: 10/28/2022] Open
Abstract
The article proposes a nonlinear optimal control method for synchronization of neurons that exhibit nonlinear dynamics and are subject to time-delays. The model of the Hindmarsh-Rose (HR) neurons is used as a case study. The dynamic model of the coupled HR neurons undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure relies on Taylor series expansion of the model and on computation of the associated Jacobian matrices. For the approximately linearized model of the coupled HR neurons an H-infinity controller is designed. For the selection of the controller's feedback gain an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The stability properties of the control loop are proven through Lyapunov analysis. First, it is shown that the H-infinity tracking performance criterion is satisfied. Moreover, it is proven that the control loop is globally asymptotically stable.
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20
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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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21
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Gong S, Yang S, Guo Z, Huang T. Global Exponential Synchronization of Memristive Competitive Neural Networks with Time-Varying Delay via Nonlinear Control. Neural Process Lett 2018. [DOI: 10.1007/s11063-017-9777-1] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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22
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Liu Z. Design of nonlinear optimal control for chaotic synchronization of coupled stochastic neural networks via Hamilton-Jacobi-Bellman equation. Neural Netw 2018; 99:166-177. [PMID: 29427843 DOI: 10.1016/j.neunet.2018.01.003] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Revised: 01/12/2018] [Accepted: 01/16/2018] [Indexed: 10/18/2022]
Abstract
This paper presents a new theoretical design of nonlinear optimal control on achieving chaotic synchronization for coupled stochastic neural networks. To obtain an optimal control law, the proposed approach is developed rigorously by using Hamilton-Jacobi-Bellman (HJB) equation, Lyapunov technique, and inverse optimality, and hence guarantees that the chaotic drive network synchronizes with the chaotic response network influenced by uncertain noise signals. Furthermore, the paper provides four numerical examples to demonstrate the effectiveness of the proposed approach.
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Affiliation(s)
- Ziqian Liu
- Department of Engineering, State University of New York Maritime College, 6 Pennyfield Avenue, Throggs Neck, NY 10465, USA.
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23
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Zhu X, Yang X, Alsaadi FE, Hayat T. Fixed-Time Synchronization of Coupled Discontinuous Neural Networks with Nonidentical Perturbations. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9770-8] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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24
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Sampled-data synchronization control for chaotic neural networks subject to actuator saturation. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2017.02.063] [Citation(s) in RCA: 97] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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25
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Chen H, Shi P, Lim CC. Exponential Synchronization for Markovian Stochastic Coupled Neural Networks of Neutral-Type via Adaptive Feedback Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:1618-1632. [PMID: 27093709 DOI: 10.1109/tnnls.2016.2546962] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this paper, we investigate the adaptive exponential synchronization in both the mean square and the almost sure senses for an array of N identical Markovian stochastic coupled neural networks of neutral-type with time-varying delay and random coupling strength. The generalized Lyapunov theorem of the exponential stability in the mean square for the neutral stochastic Markov system with the time-varying delay is first established. The time-varying delay in the system is assumed to be a bounded measurable function. Then, sufficient conditions to guarantee the exponential synchronization in the mean square for the underlying system are developed under an adaptive feedback controller, which are given in terms of the M -matrix and the algebraic inequalities. Under the same conditions, the almost sure exponential synchronization is also presented. A numerical example is given to show the effectiveness and potential of the proposed theoretical results.
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26
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Adaptive Synchronization of Stochastic Memristor-Based Neural Networks with Mixed Delays. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9623-5] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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27
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Hu J, Zeng C. Adaptive exponential synchronization of complex-valued Cohen–Grossberg neural networks with known and unknown parameters. Neural Netw 2017; 86:90-101. [DOI: 10.1016/j.neunet.2016.11.001] [Citation(s) in RCA: 54] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2016] [Revised: 09/24/2016] [Accepted: 11/04/2016] [Indexed: 11/25/2022]
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28
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Yang X, Feng Z, Feng J, Cao J. Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw 2017; 85:157-164. [DOI: 10.1016/j.neunet.2016.10.006] [Citation(s) in RCA: 58] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2016] [Revised: 09/05/2016] [Accepted: 10/21/2016] [Indexed: 10/20/2022]
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29
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Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhao H. Parameters estimation and synchronization of uncertain coupling recurrent dynamical neural networks with time-varying delays based on adaptive control. Neural Comput Appl 2016. [DOI: 10.1007/s00521-016-2822-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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30
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Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control. Neural Netw 2016; 84:67-79. [DOI: 10.1016/j.neunet.2016.08.009] [Citation(s) in RCA: 50] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2016] [Revised: 08/16/2016] [Accepted: 08/23/2016] [Indexed: 11/17/2022]
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31
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Cai Z, Huang L, Zhang L. New conditions on synchronization of memristor-based neural networks via differential inclusions. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.12.084] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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32
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Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.11.094] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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33
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Shen W, Zeng Z, Wen S. Synchronization of complex dynamical network with piecewise constant argument of generalized type. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.08.014] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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34
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Zhou L, Zhao Z. Exponential stability of a class of competitive neural networks with multi-proportional delays. Neural Process Lett 2015. [DOI: 10.1007/s11063-015-9486-6] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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35
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Hu HX, Yu W, Xuan Q, Yu L, Xie G. Consensus of multi-agent systems in the cooperation–competition network with inherent nonlinear dynamics: A time-delayed control approach. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.01.059] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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36
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Cai Z, Huang L, Zhang L. New exponential synchronization criteria for time-varying delayed neural networks with discontinuous activations. Neural Netw 2015; 65:105-14. [DOI: 10.1016/j.neunet.2015.02.001] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2014] [Revised: 11/22/2014] [Accepted: 02/01/2015] [Indexed: 11/25/2022]
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37
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38
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Wu ZG, Shi P, Su H, Chu J. Local synchronization of chaotic neural networks with sampled-data and saturating actuators. IEEE TRANSACTIONS ON CYBERNETICS 2014; 44:2635-2645. [PMID: 24710840 DOI: 10.1109/tcyb.2014.2312004] [Citation(s) in RCA: 68] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
This paper investigates the problem of local synchronization of chaotic neural networks with sampled-data and actuator saturation. A new time-dependent Lyapunov functional is proposed for the synchronization error systems. The advantage of the constructed Lyapunov functional lies in the fact that it is positive definite at sampling times but not necessarily between sampling times, and makes full use of the available information about the actual sampling pattern. A local stability condition of the synchronization error systems is derived, based on which a sampled-data controller with respect to the actuator saturation is designed to ensure that the master neural networks and slave neural networks are locally asymptotically synchronous. Two optimization problems are provided to compute the desired sampled-data controller with the aim of enlarging the set of admissible initial conditions or the admissible sampling upper bound ensuring the local synchronization of the considered chaotic neural networks. A numerical example is used to demonstrate the effectiveness of the proposed design technique.
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Shi Y, Zhu P. Synchronization of Stochastic Competitive Neural Networks with Different Timescales and Reaction-Diffusion Terms. Neural Comput 2014; 26:2005-24. [DOI: 10.1162/neco_a_00629] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
We propose a feedback controller for the synchronization of stochastic competitive neural networks with different timescales and reaction-diffusion terms. By constructing a proper Lyapunov-Krasovskii functional, as well as employing stochastic analysis theory, the LaShall-type invariance principle for stochastic differential delay equations, and a linear matrix inequality (LMI) technique, a feedback controller is designed to achieve the asymptotical synchronization of coupled stochastic competitive neural networks. A simulation example is given to show the effectiveness of the theoretical results.
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Affiliation(s)
- Yanchao Shi
- School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Peiyong Zhu
- School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China
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Shi Y, Zhu P. Synchronization of memristive competitive neural networks with different time scales. Neural Comput Appl 2014. [DOI: 10.1007/s00521-014-1598-9] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Wu H, Zhang X, Li R, Yao R. Adaptive exponential synchronization of delayed Cohen–Grossberg neural networks with discontinuous activations. INT J MACH LEARN CYB 2014. [DOI: 10.1007/s13042-014-0258-9] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Yang X, Cao J, Yu W. Exponential synchronization of memristive Cohen-Grossberg neural networks with mixed delays. Cogn Neurodyn 2014; 8:239-49. [PMID: 24808932 DOI: 10.1007/s11571-013-9277-6] [Citation(s) in RCA: 120] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2013] [Revised: 11/19/2013] [Accepted: 12/24/2013] [Indexed: 10/25/2022] Open
Abstract
This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen-Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen-Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.
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Affiliation(s)
- Xinsong Yang
- Department of Mathematics, Chongqing Normal University, Chongqing, 401331 China
| | - Jinde Cao
- Department of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096 China ; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jidda, 21589 Saudi Arabia
| | - Wenwu Yu
- Department of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096 China ; School of Electrical and Computer Engineering, RMIT University, Melbourne, VIC 3001 Australia
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Nie X, Cao J, Fei S. Multistability and instability of delayed competitive neural networks with nondecreasing piecewise linear activation functions. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2013.03.030] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Yang X, Cao J, Lu J. Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2012; 23:60-71. [PMID: 24808456 DOI: 10.1109/tnnls.2011.2177671] [Citation(s) in RCA: 76] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In this paper, a general model of coupled neural networks with Markovian jumping and random coupling strengths is introduced. In the process of evolution, the proposed model switches from one mode to another according to a Markovian chain, and all the modes have different constant time-delays. The coupling strengths are characterized by mutually independent random variables. When compared with most of existing dynamical network models which share common time-delay for all modes and have constant coupling strengths, our model is more practical because different chaotic neural network models can have different time-delays and coupling strength of complex networks may randomly vary around a constant due to environmental and artificial factors. By designing a novel Lyapunov functional and using some inequalities and the properties of random variables, we derive several new sufficient synchronization criteria formulated by linear matrix inequalities. The obtained criteria depend on mode-delays and mathematical expectations and variances of the random coupling strengths as well. Numerical examples are given to demonstrate the effectiveness of the theoretical results, meanwhile right-continuous Markovian chain is also presented.
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Yan-Wu Wang, Jiang-Wen Xiao, Changyun Wen, Zhi-Hong Guan. Synchronization of Continuous Dynamical Networks With Discrete-Time Communications. ACTA ACUST UNITED AC 2011; 22:1979-86. [DOI: 10.1109/tnn.2011.2171501] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Rădac MB, Precup RE, Petriu EM, Preitl S. Application of IFT and SPSA to servo system control. IEEE TRANSACTIONS ON NEURAL NETWORKS 2011; 22:2363-2375. [PMID: 22086492 DOI: 10.1109/tnn.2011.2173804] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
This paper treats the application of two data-based model-free gradient-based stochastic optimization techniques, i.e., iterative feedback tuning (IFT) and simultaneous perturbation stochastic approximation (SPSA), to servo system control. The representative case of controlled processes modeled by second-order systems with an integral component is discussed. New IFT and SPSA algorithms are suggested to tune the parameters of the state feedback controllers with an integrator in the linear-quadratic-Gaussian (LQG) problem formulation. An implementation case study concerning the LQG-based design of an angular position controller for a direct current servo system laboratory equipment is included to highlight the pros and cons of IFT and SPSA from an application's point of view. The comparison of IFT and SPSA algorithms is focused on an insight into their implementation.
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Affiliation(s)
- Mircea-Bogdan Rădac
- Department of Automation and Applied Informatics, Politehnica University of Timisoara, Timisoara 300223, Romania.
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