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Long H, Ci J, Guo Z, Wen S, Huang T. Synchronization of coupled switched neural networks subject to hybrid stochastic disturbances. Neural Netw 2023; 166:459-470. [PMID: 37574620 DOI: 10.1016/j.neunet.2023.07.045] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Revised: 05/29/2023] [Accepted: 07/27/2023] [Indexed: 08/15/2023]
Abstract
In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Han Long
- College of Science, National University of Defense Technology, Changsha 410073, China.
| | - Jingxuan Ci
- School of Mathematics, Hunan University, Changsha 410082, China.
| | - Zhenyuan Guo
- School of Mathematics, Hunan University, Changsha 410082, China.
| | - Shiping Wen
- Centre for Artificial Intelligence, Faculty of Engineering Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia.
| | - Tingwen Huang
- Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar.
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2
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Lu B, Jiang H, Hu C, Abdurahman A, Liu M. Adaptive pinning cluster synchronization of a stochastic reaction-diffusion complex network. Neural Netw 2023; 166:524-540. [PMID: 37579581 DOI: 10.1016/j.neunet.2023.07.034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2023] [Revised: 06/01/2023] [Accepted: 07/26/2023] [Indexed: 08/16/2023]
Abstract
This work aims to achieve cluster synchronization of a complex network by some pinning control strategies. Firstly, the network not only is affected by the reaction-diffusion and the directed coupling phenomena, but also is disturbed by the stochastic noise and Markovian switching. Secondly, switched constant gain pinning, centralized and decentralized adaptive pinning are proposed respectively to realize the cluster synchronization of the considered network. In these adaptive pinning controllers, the control gain and coupling strength can been adjusted automatically while only a part of the nodes are controlled. Thirdly, the target state of cluster synchronization is taken as the average state related to the directed topology of all nodes in the same cluster, and does not need to be given separately as an isolated node. Finally, to verify the theoretical results, some simulations of directed coupled reaction-diffusion neural networks with stochastic noise and Markovian switching are given.
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Affiliation(s)
- Binglong Lu
- School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, Henan, China.
| | - Haijun Jiang
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, Xinjiang, China.
| | - Cheng Hu
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, Xinjiang, China.
| | - Abdujelil Abdurahman
- College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, Xinjiang, China.
| | - Mei Liu
- School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, Henan, China.
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3
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Li JY, Huang YC, Rao HX, Xu Y, Lu R. Finite-time cluster synchronization for complex dynamical networks under FDI attack: A periodic control approach. Neural Netw 2023; 165:228-237. [PMID: 37307666 DOI: 10.1016/j.neunet.2023.04.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Revised: 03/05/2023] [Accepted: 04/10/2023] [Indexed: 06/14/2023]
Abstract
In this paper, the finite-time cluster synchronization problem is addressed for complex dynamical networks (CDNs) with cluster characteristics under false data injection (FDI) attacks. A type of FDI attack is taken into consideration to reflect the data manipulation that controllers in CDNs may suffer. In order to improve the synchronization effect while reducing the control cost, a new periodic secure control (PSC) strategy is proposed in which the set of pinning nodes changes periodically. The aim of this paper is to derive the gains of the periodic secure controller such that the synchronization error of the CDN remains at a certain threshold in finite time with the presence of external disturbances and false control signals simultaneously. Through considering the periodic characteristics of PSC, a sufficient condition is obtained to guarantee the desired cluster synchronization performance, based on which the gains of the periodic cluster synchronization controllers are acquired by resolving an optimization problem proposed in this paper. A numerical case is carried out to validate the cluster synchronization performance of the PSC strategy under cyber attacks.
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Affiliation(s)
- Jun-Yi Li
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, 510006, Guangzhou, China; Pazhou Lab, 510330, Guangzhou, China.
| | - Yang-Cheng Huang
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, 510006, Guangzhou, China.
| | - Hong-Xia Rao
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, 510006, Guangzhou, China.
| | - Yong Xu
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, 510006, Guangzhou, China.
| | - Renquan Lu
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, 510006, Guangzhou, China.
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Li JY, Wang Z, Lu R, Xu Y. Cluster Synchronization Control for Discrete-Time Complex Dynamical Networks: When Data Transmission Meets Constrained Bit Rate. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:2554-2568. [PMID: 34495846 DOI: 10.1109/tnnls.2021.3106947] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
In this article, the cluster synchronization control problem is studied for discrete-time complex dynamical networks when the data transmission is subject to constrained bit rate. A bit-rate model is presented to quantify the limited network bandwidth, and the effects from the constrained bit rate onto the control performance of the cluster synchronization are evaluated. A sufficient condition is first proposed to guarantee the ultimate boundedness of the error dynamics of the cluster synchronization, and then, a bit-rate condition is established to reveal the fundamental relationship between the bit rate and the certain performance index of the cluster synchronization. Subsequently, two optimization problems are formulated to design the desired synchronization controllers with aim to achieve two distinct synchronization performance indices. The codesign issue for the bit-rate allocation protocol and the controller gains is further discussed to reduce the conservatism by locally minimizing a certain asymptotic upper bound of the synchronization error dynamics. Finally, three illustrative simulation examples are utilized to validate the feasibility and effectiveness of the developed synchronization control scheme.
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Song Y, Jiang S, Liu Y, Cai S, Lu X. Uncertainty meets fixed-time control in neural networks. Neurocomputing 2023. [DOI: 10.1016/j.neucom.2022.10.051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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6
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Peng Y, Wang Y, Gao P, Zhang L. The stationarity control of the average links for the Hebb complex dynamical network via external stimulus signals. ISA TRANSACTIONS 2023; 132:338-345. [PMID: 35725668 DOI: 10.1016/j.isatra.2022.06.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2021] [Revised: 06/02/2022] [Accepted: 06/02/2022] [Indexed: 06/15/2023]
Abstract
The model of complex dynamical network (CDN) can be represented as the mathematic graph, in which some characteristics may emerge from the dynamic nodes group (NG) and links group (LG). This paper primarily focuses on the feature appearing from the dynamic links. The average link weight (ALW), as a novel quantitative index to describe the characteristic of dynamic links is introduced. Inspired by the Hebb's neuroscience theory, the Hebb complex dynamical network (HCDN) is constructed. The ALW of the HCDN can track a given target via external stimulus signals with adaptive amplifiers' proportional coefficients. In other words, the stationary network implies the ALW is a constant in time. Finally, two simulation examples are performed to validate the proposed adaptive update law's effectiveness.
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Affiliation(s)
- Yi Peng
- School of Automation, Guangdong University of Technology, Guangzhou, Guangdong 510006, PR China
| | - Yinhe Wang
- School of Automation, Guangdong University of Technology, Guangzhou, Guangdong 510006, PR China
| | - Peitao Gao
- School of Automation, Guangdong University of Technology, Guangzhou, Guangdong 510006, PR China.
| | - Lili Zhang
- School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, Guangdong 510006, PR China
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Qin X, Jiang H, Qiu J, Hu C, Ren Y. Strictly intermittent quantized control for fixed/predefined-time cluster lag synchronization of stochastic multi-weighted complex networks. Neural Netw 2023; 158:258-271. [PMID: 36481458 DOI: 10.1016/j.neunet.2022.10.033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Revised: 08/27/2022] [Accepted: 10/31/2022] [Indexed: 11/21/2022]
Abstract
This article addresses the fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization of stochastic multi-weighted complex networks (SMWCNs) via strictly intermittent quantized control (SIQC). Firstly, by exploiting mathematical induction and reduction to absurdity, a novel F-T stability lemma is proved and an accurate estimation of settling time (ST) is obtained. Subsequently, by virtue of the proposed F-T stability, some simple conditions that ensure the F-T cluster lag synchronization of SMWCNs are derived by developing a SIQC strategy. Furthermore, the P-T cluster lag synchronization is also explored based on a SIQC design, where the ST can be predefined by an adjustable constant of the controller. Note that the designed controllers here are simpler and more economical than the traditional design whose the linear part is still activated during the rest interval. Finally, two numerical examples are provided to verify the effectiveness of the theoretical results.
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Affiliation(s)
- Xuejiao Qin
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China
| | - Haijun Jiang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China.
| | - Jianlong Qiu
- School of Automation and Electrical Engineering, Linyi University, Linyi 276005, PR China
| | - Cheng Hu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China
| | - Yue Ren
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China
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8
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Further Results on Fixed-Time Cluster Synchronization of Coupled Neural Networks. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11081-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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9
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Shi J, Zhou P, Cai S, Jia Q. On finite-/fixed-time synchronization of multi-weighted dynamical networks: a new unified control approach. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07979-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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10
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Zhou W, Sun Y, Zhang X, Shi P. Cluster Synchronization of Coupled Neural Networks With Lévy Noise via Event-Triggered Pinning Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:6144-6157. [PMID: 33886481 DOI: 10.1109/tnnls.2021.3072475] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Cluster synchronization means that all multiagents are divided into different clusters according to the equations or roles of nodes in a complex network, and by designing an appropriate algorithm, each cluster can achieve synchronization to a certain value or an isolated node. However, the synchronization values between different clusters are different. With a feedback controller based on the calculation of the control input value and a trigger condition leading to the updating instants, this article introduces the trigger mechanism and designs a new data sampling strategy to achieve cluster synchronization of the coupled neural networks (CNNs), which reduces the number of updates of the controller, thereby reducing unnecessary waste of limited resources. In addition, an example proposes a synchronization algorithm and gives iterative procedures to calculate the trigger instants and prove the validity of the theoretical results.
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Li H, Cao J, Kashkynbayev A, Cai S. Adaptive dynamic event-triggered cluster synchronization in an array of coupled neural networks subject to cyber-attacks. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.09.047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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12
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Hou M, He Q, Ma Y. Preassigned/fixed-time stochastic synchronization of complex networks via simpler nonchattering quantified adaptive control strategies. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07503-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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13
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Delayed distributed impulsive synchronization of coupled neural networks with mixed couplings. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.07.045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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14
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Yuan W, Shi S, Ma Y. Fixed-time stochastic synchronization of impulsive multi-weighted complex dynamical networks with non-chattering control. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2021.12.031] [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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15
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Dong H, Luo M, Xiao M. Synchronization for stochastic coupled networks with Lévy noise via event-triggered control. Neural Netw 2021; 141:40-51. [PMID: 33862364 DOI: 10.1016/j.neunet.2021.03.028] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2020] [Revised: 02/01/2021] [Accepted: 03/15/2021] [Indexed: 10/21/2022]
Abstract
This paper addresses the realization of almost sure synchronization problem for a new array of stochastic networks associated with delay and Lévy noise via event-triggered control. The coupling structure of the network is governed by a continuous-time homogeneous Markov chain. The nodes in the networks communicate with each other and update their information only at discrete-time instants so that the network workload can be minimized. Under the framework of stochastic process including Markov chain and Lévy process, and the convergence theorem of non-negative semi-martingales, we show that the Markovian coupled networks can achieve the almost sure synchronization by event-triggered control methodology. The results are further extended to the directed topology, where the coupling structure can be asymmetric. Furthermore, we also proved that the Zeno behavior can be excluded under our proposed approach, indicating that our framework is practically feasible. Numerical simulations are provided to demonstrate the effectiveness of the obtained theoretical results.
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Affiliation(s)
- Hailing Dong
- School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China.
| | - Ming Luo
- School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China.
| | - Mingqing Xiao
- Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, USA.
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Finite-time cluster synchronization in complex-variable networks with fractional-order and nonlinear coupling. Neural Netw 2021; 135:212-224. [PMID: 33421899 DOI: 10.1016/j.neunet.2020.12.015] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Revised: 10/31/2020] [Accepted: 12/14/2020] [Indexed: 11/22/2022]
Abstract
This paper is primarily concentrated on finite-time cluster synchronization of fractional-order complex-variable networks with nonlinear coupling by utilizing the non-decomposition method. Firstly, two control strategies are designed which are relevant to complex-valued sign functions. Thereafter, by employing fractional-order stability theory and complex function theory, several criteria are deduced to ensure finite-time cluster synchronization under the framework within a new norm consisting of absolute values for real and imaginary components. Furthermore, the setting time is effectively estimated based on some significant properties of fractional-order Caputo derivation and Mittag-Leffler functions. Lastly, two numerical examples are given to verify the effectiveness of theoretical results.
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17
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Prescribed-time cluster synchronization of uncertain complex dynamical networks with switching via pinning control. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.08.043] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Shao S, Liu X, Cao J. Prespecified-time synchronization of switched coupled neural networks via smooth controllers. Neural Netw 2020; 133:32-39. [PMID: 33125916 DOI: 10.1016/j.neunet.2020.10.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2020] [Revised: 08/18/2020] [Accepted: 10/12/2020] [Indexed: 10/23/2022]
Abstract
This paper considers the prespecified-time synchronization issue of switched coupled neural networks (SCNNs) under some smooth controllers. Different from the traditional finite-time synchronization (FTS), the synchronization time obtained in this paper is independent of control gains, initial values or network topology, which can be pre-set as to the task requirements. Moreover, unlike the existing nonsmooth or even discontinuous FTS control strategies, the new proposed control protocols are fully smooth, which abandon the common fractional power feedbacks or signum functions. Finally, two illustrative examples are provided to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Shao Shao
- Research Center for Complex Networks & Swarm Intelligence, School of Computer Science & Technology, Jiangsu Normal University, Xuzhou 221116, China
| | - Xiaoyang Liu
- Research Center for Complex Networks & Swarm Intelligence, School of Computer Science & Technology, Jiangsu Normal University, Xuzhou 221116, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul, Korea.
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