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Chen H, Wang Y, Liu C, Xiao Z, Tao J. Finite-time synchronization for coupled neural networks with time-delay jumping coupling. ISA Trans 2024; 147:13-21. [PMID: 38272709 DOI: 10.1016/j.isatra.2024.01.022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Revised: 12/20/2023] [Accepted: 01/20/2024] [Indexed: 01/27/2024]
Abstract
The finite-time synchronization problem is studied for coupled neural networks (CNNs) with time-delay jumping coupling. Markovian switching topologies, imprecise delay models, uncertain parameters and the unavailable of topology modes are considered in this work. A mode-dependent delay with pre-known conditional probability is built to handle the imprecise delay model problem. A hidden Markov model with uncertain parameters is introduced to describe the mode mismatch problem, and an asynchronous controller is designed. Besides, a set of Bernoulli processes models the random packet dropouts during data communication. Based on Markovian switching topologies, mode-dependent delays, uncertain probabilities and packet dropout, a sufficient condition that guarantees the CNNs reach finite-time synchronization (FTS) is derived. Finally, a numerical example is derived to demonstrate the efficiency of the proposed synchronous technique.
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Affiliation(s)
- Hui Chen
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Yiman Wang
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Chang Liu
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China; Pazhou Lab, Guangzhou 510330, China.
| | - Zijing Xiao
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
| | - Jie Tao
- Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
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2
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Wei A, Yao Z, Zhang Y, Wang K. Finite-time synchronization of delayed semi-Markov reaction-diffusion systems: An asynchronous boundary control scheme. ISA Trans 2024:S0019-0578(24)00138-1. [PMID: 38570256 DOI: 10.1016/j.isatra.2024.03.030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Revised: 03/25/2024] [Accepted: 03/25/2024] [Indexed: 04/05/2024]
Abstract
This paper tries to study the problem of finite-time synchronization for delayed semi-Markov reaction-diffusion systems. Based on the spatial and parametric characteristics of the considered systems, a new asynchronous boundary control scheme is proposed to ensure the finite-time synchronization of the drive and response systems. In the asynchronous boundary control scheme, only an actuator should be placed at the spatial boundary, which is more easier to implement and economical than the other non-boundary control strategies. Besides, the system parameters and controller follow two asynchronous semi-Markov chains for jumping, which is more practical than obeying one semi-Markov chain. Moreover, for the considered systems, we proposes a new lemma of finite-time stability, and by employing the inequality methods and variable substitution, we derive the criterion of finite-time synchronization and a correlative corollary. Finally, a numerical example and an application example on secure communication are carried out to support the developed approach.
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Affiliation(s)
- Angang Wei
- China Huaneng Group Clean Energy Technology Research Institute Co., Ltd., China; Department of Mechanical Engineering, Tsinghua University, Beijing 102209, China.
| | - Zhongyuan Yao
- Jiangsu Clean Energy Branch of Huaneng International Power Co., Ltd., Nanjing 210005, China.
| | - Yu Zhang
- Jiangsu Clean Energy Branch of Huaneng International Power Co., Ltd., Nanjing 210005, China.
| | - Kaiming Wang
- Hunan Provincial Key Laboratory of Intelligent Manufacturing Technology for High-performance Mechanical Equipment, Changsha University of Science and Technology, Changsha 410114, China; Key Laboratory of Vibration and Control of Aero-Propulsion System, Ministry of Education, Northeastern University, Shenyang 110819, China.
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3
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Peng T, Wu Y, Tu Z, Alofi AS, Lu J. Fixed-time and prescribed-time synchronization of quaternion-valued neural networks: A control strategy involving Lyapunov functions. Neural Netw 2023; 160:108-121. [PMID: 36630738 DOI: 10.1016/j.neunet.2022.12.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Revised: 11/26/2022] [Accepted: 12/19/2022] [Indexed: 01/05/2023]
Abstract
A control strategy containing Lyapunov functions is proposed in this paper. Based on this strategy, the fixed-time synchronization of a time-delay quaternion-valued neural network (QVNN) is analyzed. This strategy is extended to the prescribed-time synchronization of the QVNN. Furthermore, an improved two-step switching control strategy is also proposed based on this flexible control strategy. Compared with some existing methods, the main method of this paper is a non-decomposition one, does not contain a sign function in the controller, and has better synchronization accuracy. Two numerical examples verify the above advantages.
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Affiliation(s)
- Tao Peng
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China; Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China.
| | - Yanqiu Wu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China.
| | - Zhengwen Tu
- School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China.
| | - A S Alofi
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
| | - Jianquan Lu
- Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China; School of Automation and Electrical Engineering, Linyi University, Linyi 276005, China.
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Man J, Song X, Song S, Lu J. Finite-time synchronization of reaction-diffusion memristive neural networks: A gain-scheduled integral sliding mode control scheme. ISA Trans 2022; 130:692-701. [PMID: 36055825 DOI: 10.1016/j.isatra.2022.08.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Revised: 07/26/2022] [Accepted: 08/12/2022] [Indexed: 06/15/2023]
Abstract
The finite-time synchronization issue of reaction-diffusion memristive neural networks (RDMNNs) is studied in this paper. To better synchronize the parameter-varying drive and response systems, an innovative gain-scheduled integral sliding mode control scheme is proposed, where the 2n controller gains can be scheduled and an integral switching surface function that contains a discontinuous term is involved. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining reciprocally convex combination (RCC) method, a less conservative finite-time synchronization criterion for RDMNNs is derived in the form of linear matrix inequalities (LMIs). Finally, three numerical simulations are exploited to illustrate the effectiveness, superiority and practicability of this paper.
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Affiliation(s)
- Jingtao Man
- School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China.
| | - Xiaona Song
- School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China.
| | - Shuai Song
- School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China
| | - Junwei Lu
- School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042, China
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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] [What about the content of this article? (0)] [Affiliation(s)] [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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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] [What about the content of this article? (0)] [Affiliation(s)] [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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Modiri A, Mobayen S. Adaptive terminal sliding mode control scheme for synchronization of fractional-order uncertain chaotic systems. ISA Trans 2020; 105:33-50. [PMID: 32493578 DOI: 10.1016/j.isatra.2020.05.039] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2019] [Revised: 05/02/2020] [Accepted: 05/24/2020] [Indexed: 06/11/2023]
Abstract
The main goal in this article is synchronization of fractional-order uncertain chaotic systems in the finite time. For this aim, a terminal sliding mode controller with fractional sliding surface is employed to synchronize the states of two different fractional order chaotic systems with parameter uncertainties and external disturbances. This approach is robust when the effects of perturbations are derived into account. A fractional-order adaptive terminal sliding mode controller is developed to estimate the upper bounds of perturbations. Both suggested control laws are useful for fractional-order uncertain chaotic master-slave systems. Demonstrative simulation outcomes for Lorenz and Chen fractional-order systems with model perturbations and the engineering application on message telecommunication indicate the efficiency and usefulness of the recommended design.
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Affiliation(s)
- Arshia Modiri
- Advanced Control Systems Laboratory, Department of Electrical Engineering, Faculty of Engineering, University of Zanjan, Zanjan 3879145371, Iran
| | - Saleh Mobayen
- Advanced Control Systems Laboratory, Department of Electrical Engineering, Faculty of Engineering, University of Zanjan, Zanjan 3879145371, Iran; Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, ROC.
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Wouapi KM, Fotsin BH, Louodop FP, Feudjio KF, Njitacke ZT, Djeudjo TH. Various firing activities and finite-time synchronization of an improved Hindmarsh-Rose neuron model under electric field effect. Cogn Neurodyn 2020; 14:375-397. [PMID: 32399078 PMCID: PMC7203348 DOI: 10.1007/s11571-020-09570-0] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2019] [Revised: 01/05/2020] [Accepted: 01/10/2020] [Indexed: 11/26/2022] Open
Abstract
Nowadays, it is important to realize systems that can model the electrical activity of neurons taking into account almost all the properties of the intracellular and extracellular environment in which they are located. It is in this sense that we propose in this paper, the improved model of Hindmarsh-Rose (HR) which takes into account the fluctuation of the membrane potential created by the variation of the ion concentration in the cell. Considering the effect of the electric field that is produced on the dynamic behavior of neurons, the essential properties of the model such as equilibrium point and its stability, bifurcation diagrams, Lyapunov spectrum, frequency spectra, time series of the membrane potential and phase portraits are thoroughly investigated. We thus prove that Hopf bifurcation occurs in this system when the parameters are chosen appropriately. We also observe that by varying specific parameters of the electric field, the model presents a very rich and striking event, namely hysteresis phenomenon, which justifies the coexistence of multiple attractors. Besides, by applying a suitable sinusoidal excitation current, we prove that the neuron under electric field effect can present several important electrical activities including quiescent, spiking, bursting and even chaos. We propose the improved HR model under electric field effect (mHR) to study the finite-time synchronization between two neurons when performing synapse coupling across the membrane potential and the electric field coupling. As a result, we find that the synchronization between the two neurons is weakly influenced by the variation of the intensity of the electric field coupling while it is strongly impacted when the intensity of the synapse coupling is modified. From these results, it is obvious that the electric field can be another effective bridge connection to encourage the exchange and coding of the signal. Using the finite-time synchronization algorithm, we theoretically quantify the synchronization time between these neurons. Finally, Pspice simulations are presented to show the feasibility of the proposed model as well as that of the developed synchronization strategy.
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Affiliation(s)
- K. Marcel Wouapi
- Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (URMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - B. Hilaire Fotsin
- Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (URMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - F. Patrick Louodop
- Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (URMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - K. Florent Feudjio
- Laboratoire d’Energie et des Systemes Electriques et Electroniques, Department of Physics, University of Yaounde I, PO Box 812, Yaoundé, Cameroon
| | - Z. Tabekoueng Njitacke
- Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon
| | - T. Hermann Djeudjo
- Energy and Environmental Technologies Laboratory, Department of Physics, University of Yaounde I, PO Box 812, Yaoundé, Cameroon
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Wei F, Chen G, Wang W. Finite-time synchronization of memristor neural networks via interval matrix method. Neural Netw 2020; 127:7-18. [PMID: 32305714 DOI: 10.1016/j.neunet.2020.04.003] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2019] [Revised: 03/17/2020] [Accepted: 04/02/2020] [Indexed: 11/23/2022]
Abstract
In this paper, the finite-time synchronization problems of two types of driven-response memristor neural networks (MNNs) without time-delay and with time-varying delays are investigated via interval matrix method, respectively. Based on interval matrix transformation, the driven-response MNNs are transformed into a kind of system with interval parameters, which is different from the previous research approaches. Several sufficient conditions in terms of linear matrix inequalities (LMIs) are driven to guarantee finite-time synchronization for MNNs. Correspondingly, two types of nonlinear feedback controllers are designed. Meanwhile, the upper-bounded of the settling time functions are estimated. Finally, two numerical examples with simulations are given to illustrate the correctness of the theoretical results and the effectiveness of the proposed controllers.
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Hua L, Zhong S, Shi K, Zhang X. Further results on finite-time synchronization of delayed inertial memristive neural networks via a novel analysis method. Neural Netw 2020; 127:47-57. [PMID: 32334340 DOI: 10.1016/j.neunet.2020.04.009] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Revised: 04/07/2020] [Accepted: 04/09/2020] [Indexed: 10/24/2022]
Abstract
In this paper, we propose a novel analysis method to investigate the finite-time synchronization (FTS) control problem of the drive-response inertial memristive neural networks (IMNNs) with mixed time-varying delays (MTVDs). Firstly, an improved control scheme is proposed under the delay-independent conditions, which can work even when the past state cannot be measured or the specific time delay function is unknown. Secondly, based on the assumption of bounded activation functions, we establish a new Lemma, which can effectively deal with the difficulties caused by memristive connection weights and MTVDs. Thirdly, by constructing a suitable Lyapunov functions and using a new inequality method, novel sufficient conditions to ensure the FTS for the discussed IMNNs are obtained. Compared with the existing results, our results obtained in a more general framework are more practical. Finally, some numerical simulations are given to substantiate the effectiveness of the theoretical results.
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Affiliation(s)
- Lanfeng Hua
- School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China.
| | - Shouming Zhong
- School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China.
| | - Kaibo Shi
- School of Information Science and Engineering, Chengdu University, Chengdu, Sichuan 610106, PR China.
| | - Xiaojun Zhang
- School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China.
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Qiao Y, Yan H, Duan L, Miao J. Finite-time synchronization of fractional-order gene regulatory networks with time delay. Neural Netw 2020; 126:1-10. [PMID: 32172040 DOI: 10.1016/j.neunet.2020.02.004] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2019] [Revised: 12/16/2019] [Accepted: 02/10/2020] [Indexed: 10/25/2022]
Abstract
As multi-gene networks transmit signals and products by synchronous cooperation, investigating the synchronization of gene regulatory networks may help us to explore the biological rhythm and internal mechanisms at molecular and cellular levels. We aim to induce a type of fractional-order gene regulatory networks to synchronize at finite-time point by designing feedback controls. Firstly, a unique equilibrium point of the network is proved by applying the principle of contraction mapping. Secondly, some sufficient conditions for finite-time synchronization of fractional-order gene regulatory networks with time delay are explored based on two kinds of different control techniques and fractional Lyapunov function approach, and the corresponding setting time is estimated. Finally, some numerical examples are given to demonstrate the effectiveness of the theoretical results.
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Affiliation(s)
- Yuanhua Qiao
- College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
| | - Hongyun Yan
- College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
| | - Lijuan Duan
- Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China; Beijing Key Laboratory of Trusted Computing, Beijing 100124, China; National Engineering Laboratory for Key Technologies of Information Security Level Protection, Beijing 100124, China.
| | - Jun Miao
- School of Computer Science, Beijing Information Science and Technology University, Beijing 100101, China
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Wan P, Sun D, Zhao M. Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control. Neural Netw 2019; 123:1-11. [PMID: 31812925 DOI: 10.1016/j.neunet.2019.11.012] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Revised: 10/28/2019] [Accepted: 11/14/2019] [Indexed: 11/26/2022]
Abstract
This paper proposes a unified theoretical framework to study the problem of finite/fixed-time drive-response anti-synchronization for a class of Markovian stochastic neural networks. State feedback switching controllers without the sign function are designed to achieve the finite/fixed-time anti-synchronization of the addressed systems. Compared with the existing synchronization criteria, our results indicate that the controllers via the switching control without the sign function are given with less conservativeness, and the controllers without any sign function can deal with the chattering problem. By employing Lyapunov functional method and properties of the Weiner process, several finite/fixed-time synchronization criteria are presented and the corresponding settling times are calculated as well. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.
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Affiliation(s)
- Peng Wan
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China; School of Automation, Chongqing University, Chongqing 400044, China
| | - Dihua Sun
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China; School of Automation, Chongqing University, Chongqing 400044, China.
| | - Min Zhao
- Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044, China; School of Automation, Chongqing University, Chongqing 400044, China
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13
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Wei R, Cao J, Alsaedi A. Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays. Cogn Neurodyn 2017; 12:121-134. [PMID: 29435092 DOI: 10.1007/s11571-017-9455-z] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2017] [Revised: 07/08/2017] [Accepted: 09/14/2017] [Indexed: 10/18/2022] Open
Abstract
This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.
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Affiliation(s)
- Ruoyu Wei
- 1Research Center for Complex Systems and Network Sciences, School of Mathematics, Southeast University, Nanjing, 210096 China
| | - Jinde Cao
- 1Research Center for Complex Systems and Network Sciences, School of Mathematics, Southeast University, Nanjing, 210096 China
| | - Ahmed Alsaedi
- 2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia
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Velmurugan G, Rakkiyappan R, Cao J. Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Neural Netw 2015; 73:36-46. [PMID: 26547242 DOI: 10.1016/j.neunet.2015.09.012] [Citation(s) in RCA: 155] [Impact Index Per Article: 17.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2015] [Revised: 08/10/2015] [Accepted: 09/27/2015] [Indexed: 10/22/2022]
Abstract
In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results.
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Affiliation(s)
- G Velmurugan
- Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India.
| | - R Rakkiyappan
- Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India.
| | - Jinde Cao
- Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, Jiangsu, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
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15
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Shen J, Cao J. Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn Neurodyn 2011; 5:373-85. [PMID: 23115594 DOI: 10.1007/s11571-011-9163-z] [Citation(s) in RCA: 88] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2010] [Revised: 04/10/2011] [Accepted: 06/20/2011] [Indexed: 11/29/2022] Open
Abstract
This paper investigates finite-time synchronization of an array of coupled neural networks via discontinuous controllers. Based on Lyapunov function method and the discontinuous version of finite-time stability theory, some sufficient criteria for finite-time synchronization are obtained. Furthermore, we propose switched control and adaptive tuning parameter strategies in order to reduce the settling time. In addition, pinning control scheme via a single controller is also studied in this paper. With the hypothesis that the coupling network topology contains a directed spanning tree and each of the strongly connected components is detail-balanced, we prove that finite-time synchronization can be achieved via pinning control. Finally, some illustrative examples are given to show the validity of the theoretical results.
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Affiliation(s)
- Jun Shen
- Department of Mathematics, Southeast University, Nanjing, 210096 China
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