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Kong F, Zhu Q, Karimi HR. Fixed-time periodic stabilization of discontinuous reaction-diffusion Cohen-Grossberg neural networks. Neural Netw 2023; 166:354-365. [PMID: 37544092 DOI: 10.1016/j.neunet.2023.07.017] [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: 01/02/2023] [Revised: 05/22/2023] [Accepted: 07/12/2023] [Indexed: 08/08/2023]
Abstract
This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.
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Affiliation(s)
- Fanchao Kong
- School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui 241000, China; MOE-LCSM, School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha 410081, China.
| | - Quanxin Zhu
- MOE-LCSM, School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha 410081, China.
| | - Hamid Reza Karimi
- Department of Mechanical Engineering, Politecnico di Milano, Milan 20156, Italy.
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2
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Liu G, Hua C, Liu PX, Park JH. Input-to-State Stability for Time-Delay Systems With Large Delays. IEEE TRANSACTIONS ON CYBERNETICS 2023; 53:1598-1606. [PMID: 34478396 DOI: 10.1109/tcyb.2021.3106793] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In this article, we consider the input-to-state stability (ISS) problem for a class of time-delay systems with intermittent large delays, which may cause the invalidation of traditional delay-dependent stability criteria. The topic of this article features that it proposes a novel kind of stability criterion for time-delay systems, which is delay dependent if the time delay is smaller than a prescribed allowable size. While if the time delay is larger than the allowable size, the ISS can be preserved as well provided that the large-delay periods satisfy the kind of duration condition. Different from existing results on similar topics, we present the main result based on a unified Lyapunov-Krasovskii function (LKF). In this way, the frequency restriction can be removed and the analysis complexity can be simplified. A numerical example is provided to verify the proposed results.
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3
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Zhang H, Zeng Z. Stability and Synchronization of Nonautonomous Reaction-Diffusion Neural Networks With General Time-Varying Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:5804-5817. [PMID: 33861715 DOI: 10.1109/tnnls.2021.3071404] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article investigates the stability and synchronization of nonautonomous reaction-diffusion neural networks with general time-varying delays. Compared with the existing works concerning reaction-diffusion neural networks, the main innovation of this article is that the network coefficients are time-varying, and the delays are general (which means that fewer constraints are posed on delays; for example, the commonly used conditions of differentiability and boundedness are no longer needed). By Green's formula and some analytical techniques, some easily checkable criteria on stability and synchronization for the underlying neural networks are established. These obtained results not only improve some existing ones but also contain some novel results that have not yet been reported. The effectiveness and superiorities of the established criteria are verified by three numerical examples.
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4
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Su H, Qiu Q, Chen X, Zeng Z. Distributed Adaptive Containment Control for Coupled Reaction-Diffusion Neural Networks With Directed Topology. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:6320-6330. [PMID: 33284762 DOI: 10.1109/tcyb.2020.3034634] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this article, we consider the problem of distributed adaptive leader-follower coordination of partial differential systems (i.e., reaction-diffusion neural networks, RDNNs) with directed communication topology in the case of multiple leaders. Different from the dynamical networks with ordinary differential dynamics, the design of adaptive protocols is more difficult due to the existence of spatial variables and nonlinear terms in the model. Under directed networks, a novel adaptive control protocol is proposed to solve the containment control problem of RDNNs. By constructing proper Lyapunov functional and adopting some important prior knowledge, the stability of containment for coupled RDNNs is theoretically proved. Furthermore, a corollary about the leader-follower synchronization with a leader for coupled RDNNs with directed communication topology is given. In the end, two numerical examples are provided to illustrate the obtained theoretical results.
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5
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Spatial-temporal dynamics of a non-monotone reaction-diffusion Hopfield’s neural network model with delays. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07036-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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6
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Lin S, Liu X. Synchronization and control for directly coupled reaction-diffusion neural networks with multiple weights and hybrid coupling. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.02.061] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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7
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Xu Y, Sun F, Li W. Exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms via intermittent control. Neural Comput Appl 2021. [DOI: 10.1007/s00521-021-06214-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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8
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Wang ZP, Wu HN, Wang JL, Li HX. Quantized Sampled-Data Synchronization of Delayed Reaction-Diffusion Neural Networks Under Spatially Point Measurements. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:5740-5751. [PMID: 31940579 DOI: 10.1109/tcyb.2019.2960094] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article considers the synchronization problem of delayed reaction-diffusion neural networks via quantized sampled-data (SD) control under spatially point measurements (SPMs), where distributed and discrete delays are considered. The synchronization scheme, which takes into account the communication limitations of quantization and variable sampling, is based on SPMs and only available in a finite number of fixed spatial points. By utilizing inequality techniques and Lyapunov-Krasovskii functional, some synchronization criteria via a quantized SD controller under SPMs are established and presented by linear matrix inequalities, which can ensure the exponential stability of the synchronization error system containing the drive and response dynamics. Finally, two numerical examples are offered to support the proposed quantized SD synchronization method.
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9
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Existence, Uniqueness and Stability of Mild Solutions to a Stochastic Nonlocal Delayed Reaction–Diffusion Equation. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10559-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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10
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Wang ZP, Wu HN, Li HX. Fuzzy Control Under Spatially Local Averaged Measurements for Nonlinear Distributed Parameter Systems With Time-Varying Delay. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:1359-1369. [PMID: 31180904 DOI: 10.1109/tcyb.2019.2916656] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equations (PDdEs), where the fast-varying time delay and slow-varying one are considered. A Takagi-Sugeno (T-S) fuzzy PDdE model is first derived to exactly describe the nonlinear DDPSs. Then, by virtue of the T-S fuzzy PDdE model and a Lyapunov-Krasovskii functional, an FC design under SLAMs, where the membership functions of the proposed FC law are determined by the measurement output and independent of the fuzzy PDdE plant model, is developed on basis of spatial linear matrix inequalities (SLMIs) to guarantee the exponential stability for the resulting closed-loop DDPSs. Lastly, a numerical example is offered to support the presented approach.
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11
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Gholami Y. Existence and global asymptotic stability criteria for nonlinear neutral-type neural networks involving multiple time delays using a quadratic-integral Lyapunov functional. ADVANCES IN DIFFERENCE EQUATIONS 2021; 2021:112. [PMID: 33619432 PMCID: PMC7888700 DOI: 10.1186/s13662-021-03274-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 02/03/2021] [Indexed: 06/12/2023]
Abstract
In this paper we consider a standard class of the neural networks and propose an investigation of the global asymptotic stability of these neural systems. The main aim of this investigation is to define a novel Lyapunov functional having quadratic-integral form and use it to reach a stability criterion for the under study neural networks. Since some fundamental characteristics, such as nonlinearity, including time-delays and neutrality, help us design a more realistic and applicable model of neural systems, we will use all of these factors in our neural dynamical systems. At the end, some numerical simulations are presented to illustrate the obtained stability criterion and show the essential role of the time-delays in appearance of the oscillations and stability in the neural networks.
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Affiliation(s)
- Yousef Gholami
- Department of Applied Mathematics, Sahand University of Technology, P.O. Box: 51335-1996, Tabriz, Iran
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12
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Huang Y, Hou J, Yang E. General decay anti-synchronization of multi-weighted coupled neural networks with and without reaction–diffusion terms. Neural Comput Appl 2020. [DOI: 10.1007/s00521-019-04313-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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13
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Wang Z, Cao J, Cai Z, Rutkowski L. Anti-Synchronization in Fixed Time for Discontinuous Reaction-Diffusion Neural Networks With Time-Varying Coefficients and Time Delay. IEEE TRANSACTIONS ON CYBERNETICS 2020; 50:2758-2769. [PMID: 31095503 DOI: 10.1109/tcyb.2019.2913200] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This paper studies the fixed-time anti-synchronization (FTAS) of discontinuous reaction-diffusion neural networks (DRDNNs) with both time-varying coefficients and time delay. First, differential inclusion theory is used to deal with the influence caused by discontinuous activations. In addition, a new fixed-time convergence theorem is used to handle the time-varying coefficients. Second, a novel state-feedback control algorithm and integral state-feedback control algorithm are proposed to realize FTAS of DRDNNs. During the generalized (adaptive) pinning control strategy, a guideline is proposed to select neurons to pin the designed controller. Furthermore, we present several criteria on FTAS by using the generalized Lyapunov function method. Different from the traditional Lyapunov function with negative definite derivative, the derivative of the Lyapunov function can be positive in this paper. Finally, we give two numerical simulations to substantiate the merits of the obtained results.
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14
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Liu P, Zheng WX, Zeng Z. On Complete Stability of Recurrent Neural Networks With Time-Varying Delays and General Piecewise Linear Activation Functions. IEEE TRANSACTIONS ON CYBERNETICS 2020; 50:2249-2263. [PMID: 30575557 DOI: 10.1109/tcyb.2018.2884836] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This paper addresses the problem of complete stability of delayed recurrent neural networks with a general class of piecewise linear activation functions. By applying an appropriate partition of the state space and iterating the defined bounding functions, some sufficient conditions are obtained to ensure that an n -neuron neural network is completely stable with exactly ∏i=1n(2Ki-1) equilibrium points, among which ∏i=1nKi equilibrium points are locally exponentially stable and the others are unstable, where Ki (i=1,…,n) are non-negative integers which depend jointly on activation functions and parameters of neural networks. The results of this paper include the existing works on the stability analysis of recurrent neural networks with piecewise linear functions as special cases and hence can be considered as the improvement and extension of the existing stability results in the literature. A numerical example is provided to illustrate the derived theoretical results.
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15
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Song X, Man J, Song S, Wang Z. An improved result on synchronization control for memristive neural networks with inertial terms and reaction-diffusion items. ISA TRANSACTIONS 2020; 99:74-83. [PMID: 31699400 DOI: 10.1016/j.isatra.2019.10.008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2019] [Revised: 10/22/2019] [Accepted: 10/22/2019] [Indexed: 06/10/2023]
Abstract
This paper investigates the synchronization issue of the memristive neural networks (MNNs) with inertial terms and reaction-diffusion items. In order to smoothly derive the controller gains and obtain an excellent control effect, the desired controller that contains a discontinuous function is proposed. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining the inequality techniques, several sufficient conditions in terms of algebraic inequalities are obtained to guarantee the synchronization of the proposed drive and response systems. Finally, three numerical simulations are exploited to support the acquired theoretical results.
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Affiliation(s)
- Xiaona Song
- School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China.
| | - Jingtao Man
- School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China.
| | - Shuai Song
- School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China.
| | - Zhen Wang
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
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16
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Wang S, Guo Z, Wen S, Huang T. Global synchronization of coupled delayed memristive reaction–diffusion neural networks. Neural Netw 2020; 123:362-371. [DOI: 10.1016/j.neunet.2019.12.016] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Revised: 11/18/2019] [Accepted: 12/14/2019] [Indexed: 11/16/2022]
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17
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Chen WH, Deng X, Lu X. Impulsive synchronization of two coupled delayed reaction–diffusion neural networks using time-varying impulsive gains. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.08.098] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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18
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Wang S, Guo Z, Wen S, Huang T, Gong S. Finite/fixed-time synchronization of delayed memristive reaction-diffusion neural networks. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.06.092] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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19
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Finite-time nonfragile time-varying proportional retarded synchronization for Markovian Inertial Memristive NNs with reaction-diffusion items. Neural Netw 2019; 123:317-330. [PMID: 31896463 DOI: 10.1016/j.neunet.2019.12.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Revised: 10/23/2019] [Accepted: 12/10/2019] [Indexed: 11/22/2022]
Abstract
The issue of synchronization for a class of inertial memristive neural networks over a finite-time interval is investigated in this paper. Specifically, reaction-diffusion items and Markovian jump parameters are both considered in the system model, meanwhile, a novel nonfragile time-varying proportional retarded control strategy is proposed. First, a befitting variable substitution is invoked to transform the original second-order differential system into a first-order one so that the corresponding synchronization error system that is represented by a first-order differential form is established. Second, by utilizing the integral inequality technique, reciprocally convex combination approach and free-weighting matrix method, a less conservative synchronization criterion in terms of linear matrix inequalities is obtained. Finally, three simulations are exploited to illustrate the feasibility, practicability and superiority of the designed controller so that the acquired theoretical results are supported.
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20
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Wang ZP, Wu HN, Wang XH. Sampled-data control for linear time-delay distributed parameter systems. ISA TRANSACTIONS 2019; 92:75-83. [PMID: 30826110 DOI: 10.1016/j.isatra.2019.02.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Revised: 01/27/2019] [Accepted: 02/01/2019] [Indexed: 06/09/2023]
Abstract
Some real systems have spatiotemporal dynamics and are time-delay distributed parameter systems (DPSs). The existence of time-delay may lead to system instability. The analysis and design of DPSs with time-delay is essentially more complicated. To take into account the factor of time-delay and fully enjoy the benefits of the digital technology in control engineering, it is a theoretical and practical value to consider the sampled-data control (SDC) problem of DPSs with time-delay. However, there are few attempts to solve the SDC problem of time-delay DPSs. In this paper, we introduce a SDC for linear time-delay DPSs described by parabolic partial differential equations (PDEs). A SDC design is developed in the formulation of spatial linear matrix inequalities (LMIs) by constructing an appropriate Lyapunov functional, which can stabilize exponentially the time-delay DPSs. This stabilization condition can be applied to either slowing-varying time delay or fast-varying one. Finally, simulation results of a numerical example are provided to illustrate the effectiveness of the proposed method.
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Affiliation(s)
- Zi-Peng Wang
- School of Electrical Engineering, University of Jinan, Jinan 250022, China.
| | - Huai-Ning Wu
- Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China.
| | - Xiao-Hong Wang
- School of Electrical Engineering, University of Jinan, Jinan 250022, China.
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21
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Zhang H, Zeng Z, Han QL. Synchronization of Multiple Reaction-Diffusion Neural Networks With Heterogeneous and Unbounded Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2019; 49:2980-2991. [PMID: 29994282 DOI: 10.1109/tcyb.2018.2837090] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The synchronization problem of multiple/coupled reaction-diffusion neural networks with time-varying delays is investigated. Differing from the existing considerations, state delays among distinct neurons and coupling delays among different subnetworks are included in the proposed model, the assumptions posed on the arisen delays are very weak, time-varying, heterogeneous, even unbounded delays are permitted. To overcome the difficulties from this kind of delay as well as diffusion effects, a comparison-based approach is applied to this model and a series of algebraic criteria are successfully obtained to verify the global asymptotical synchronization. By specifying the existing delays, some M -matrix-based criteria are derived to justify the power-rate synchronization and exponential synchronization. In addition, new criterion on synchronization of general connected neural networks without diffusion effects is also given. Finally, two simulation examples are given to verify the effectiveness of the obtained theoretical results and provide a comparison with the existing criterion.
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22
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Wang Y, Song G, Zhao J, Sun J, Zhuang G. Reliable mixed H ∞ and passive control for networked control systems under adaptive event-triggered scheme with actuator faults and randomly occurring nonlinear perturbations. ISA TRANSACTIONS 2019; 89:45-57. [PMID: 30583953 DOI: 10.1016/j.isatra.2018.12.023] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Revised: 11/02/2018] [Accepted: 12/14/2018] [Indexed: 06/09/2023]
Abstract
In this paper, the problem of reliable mixed H∞ and passive control for a class of nonlinear networked control systems under the adaptive event-triggered scheme with actuator faults and randomly occurring nonlinear perturbations is studied. Firstly, a series of independent stochastic variables with certain probabilistic distribution are presented to formulate the phenomena of actuator faults. Then, different from the traditional event-triggered scheme, the threshold of adaptive event-triggered scheme is determined by an online adaptive control law instead of the preset constant value. Further, based on a novel Lyapunov functional by taking the adaptive control law into account, sufficient conditions for asymptotically stable with mixed H∞ and passive performance are obtained in terms of a set of LMIs. If these LMIs are feasible, the reliable mixed H∞ and passive control gain and the weight parameter of adaptive event-triggered scheme can be gained simultaneously. Finally, two numerical examples are provided to show the effectiveness of the developed technique.
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Affiliation(s)
- Yanqian Wang
- School of Information and Control Engineering, Qingdao University of Technology, Qingdao, Shandong, 266033, China; Department of Civil and Environmental Engineering, University of South Florida, Tampa, FL, 33620, USA.
| | - Gongfei Song
- CICAEET, School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, 210044, China
| | - Junjie Zhao
- School of Electrical and Information Engineering, Jiangsu University of Technology, Changzhou, Jiangsu, 213001, China
| | - Jing Sun
- School of Information and Electronic Engineering, Shandong Institute of Business and Technology, Yantai, Shandong, 264005, China
| | - Guangming Zhuang
- School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong, China
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Hou J, Huang Y, Yang E. ψ-type stability of reaction–diffusion neural networks with time-varying discrete delays and bounded distributed delays. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.02.058] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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24
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Zhang H, Pal NR, Sheng Y, Zeng Z. Distributed Adaptive Tracking Synchronization for Coupled Reaction-Diffusion Neural Network. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2019; 30:1462-1475. [PMID: 30281497 DOI: 10.1109/tnnls.2018.2869631] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper considers the tracking synchronization problem for a class of coupled reaction-diffusion neural networks (CRDNNs) with undirected topology. For the case where the tracking trajectory has identical individual dynamic as that of the network nodes, the edge-based and vertex-based adaptive strategies on coupling strengths as well as adaptive controllers, which demand merely the local neighbor information, are proposed to synchronize the CRDNNs to the tracking trajectory. To reduce the control costs, an adaptive pinning control technique is employed. For the case where the tracking trajectory has different individual dynamic from that of the network nodes, the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area, which is adjustable according to the parameters of the adaptive strategy. This kind of adaptive design can enhance the robustness of the network against the external disturbance posed on the tracking trajectory. The obtained theoretical results are verified by two representative examples.
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25
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Memory-based State Estimation of T–S Fuzzy Markov Jump Delayed Neural Networks with Reaction–Diffusion Terms. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10026-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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26
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Yang Z, Zhou W, Huang T. Input-to-state stability of delayed reaction-diffusion neural networks with impulsive effects. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2018.12.019] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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27
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H∞ Consensus Control for Heterogeneous Multi-Agent via Output under Markov Switching Topologies. ELECTRONICS 2018. [DOI: 10.3390/electronics7120453] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The paper investigates H ∞ consensus problem of heterogeneous multi-agent systems including agents with first- and second-order integrators in the presence of disturbance and communication time delays under Markov switching topologies. Based on current messages, outdated information stored in memory and communication time delay information from neighbors, a more general kind of distributed consensus algorithm is proposed, which is faster consensus convergence. By applying stochastic stability analysis, model transformation techniques and graph theory, sufficient conditions of mean square consensus and H ∞ consensus are obtained, respectively. Finally, simulation examples are given to illustrate the effectiveness of obtained theoretical results.
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28
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Event-Triggered Containment Control of Multi-Agent Systems With High-Order Dynamics and Input Delay. ELECTRONICS 2018. [DOI: 10.3390/electronics7120343] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper studies the problem of distributed containment control for multi-agent systems with high-order dynamics and input delays. Two event-triggered control algorithms are proposed for multi-agent systems without and with input delay, respectively. The communication instants between two linked followers are determined by the event-triggering condition, and every follower can detect the event based on its own control input. For the followers, edge-based estimators are adopted to predict state differences to neighbors. Control inputs of the followers are calculated based on the predicted values of the state differences. To deal with the input delay, a delay comprehension approach is developed. It is proved that for arbitrarily large but bounded input delays, the followers can move into the convex hull spanned by the leaders asymptotically. Simulation results show the effectiveness of the proposed algorithms.
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29
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Lu X, Chen WH, Ruan Z, Huang T. A new method for global stability analysis of delayed reaction–diffusion neural networks. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.08.015] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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30
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Tang HA, Duan S, Hu X, Wang L. Passivity and synchronization of coupled reaction–diffusion neural networks with multiple time-varying delays via impulsive control. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.08.005] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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31
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Zhou L. Delay-dependent and delay-independent passivity of a class of recurrent neural networks with impulse and multi-proportional delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.04.076] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Zhang H, Sheng Y, Zeng Z. Synchronization of Coupled Reaction-Diffusion Neural Networks With Directed Topology via an Adaptive Approach. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:1550-1561. [PMID: 28320679 DOI: 10.1109/tnnls.2017.2672781] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper investigates the synchronization issue of coupled reaction-diffusion neural networks with directed topology via an adaptive approach. Due to the complexity of the network structure and the presence of space variables, it is difficult to design proper adaptive strategies on coupling weights to accomplish the synchronous goal. Under the assumptions of two kinds of special network structures, that is, directed spanning path and directed spanning tree, some novel edge-based adaptive laws, which utilized the local information of node dynamics fully are designed on the coupling weights for reaching synchronization. By constructing appropriate energy function, and utilizing some analytical techniques, several sufficient conditions are given. Finally, some simulation examples are given to verify the effectiveness of the obtained theoretical results.
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Shan Q, Zhang H, Wang Z, Zhang Z. Global Asymptotic Stability and Stabilization of Neural Networks With General Noise. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:597-607. [PMID: 28055925 DOI: 10.1109/tnnls.2016.2637567] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Neural networks (NNs) in the stochastic environment were widely modeled as stochastic differential equations, which were driven by white noise, such as Brown or Wiener process in the existing papers. However, they are not necessarily the best models to describe dynamic characters of NNs disturbed by nonwhite noise in some specific situations. In this paper, general noise disturbance, which may be nonwhite, is introduced to NNs. Since NNs with nonwhite noise cannot be described by Itô integral equation, a novel modeling method of stochastic NNs is utilized. By a framework in light of random field approach and Lyapunov theory, the global asymptotic stability and stabilization in probability or in the mean square of NNs with general noise are analyzed, respectively. Criteria for the concerned systems based on linear matrix inequality are proposed. Some examples are given to illustrate the effectiveness of the obtained results.
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Liu L, Chen WH, Lu X. Impulsive H∞ synchronization for reaction–diffusion neural networks with mixed delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.07.023] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Sheng Y, Zhang H, Zeng Z. Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays. IEEE TRANSACTIONS ON CYBERNETICS 2017; 47:3005-3017. [PMID: 28436913 DOI: 10.1109/tcyb.2017.2691733] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.
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Synchronization of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions and unbounded delays. Neural Netw 2017; 93:89-98. [DOI: 10.1016/j.neunet.2017.05.002] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Revised: 04/20/2017] [Accepted: 05/03/2017] [Indexed: 11/22/2022]
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Exponential stability analysis for delayed complex-valued memristor-based recurrent neural networks. Neural Comput Appl 2017. [DOI: 10.1007/s00521-017-3166-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Zhang H, Shan Q, Wang Z. Stability Analysis of Neural Networks With Two Delay Components Based on Dynamic Delay Interval Method. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2017; 28:259-267. [PMID: 26685269 DOI: 10.1109/tnnls.2015.2503749] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this paper, a dynamic delay interval (DDI) method is proposed to deal with the stability problem of neural networks with two delay components. This method extends the fixed interval of a time-varying delay to a dynamic one, which relaxes the restriction on upper and lower bounds of the delay intervals. Combining the reciprocally convex combination technique and Wirtinger integral inequality, the DDI method leads to some much less conservative delay-dependent stability criteria based on a linear matrix inequality for neural networks with two delay components. Furthermore, the criteria for the system with a single time-varying delay are provided. Some examples are given to illustrate the effectiveness of the obtained results.
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Liu L, Chen WH, Lu X. Aperiodically intermittent H ∞ synchronization for a class of reaction-diffusion neural networks. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.10.020] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Xin Y, Li Y, Cheng Z, Huang X. Global exponential stability for switched memristive neural networks with time-varying delays. Neural Netw 2016; 80:34-42. [DOI: 10.1016/j.neunet.2016.04.002] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2015] [Revised: 03/10/2016] [Accepted: 04/05/2016] [Indexed: 11/27/2022]
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Nie X, Zheng WX. Dynamical Behaviors of Multiple Equilibria in Competitive Neural Networks With Discontinuous Nonmonotonic Piecewise Linear Activation Functions. IEEE TRANSACTIONS ON CYBERNETICS 2016; 46:679-693. [PMID: 25826814 DOI: 10.1109/tcyb.2015.2413212] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is shown that under some conditions, such n -neuron competitive neural networks can have 5(n) equilibria, among which 3(n) equilibria are locally stable and the others are unstable. More importantly, it is revealed that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibria and locally stable equilibria than the ones with other activation functions, such as the continuous Mexican-hat-type activation function and discontinuous two-level activation function. Furthermore, the 3(n) locally stable equilibria given in this paper are located in not only saturated regions, but also unsaturated regions, which is different from the existing results on multistability of neural networks with multiple level activation functions. A simulation example is provided to illustrate and validate the theoretical findings.
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