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Hua L, Zhu H, Zhong S, Zhang Y, Shi K, Kwon OM. Fixed-Time Stability of Nonlinear Impulsive Systems and its Application to Inertial Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024; 35:1872-1883. [PMID: 35771779 DOI: 10.1109/tnnls.2022.3185664] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
This article is concerned with the fixed-time stability (FTS) problem of nonlinear impulsive systems (NISs). By means of the impulsive control mechanism and Lyapunov functions theory, several sufficient conditions are established to ensure the FTS of general NISs. Meanwhile, some novel impulse-dependent settling-time estimation schemes are developed, which fully considers the influence of stabilizing impulses and destabilizing impulses on the convergence rate of the system states. The proposed schemes establish a quantitative relationship between the upper bound of the settling time and impulse effects. It shows that stabilizing impulses can accelerate the convergence rate of the system states and leads to the upper bound of the settling time being smaller. Conversely, destabilizing impulses can reduce it and make the upper bound of the settling time larger. Then, the theoretical results are applied to delayed inertial neural networks (DINNs), where two kinds of controllers are designed to realize fixed-time synchronization of the considered systems in the impulse sense. Finally, some numerical examples are provided to illustrate the validity of the proposed theoretical results.
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2
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Liu H, Cheng J, Cao J, Katib I. Preassigned-time synchronization for complex-valued memristive neural networks with reaction-diffusion terms and Markov parameters. Neural Netw 2024; 169:520-531. [PMID: 37948970 DOI: 10.1016/j.neunet.2023.11.011] [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: 07/09/2023] [Revised: 10/01/2023] [Accepted: 11/05/2023] [Indexed: 11/12/2023]
Abstract
This study addresses the preassigned-time synchronization for complex-valued memristive neural networks with reaction-diffusion terms and Markov parameters. Employing a preassigned-time stable control strategy, two distinct controllers with varying power exponent parameters are designed to ensure that synchronization can be achieved within a predefined time frame. Unlike existing finite/fixed-time results, a priori specification of the settling time is addressed. Furthermore, Green's formula and boundary conditions are efficiently applied to overcome potential symmetry loss. Additionally, the activation function's constraint range is more lenient compared to existing constraints. Finally, the effectiveness of the presented methods are demonstrated through two examples.
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Affiliation(s)
- Hongliang Liu
- School of Mathematics and Physics, University of South China, Hengyang, 421001, PR China
| | - Jun Cheng
- School of Mathematics and Statistics, Guangxi Normal University, Guilin, 541004, PR China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, PR China
| | - Iyad Katib
- Department of Computer Science, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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Liu F, Meng W, Yao D. Bounded Antisynchronization of Multiple Neural Networks via Multilevel Hybrid Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:8250-8261. [PMID: 35358050 DOI: 10.1109/tnnls.2022.3148194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The bounded antisynchronization (AS) problem of multiple discrete-time neural networks (NNs) based on the fuzzy model is studied, in consideration of the differences in quantity and communication among different NN groups, the variabilities of dynamics, and communication topological affected by environments. To reduce the energy consumption of communication, a cluster pinning communication mechanism is proposed, and an impulsive observer is designed to estimate the state of target NN. Then, a multilevel hybrid controller based on the impulsive observer is built including the AS controller and the bounded synchronization (BS) controller. Sufficient conditions for bounded AS are obtained by analyzing the stability of the BS augmented error (BSAE) and the AS augmented error (ASAE) based on the fuzzy-based Lyapunov functional (FBLF). Finally, a numerical example and an application example are given to verify the validity of the obtained results.
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Zhang H, Zeng Z. Adaptive Synchronization of Reaction-Diffusion Neural Networks With Nondifferentiable Delay via State Coupling and Spatial Coupling. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:7555-7566. [PMID: 35100127 DOI: 10.1109/tnnls.2022.3144222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.
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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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Kong F, Zhu Q, Huang T. New Fixed-Time Stability Criteria of Time-Varying Delayed Discontinuous Systems and Application to Discontinuous Neutral-Type Neural Networks. IEEE TRANSACTIONS ON CYBERNETICS 2023; 53:2358-2367. [PMID: 34653013 DOI: 10.1109/tcyb.2021.3117945] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
This article mainly focuses on putting forward new fixed-time (FIXT) stability lemmas of delayed Filippov discontinuous systems (FDSs). By providing the new inequality conditions imposed on the Lyapunov-Krasovskii functions (LKF), novel FIXT stability lemmas are investigated with the help of inequality techniques. The new settling time is also given and its accuracy is improved in comparison with pioneer ones. For the purpose of illustrating the applicability, a class of discontinuous fuzzy neutral-type neural networks (DFNTNNs) is considered, which includes the previous NTNNs. New criteria are derived and detailed FIXT synchronization results have been obtained. Finally, typical examples are carried out to demonstrate the validity of the main results.
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Kong F, Zhu Q. Fixed-Time Stabilization of Discontinuous Neutral Neural Networks With Proportional Delays via New Fixed-Time Stability Lemmas. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:775-785. [PMID: 34375288 DOI: 10.1109/tnnls.2021.3101252] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
When studying the stability of time-delayed discontinuous systems, Lyapunov-Krasovskii functional (LKF) is an essential tool. More relaxed conditions imposed on the LKF are preferred and can take more advantages in real applications. In this article, novel conditions imposed on the LKF are first given which are different from the previous ones. New fixed-time (FXT) stability lemmas are established using some inequality techniques which can greatly extend the pioneers. The new estimations of the settling times (STs) are also obtained. For the purpose of examining the applicability of the new FXT stability lemmas, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is formulated which is more generalized than the existing ones. Using differential inclusions theory, set-valued map, and the newly obtained FXT stability lemma, some algebraic FXT stabilization criteria are derived. Finally, examples are given to show the correctness of the established results.
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Kong F, Zhu Q, Huang T. New Fixed-Time Stability Analysis of Delayed Discontinuous Systems via an Augmented Indefinite Lyapunov-Krasovskii Functional. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:13438-13447. [PMID: 34874880 DOI: 10.1109/tcyb.2021.3128142] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
This article discusses the fixed-time stability (FTS) of a kind of delayed discontinuous system (DS) in Filippov sense. Based on the set-valued map, the FTS analysis of the general solution is first transformed into the zero solution of the differential inclusion. Second, the new criteria of the Lyapunov-Krasovskii functional (LKF) are given and LKF is proved to possess the indefinite derivatives by using the simple integral inequalities. In addition, the FTS of the considered delayed DS is achieved and the new settling time is estimated. Third, to demonstrate the applicability of the new FTS theorems, the FTS control of a class of discontinuous inertial neural networks (DINNs) with time-varying delays is solved. Finally, two numerical examples are given to examine the theoretical results and simulations are also provided to make some illustrations.
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Sheng Y, Zeng Z, Huang T. Finite-Time Stabilization of Competitive Neural Networks With Time-Varying Delays. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:11325-11334. [PMID: 34133310 DOI: 10.1109/tcyb.2021.3082153] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article investigates finite-time stabilization of competitive neural networks with discrete time-varying delays (DCNNs). By virtue of comparison strategies and inequality techniques, finite-time stabilization of the underlying DCNNs is analyzed by designing a discontinuous state feedback controller, which simplifies the controller design and proof processes of some existing results. Meanwhile, global exponential stabilization of the DCNNs is provided under a continuous state feedback controller. In addition, global exponential stability of the DCNNs is shown as an M-matrix, which contains some published outcomes as special cases. Finally, three examples are given to illuminate the validity of the theories.
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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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Fixed-time passivity of coupled quaternion-valued neural networks with multiple delayed couplings. Soft comput 2022. [DOI: 10.1007/s00500-022-07500-2] [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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Liu Y, Zhang G, Hu J. Fixed-Time Anti-synchronization and Preassigned-Time Synchronization of Discontinuous Fuzzy Inertial Neural Networks with Bounded Distributed Time-Varying Delays. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11011-4] [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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Song X, Man J, Park JH, Song S. Finite-Time Synchronization of Reaction-Diffusion Inertial Memristive Neural Networks via Gain-Scheduled Pinning Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:5045-5056. [PMID: 33819162 DOI: 10.1109/tnnls.2021.3068734] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
For the considered reaction-diffusion inertial memristive neural networks (IMNNs), this article proposes a novel gain-scheduled generalized pinning control scheme, where three pinning control strategies are involved and 2n controller gains can be scheduled for different system parameters. Moreover, a time delay is considered in the controller to make it has a memory function. With the designed controller, drive-and-response systems can be synchronized within a finite-time interval. Note that the final finite-time synchronization criterion is obtained in the forms of linear matrix inequalities (LMIs) by introducing a memristor-dependent sign function into the controller and constructing a new Lyapunov-Krasovskii functional (LKF). Furthermore, by utilizing some improved integral inequality methods, the conservatism of the main results can be greatly reduced. Finally, three numerical examples are provided to illustrate the feasibility, superiority, and practicability of this article.
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Wang L, Zhang CK. Exponential Synchronization of Memristor-Based Competitive Neural Networks With Reaction-Diffusions and Infinite Distributed Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; PP:745-758. [PMID: 35622804 DOI: 10.1109/tnnls.2022.3176887] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Taking into account the infinite distributed delays and reaction-diffusions, this article investigates the global exponential synchronization problem of a class of memristor-based competitive neural networks (MCNNs) with different time scales. Based on the Lyapunov-Krasovskii functional and inequality approach, an adaptive control approach is proposed to ensure the exponential synchronization of the addressed drive-response networks. The closed-loop system is a discontinuous and delayed partial differential system in a cascade form, involving the spatial diffusion, the infinite distributed delays, the parametric adaptive law, the state-dependent switching parameters, and the variable structure controllers. By combining the theories of nonsmooth analysis, partial differential equation (PDE) and adaptive control, we present a new analytical method for rigorously deriving the synchronization of the states of the complex system. The derived m-norm (m ≥ 2)-based synchronization criteria are easily verified and the theoretical results are easily extended to memristor-based neural networks (NNs) without different time scales and reaction-diffusions. Finally, numerical simulations are presented to verify the effectiveness of the theoretical results.
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15
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Zhang L, Yang Y. Different Control Strategies for Fixed-Time Synchronization of Inertial Memristive Neural Networks. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10779-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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16
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Synchronization in Fixed Time for Reaction–Diffusion Quaternion-Valued NNs with Nonlinear Interconnected Protocol and Its Application. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10579-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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17
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Asymptotical stability of fractional neutral-type delayed neural networks with reaction-diffusion terms. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.07.042] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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18
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Wang Z, Cao J, Cai Z, Tan X, Chen R. Finite-time synchronization of reaction-diffusion neural networks with time-varying parameters and discontinuous activations. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.02.065] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Ni X, Wen S, Wang H, Guo Z, Zhu S, Huang T. Observer-Based Quasi-Synchronization of Delayed Dynamical Networks With Parameter Mismatch Under Impulsive Effect. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:3046-3055. [PMID: 32745009 DOI: 10.1109/tnnls.2020.3009271] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article focuses on the observer-based quasi-synchronization problem of delayed dynamical networks with parameter mismatch under impulsive effect. First, since the state of each node is unknown in the real situation, the state estimation strategy is proposed to estimate the state of each node, so as to design an appropriate synchronization controller. Then, the corresponding controller is constructed to synchronize the slave nodes with their leader node. In this article, we take the impulsive effect into consideration, which means that an impulsive signal will be applied to the system every so often. Due to the existence of parameter mismatch and time-varying delay, by constructing an appropriate Lyapunouv function, we will eventually obtain a differential equation with constant and time-varying delay terms. Then, we analyze its trajectory by introducing the Cauchy matrix and prove its boundedness by contradiction. Finally, a numerical simulation is presented to illustrate the validness of obtained results.
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Song X, Man J, Song S, Ahn CK. Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021; 32:2952-2964. [PMID: 32735537 DOI: 10.1109/tnnls.2020.3009081] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.
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Xiao J, Zeng Z, Wen S, Wu A, Wang L. A Unified Framework Design for Finite-Time and Fixed-Time Synchronization of Discontinuous Neural Networks. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:3004-3016. [PMID: 31880580 DOI: 10.1109/tcyb.2019.2957398] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this article, the problems of finite-time/fixed-time synchronization have been investigated for discontinuous neural networks in the unified framework. To achieve the finite-time/fixed-time synchronization, a novel unified integral sliding-mode manifold is introduced, and corresponding unified control strategies are provided; some criteria are established for selecting suitable parameters for solving the related issue, namely, the dynamics of neural network can reach the designed sliding-mode manifold in finite/fixed time, and stay on it thereafter. Moreover, the estimations of setting time are given out. The established unified framework can bring in various protocols by choosing the different parameters of controllers and sliding-mode manifold, which extend previous related results. Finally, some numerical examples are introduced to show the effectiveness and superiority of resulting conclusions.
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Hu C, He H, Jiang H. Fixed/Preassigned-Time Synchronization of Complex Networks via Improving Fixed-Time Stability. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:2882-2892. [PMID: 32203047 DOI: 10.1109/tcyb.2020.2977934] [Citation(s) in RCA: 51] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This article is concerned with the problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for discontinuous dynamic networks by improving FXT stability and developing simple control schemes. First, some more relaxed conditions for FXT stability are established and several more accurate estimates for the settling time (ST) are obtained by means of some special functions. Based on the improved FXT stability, FXT synchronization for discontinuous networks is discussed by designing a simple controller without a linear feedback term. Besides, the PAT synchronization is also explored by developing several nontrivial control protocols with finite control gains, where the synchronized time can be prespecified according to actual needs and is irrelevant with any initial value and any parameter. Finally, the improved FXT stability and the synchronization for complex networks are confirmed by two numerical examples.
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Zhang H, Zeng Z. Synchronization of Nonidentical Neural Networks With Unknown Parameters and Diffusion Effects via Robust Adaptive Control Techniques. IEEE TRANSACTIONS ON CYBERNETICS 2021; 51:660-672. [PMID: 31226097 DOI: 10.1109/tcyb.2019.2921633] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
This paper considers the self-synchronization and tracking synchronization issues for a class of nonidentically coupled neural networks model with unknown parameters and diffusion effects. Using the special structure of neural networks with global Lipschitz activation function, nonidentical terms are treated as external disturbances, which can then be compensated via robust adaptive control techniques. For the case where no common reference trajectory is given in advance, a distributed adaptive controller is proposed to drive the synchronization error to an adjustable bounded area. For the case where a reference trajectory is predesigned, two distributed adaptive controllers are proposed, respectively, to address the tracking synchronization problem with bounded and unbounded reference trajectories, different decomposition methods are given to extract the heterogeneous characteristics. To avoid the appearance of global information, such as the spectrum of the coupling matrix, corresponding adaptive designs on coupling strengths are also provided for both cases. Moreover, the upper bounds of the final synchronization errors can be gradually adjusted according to the parameters of the adaptive designs. Finally, numerical examples are given to test the effectiveness of the control algorithms.
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Kumar U, Das S, Huang C, Cao J. Fixed-time synchronization of quaternion-valued neural networks with time-varying delay. Proc Math Phys Eng Sci 2020. [DOI: 10.1098/rspa.2020.0324] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In this article, sufficient conditions for fixed-time synchronization of time-delayed quaternion-valued neural networks (QVNNs) are derived. Firstly, QVNNs are decomposed into four real-valued systems. Then using the available lemmas and by constructing the Lyapunov function, the synchronization criterion for the neural networks is proposed. Activation functions satisfy the Lipschitz condition. A suitable controller has been designed to synchronize the master–slave systems. The effectiveness of the proposed result is validated through a comparison of the settling time obtained by applying two different existing lemmas to a particular problem of synchronization of two identical QVNNs with time-varying delay with the help of suitable controllers.
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Affiliation(s)
- Umesh Kumar
- Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005, India
| | - Subir Das
- Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005, India
| | - Chuangxia Huang
- School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, Hunan, People’s Republic of China
- Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, Hunan, People’s Republic of China
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 211189, People’s Republic of China
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