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Lan J, Zhang X, Wang X. Global robust exponential stability of interval BAM neural networks with multiple time-varying delays: A direct method based on system solutions. ISA TRANSACTIONS 2024; 144:145-152. [PMID: 37951754 DOI: 10.1016/j.isatra.2023.11.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Revised: 10/31/2023] [Accepted: 11/01/2023] [Indexed: 11/14/2023]
Abstract
This paper analyzes global robust exponential stability of interval bidirectional associative memory (BAM) neural networks with multiple time-varying delays, proposes a direct method based on system solutions, and gives sufficient conditions under which interval BAM neural networks have a unique and globally robustly exponentially stable equilibrium point. This method not only avoids the difficult to set up any Lyapunov-Krasovskii functional, but also derives simpler global robust exponential stability criteria. Compared with the data from other literature, the robust exponential stability criteria obtained in this paper have been presented to have more merits theoretically and numerically.
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Affiliation(s)
- Jinbao Lan
- School of Mathematical Science, Heilongjiang University, Harbin, 150080, PR China.
| | - Xian Zhang
- School of Mathematical Science, Heilongjiang University, Harbin, 150080, PR China; Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, PR China.
| | - Xin Wang
- School of Mathematical Science, Heilongjiang University, Harbin, 150080, PR China; Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, PR China.
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Zhang JR, Lu JG, Jin XC, Yang XY. Novel results on asymptotic stability and synchronization of fractional-order memristive neural networks with time delays: The 0<δ≤1 case. Neural Netw 2023; 167:680-691. [PMID: 37722271 DOI: 10.1016/j.neunet.2023.09.007] [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: 12/02/2022] [Revised: 07/14/2023] [Accepted: 09/04/2023] [Indexed: 09/20/2023]
Abstract
This paper investigates the asymptotic stability and synchronization of fractional-order (FO) memristive neural networks with time delays. Based on the FO comparison principle and inverse Laplace transform method, the novel sufficient conditions for the asymptotic stability of a FO nonlinear system are given. Then, based on the above conclusions, the sufficient conditions for the asymptotic stability and synchronization of FO memristive neural networks with time delays are investigated. The results in this paper have a wider coverage of situations and are more practical than the previous related results. Finally, the validity of the results is checked by two examples.
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Affiliation(s)
- Jia-Rui Zhang
- Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, PR China; Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, PR China; Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai 200240, PR China
| | - Jun-Guo Lu
- Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, PR China; Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, PR China; Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai 200240, PR China.
| | - Xiao-Chuang Jin
- Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, PR China; Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, PR China; Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai 200240, PR China
| | - Xing-Yu Yang
- Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, PR China; Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, PR China; Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai 200240, PR China
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Xia Z, Liu Y, Kou KI, Wang J. Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:7248-7259. [PMID: 35030085 DOI: 10.1109/tnnls.2021.3139865] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of the optimization problems is composed of the sum of convex functions defined in the Clifford domain. Based on the generalized Clifford gradient, a system of multiple Clifford-valued recurrent neural networks (RNNs) is proposed for solving the distributed optimization problems. Each Clifford-valued RNN minimizes a local objective function individually, with local interactions with others. The convergence of the neural system is rigorously proved based on the Lyapunov theory. Two illustrative examples are delineated to demonstrate the viability of the results in this article.
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Cao J, Udhayakumar K, Rakkiyappan R, Li X, Lu J. A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:5476-5496. [PMID: 34962883 DOI: 10.1109/tnnls.2021.3129829] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.
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Quasi-Synchronization for Fractional-Order Reaction–Diffusion Quaternion-Valued Neural Networks: An LMI Approach. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11054-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Manivannan R, Cao Y, Chong KT. Unified dissipativity state estimation for delayed generalized impulsive neural networks with leakage delay effects. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.109630] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Yang J, Chen G, Wen S. Finite-time dissipative control for bidirectional associative memory neural networks with state-dependent switching and time-varying delays. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.109338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Aouiti C, Touati F. Global Dissipativity of Quaternion-Valued Fuzzy Cellular Fractional-Order Neural Networks With Time Delays. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10893-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Robust Control for Variable-Order Fractional Interval Systems Subject to Actuator Saturation. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6030159] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this paper, a class of variable-order fractional interval systems (VO-FIS) in which the system matrices are affected by the fractional order is investigated. Firstly, the sufficient conditions for robust stability of a VO-FIS with a unified order range of ν(σ)∈(0,2) are proposed. Secondly, the stabilization conditions of a VO-FIS subject to actuator saturation are derived in terms of linear matrix inequalities (LMIs). Then, by using the proposed algorithm through an optimization problem, the stability region is estimated. To summarize, the paper gives a stabilization criterion for VO-FIS subject to actuator saturation. Finally, three numerical examples are proposed to verify the effectiveness of our results.
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Xiao S, Wang Z, Wang C. Passivity analysis of fractional-order neural networks with interval parameter uncertainties via an interval matrix polytope approach. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2021.12.106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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On Variable-Order Fractional Discrete Neural Networks: Solvability and Stability. FRACTAL AND FRACTIONAL 2022. [DOI: 10.3390/fractalfract6020119] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution to the topic by presenting a variable-order fractional discrete neural network model and by proving its Ulam–Hyers stability. In particular, two novel theorems are illustrated, one regarding the existence of the solution for the proposed variable-order network and the other regarding its Ulam–Hyers stability. Finally, numerical simulations of three-dimensional and two-dimensional variable-order fractional neural networks were carried out to highlight the effectiveness of the conceived theoretical approach.
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New criteria on the finite-time stability of fractional-order BAM neural networks with time delay. Neural Comput Appl 2021. [DOI: 10.1007/s00521-021-06605-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Xiao J, Li Y, Wen S. Mittag-Leffler synchronization and stability analysis for neural networks in the fractional-order multi-dimension field. Knowl Based Syst 2021. [DOI: 10.1016/j.knosys.2021.107404] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Fuzzy adaptive event-triggered control for a class of nonlinear systems with time-varying full state constraints. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.02.021] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Wu X, Liu S, Wang Y. Stability analysis of Riemann-Liouville fractional-order neural networks with reaction-diffusion terms and mixed time-varying delays. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.12.053] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Discrete-Time Stochastic Quaternion-Valued Neural Networks with Time Delays: An Asymptotic Stability Analysis. Symmetry (Basel) 2020. [DOI: 10.3390/sym12060936] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Stochastic disturbances often cause undesirable characteristics in real-world system modeling. As a result, investigations on stochastic disturbances in neural network (NN) modeling are important. In this study, stochastic disturbances are considered for the formulation of a new class of NN models; i.e., the discrete-time stochastic quaternion-valued neural networks (DSQVNNs). In addition, the mean-square asymptotic stability issue in DSQVNNs is studied. Firstly, we decompose the original DSQVNN model into four real-valued models using the real-imaginary separation method, in order to avoid difficulties caused by non-commutative quaternion multiplication. Secondly, some new sufficient conditions for the mean-square asymptotic stability criterion with respect to the considered DSQVNN model are obtained via the linear matrix inequality (LMI) approach, based on the Lyapunov functional and stochastic analysis. Finally, examples are presented to ascertain the usefulness of the obtained theoretical results.
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