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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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Aghayan ZS, Alfi A, Lopes AM. Disturbance observer-based delayed robust feedback control design for a class of uncertain variable fractional-order systems: Order-dependent and delay-dependent stability. ISA TRANSACTIONS 2023; 138:20-36. [PMID: 36925419 DOI: 10.1016/j.isatra.2023.03.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Revised: 02/16/2023] [Accepted: 03/04/2023] [Indexed: 06/16/2023]
Abstract
This work addresses the stabilization of variable fractional-order (VFO) neutral-type systems with structure perturbations and unknown disturbance signals using the feedback control approach. The goal is to design disturbance-observer-based delayed state- and output-feedback controllers to achieve robust stability of such VFO systems. The proposed controller consists of two parts, namely a primary controller based on the linear feedback technique, and an auxiliary controller based on the disturbance observer. A disturbance observer is developed to estimate the disturbance signal, which is generated by an exogenous system. Based on matrix inequalities, order-dependent and delay-dependent conditions are formulated via FO Lyapunov theory that guarantee the robust stability of the closed-loop system. Simulations verify the main results.
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Affiliation(s)
- Zahra Sadat Aghayan
- Faculty of Electrical Engineering, Shahrood University of Technology, Shahrood 36199-95161, Iran
| | - Alireza Alfi
- Faculty of Electrical Engineering, Shahrood University of Technology, Shahrood 36199-95161, Iran
| | - António M Lopes
- LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200 - 465, Porto, Portugal.
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Yao X, Liu Y, Zhang Z, Wan W. Synchronization Rather Than Finite-Time Synchronization Results of Fractional-Order Multi-Weighted Complex Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:7052-7063. [PMID: 34125684 DOI: 10.1109/tnnls.2021.3083886] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article investigates the synchronization of fractional-order multi-weighted complex networks (FMWCNs) with order α ∈ (0,1) . A useful fractional-order inequality t0C Dtα V(x(t)) ≤ -μV(x(t)) is extended to a more general form t0C Dtα V(x(t)) ≤ -μVγ(x(t)),γ ∈ (0,1] , which plays a pivotal role in studies of synchronization for FMWCNs. However, the inequality t0C Dtα V(x(t)) ≤ -μVγ(x(t)),γ ∈ (0,1) has been applied to achieve the finite-time synchronization for fractional-order systems in the absence of rigorous mathematical proofs. Based on reduction to absurdity in this article, we prove that it cannot be used to obtain finite-time synchronization results under bounded nonzero initial value conditions. Moreover, by using feedback control strategy and Lyapunov direct approach, some sufficient conditions are presented in the forms of linear matrix inequalities (LMIs) to ensure the synchronization for FMWCNs in the sense of a widely accepted definition of synchronization. Meanwhile, these proposed sufficient results cannot guarantee the finite-time synchronization of FMWCNs. Finally, two chaotic systems are given to verify the feasibility of the theoretical results.
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Xiao J, Zhong S, Wen S. Unified Analysis on the Global Dissipativity and Stability of Fractional-Order Multidimension-Valued Memristive Neural Networks With Time Delay. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:5656-5665. [PMID: 33950847 DOI: 10.1109/tnnls.2021.3071183] [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
The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.
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Li H, Hu C, Zhang G, Hu J, Wang L. Fixed-/Preassigned-time stabilization of delayed memristive neural networks. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.08.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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Yu T, Wang H, Cao J, Xue C. Finite-time stabilization of memristive neural networks via two-phase method. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.03.059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Liu Y, Shen B, Sun J. Stubborn state estimation for complex-valued neural networks with mixed time delays: the discrete time case. Neural Comput Appl 2022. [DOI: 10.1007/s00521-021-06707-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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Aghayan ZS, Alfi A, Machado JAT. Robust stability of uncertain fractional order systems of neutral type with distributed delays and control input saturation. ISA TRANSACTIONS 2021; 111:144-155. [PMID: 33220943 DOI: 10.1016/j.isatra.2020.11.009] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Revised: 10/31/2020] [Accepted: 11/06/2020] [Indexed: 06/11/2023]
Abstract
Time delay occurs naturally due to the limited bandwidth of any real-world system. However, this problem can deteriorate the system performance and can even result in system instability. Input saturation is also an essential issue due to the energy constraint in real actuators that makes the control design procedure more difficult. This article concerns with the stability of uncertain fractional order (FO) delay systems of neutral type including structured uncertainties, distributed delays and actuator saturation. A Lyapunov-Krasovskii functional allows the formulation of the conditions to insure the asymptotic robust stability of such systems via the linear matrix inequalities (LMI) and to compute the gain of a state feedback controller. In addition, by using the cone complementarity linearization method, we obtain the controller gains that extend the domain of attraction. Several simulations validate the theoretical analysis.
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Affiliation(s)
- Zahra Sadat Aghayan
- Faculty of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 36199-95161, Iran.
| | - Alireza Alfi
- Faculty of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 36199-95161, Iran
| | - J A Tenreiro Machado
- Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Antonio Bernardino de Almeida 431, 4249-015 Porto, Portugal
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Xiao J, Zhong S, Wen S. Improved approach to the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks based on new inequalities. Neural Netw 2020; 133:87-100. [PMID: 33152567 DOI: 10.1016/j.neunet.2020.10.008] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2020] [Revised: 09/13/2020] [Accepted: 10/15/2020] [Indexed: 11/17/2022]
Abstract
This paper studies the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks (FOMVBAMNNs) with general activation functions (AFs). First, the unified model is established for the researched systems of FOMVBAMNNs which can be turned into the corresponding multidimension-valued systems as long as the state variables, the connection weights and the AFs of the neural networks are valued to be real, complex, or quaternion. Then, without any decomposition, the criteria in unified form are derived by constructing the new Lyapunov-Krasovskii functionals (LKFs) in vector form, combining two new inequalities and considering the easy controllers. It is worth mentioning that the obtained criteria have many advantages in higher flexibility, more diversity, smaller computation, and lower conservatism. Finally, a simulation example is provided to illustrate the availability and improvements of the acquired results.
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Affiliation(s)
- Jianying Xiao
- School of Sciences, Southwest Petroleum University, Chengdu, 610050, PR China.
| | - Shouming Zhong
- School of Mathematical Sciences, University of Electronic Science and Technology, Chengdu, 611731, PR China.
| | - Shiping Wen
- Centre for Artificial Intelligence, Faculty of Engineering Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia.
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Xu X, Xu Q, Yang J, Xue H, Xu Y. Further research on exponential stability for quaternion-valued neural networks with mixed delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.004] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays. MATHEMATICS 2020. [DOI: 10.3390/math8071146] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.
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Li HL, Jiang H, Cao J. Global synchronization of fractional-order quaternion-valued neural networks with leakage and discrete delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.12.018] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Xiao J, Wen S, Yang X, Zhong S. New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality. Neural Netw 2020; 122:320-337. [DOI: 10.1016/j.neunet.2019.10.017] [Citation(s) in RCA: 66] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Revised: 09/10/2019] [Accepted: 10/28/2019] [Indexed: 11/16/2022]
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