A Survey of Fractional-Order Neural Networks

Zhang, Shuo; Chen, YangQuan; Yu, Yongguang

doi:10.1115/detc2017-67129

Cited by 10 publications

(7 citation statements)

References 54 publications

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“…Fractional differential equation has been deemed to be a powerful tool for the modeling of practical problems in biology, chemistry, physics, medicine, economics and other sciences [2]. Contrasting with classical integer-order systems, the reality can be better described by fractional-order systems for the reason that fractional-order differentiation takes into account the present state and all the history of its previous states [3][4]. In other words, fractional-order systems have memory and heredity.…”

Section: Introductionmentioning

confidence: 99%

Fixed-Time Synchronization of Delayed Fractional-Order Memristor-Based Fuzzy Cellular Neural Networks

Sun

Liu

2020

IEEE Access

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In this paper, we discussed the fixed-time synchronization of fractional-order memristorbased fuzzy cellular neural networks (FMFCNNs) with time-varying delays. Based on the differential inclusion theory and discontinuous state feedback control technique, some useful novel criteria of the fixedtime synchronization for FMFCNNs are derived by constructing appropriate Lyapunov function. The results in our paper improve and generalize current literature research results significantly. Finally, the effectiveness of our control schemes for the fixed-time synchronization is demonstrated through numerical simulations. INDEX TERMS Fractional-order memristor-based fuzzy cellular neural networks, fixed-time synchronization, state feedback control technique, Lyapunov direct method.

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Section: Introductionmentioning

confidence: 99%

Fixed-Time Synchronization of Delayed Fractional-Order Memristor-Based Fuzzy Cellular Neural Networks

Sun

Liu

2020

IEEE Access

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“…In [33] and [34], Kaslik and Sivasundaram proposed fractional-order neural networks of Hopfield type with different structures. What's more, a variable-order fractional operator was introduced into NNs in [35]. Also, Song and Cao [36] investigated the FNNs and provided the existence and uniqueness of the nontrivial solution.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Fractional-Order Neural Networks With Discrete and Distributed Delays

Xiao

Jiang

et al. 2020

IEEE Access

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This paper is concerned with the stability and Hopf bifurcation of fractional-order neural networks with discrete and distributed delays. The novelty of this paper is to take into account the discrete time delay and the distributed time delay for fractional-order systems. By introducing two virtual neurons to the original network, a new four-neuron network only involving discrete delays is formed. The sum of discrete delays is adopted as the bifurcation parameter to demonstrate the existence of Hopf bifurcation. It is found that the critical value of bifurcation can be effectively manipulated by choosing appropriate system parameters and order. Finally, numerical simulations are executed to substantiate the theoretical results and describe the relationships between the parameters and the onset of bifurcation. INDEX TERMS Stability, Hopf bifurcation, discrete delay, distributed delay, fractional-order neural networks.

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“…From estimation of fractional order systems using fractional order neural networks point of view, Zhang et al (2017) have presented fractional order neural networks. In Ruan and Liu (2017), Mittag-Leffler stability has been introduced for a class of impulse fractional order neural networks with continuous and distributed delays in which various control strategies and inequality techniques, new measures for ensuring Mittag-Leffler stability of the controlled neural network are obtained.…”

Section: Introductionmentioning

confidence: 99%

Multi-model estimation using neural network and fault detection in unknown time continuous fractional order nonlinear systems

Nassajian

Balochian

2020

Transactions of the Institute of Measurement and Control

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In this paper, multi-model estimation and fault detection using neural network is proposed for an unknown time continuous fractional order nonlinear system. Fractional differentiation is considered based on Caputo concept and the fractional order is considered to be between 0 and 1. In order to estimate a time continuous fractional order nonlinear system with unknown term in its dynamic, single-layer and double-layer RBF neural network is used. First, a parallel-series neural network observer is designed for state estimation. Weights of the neural network are updated adaptively and updating laws are presented in fractional order form. Using Lyapunov method, it is proved that state estimation error and weight estimation error of the neural network are bounded. Parameters of the neural estimator converge to ideal parameters which satisfy excitation condition stability. Then, multi-model estimation structure of fractional order nonlinear systems is presented and its application in fault detection is investigated. Finally, simulation results are presented to show efficiency of the proposed method.

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A Survey of Fractional-Order Neural Networks

Cited by 10 publications

References 54 publications

Fixed-Time Synchronization of Delayed Fractional-Order Memristor-Based Fuzzy Cellular Neural Networks

Fixed-Time Synchronization of Delayed Fractional-Order Memristor-Based Fuzzy Cellular Neural Networks

Dynamics of Fractional-Order Neural Networks With Discrete and Distributed Delays

Multi-model estimation using neural network and fault detection in unknown time continuous fractional order nonlinear systems

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