Fractional infinite-horizon optimal control problems with a feed forward neural network scheme

Yavari, Mina; Nazemi, Alireza

doi:10.1080/0954898x.2019.1688878

Cited by 2 publications

(1 citation statement)

References 39 publications

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“…Feedforward neural network is a basic structure with all the nodes in adjacent layers linked to each other [ 17 ]. Feedforward neural network is widely applied in practical problems because it does not require prior distribution information of the simples [ 18 – 22 ].…”

Section: Methodsmentioning

confidence: 99%

Teeth Category Classification by Fractional Fourier Entropy and Improved Hybrid Genetic Algorithm

Lu¹,

O’Donnell

2020

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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It is significant to classify teeth categories in dental treatment. A novel teeth classification method was proposed in this paper, which combined fractional Fourier entropy and feedforward neural network. Firstly, fractional Fourier transform was performed on the teeth CT images and the obtained spectrums were used to extract entropies as the features. Then, a feedforward neural network was employed for automatic classification. To train the parameters in the network, improved hybrid genetic algorithm was leveraged. Experiment results suggested that our method achieved state-of-the-art performance.

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Section: Methodsmentioning

confidence: 99%

Teeth Category Classification by Fractional Fourier Entropy and Improved Hybrid Genetic Algorithm

Lu¹,

O’Donnell

2020

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Artificial neural networks: a practical review of applications involving fractional calculus

Viera-Martin

Gómez-Aguilar

Solís-Pérez

et al. 2022

Eur. Phys. J. Spec. Top.

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In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.

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Fractional infinite-horizon optimal control problems with a feed forward neural network scheme

Cited by 2 publications

References 39 publications

Teeth Category Classification by Fractional Fourier Entropy and Improved Hybrid Genetic Algorithm

Teeth Category Classification by Fractional Fourier Entropy and Improved Hybrid Genetic Algorithm

Artificial neural networks: a practical review of applications involving fractional calculus

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