A novel fractional-order neural network for model reduction of large-scale systems with fractional-order nonlinear structure

Jahanbakhti, Hadi

doi:10.1007/s00500-020-04763-5

Cited by 11 publications

(4 citation statements)

References 31 publications

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“…The Adams-Bashforth method (ABM) is an efficient numerical scheme that converges toward the exact solution. One can see several types of research whose numerical results were reached by ABM [3,24,33,34,42,44,45,82,95,97]. It can lead to non-local, non-singular kernel fractional derivatives [129].…”

Section: Brief Analysis About Numerical Methodsmentioning

confidence: 99%

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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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Section: Brief Analysis About Numerical Methodsmentioning

confidence: 99%

“…From the four tables shown in this manuscript: it's important to mention that temporal models with recurrent FANN have been developed in works: [41,45,79,102,182,198,199,263,266].…”

Section: Global Projective Synchronizationmentioning

confidence: 99%

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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“…Instead of designing the FO-ANN for each closed loop control system, the overall closed loop model backlash nonlinearity [10]. A research is adopted for model reduction of large scale systems using fractional order neural networks [11]. A neural network is used to tackle the nonlinear fractional order systems for multi-model estimation and fault detection purposes [12].…”

Section: Framework Of Fo-ann-clpcmentioning

confidence: 99%

Fractional Order Neural Transient Modeling of Primary Circuit of ACP1000 Based Nuclear Power Plant in LabVIEW

Malik

Memon

Arshad

2022

PPASA

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The primary circuit of the nuclear power plant is the most advanced and sophisticated loop of the Advanced Chinese Pressurized Water Reactor (ACP1000). The primary circuit is composed of most technologically advanced nuclear systems and controllers. In this research work, closed loop dynamics of primary circuit (CLPC) of ACP1000 based nuclear power plant is identified. The closed loop dynamics is comprised of highly nonlinear coupled sevencontrol systems. The turbine power, pressurizer temperature, cold leg temperature, hot leg temperature, coolant average temperature and feed water flow are the selected parameters of interest as inputs while neutron power, reactor coolant pressure, pressurizer level, steam generator pressure, steam generator level and steam generator flow as outputs. Therefore, a closed loop multi-input multi-out (MIMO) is configured. The control oriented closed loop dynamics of the primary circuit of ACP1000 is estimated by state-of-the-art novel fractional order neural network (FO-ANN) tool developed in LabVIEW. The parameters of FO-ANN of CLPC (FO-ANN-CLPC) are optimized using fractional order backpropagation (FO-BP) algorithm. The performance of FO-ANN-CLPC is tested and validated in transient conditions and the proposed model predicted the desired reactor power with minimizing error function. The robust performance of the proposed closed loop model is evaluated by dynamic simulation for a prescribed turbine load power increase transient from 20 % to 100 % and validated against reactor power and behaviour of various thermal hydraulics parameters are observed and analyzed.

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“…Fractional calculus, as a generalization of integer-order differential and integral operators, has attracted more and more attention from experts and scholars due to its attractive properties in many fields such as physics and engineering. Many scholars have combined traditional methods with fractional calculus to improve the control performance of the system, such as sliding mode control (Razzaghian et al, 2021), adaptive control (Sui et al, 2020), neural network (Jahanbakhti, 2020) and fuzzy control (Zhang and Ai, 2021).…”

Section: Introductionmentioning

confidence: 99%

Fixed-time convergence of second-order nonlinear systems based on nonsingular fractional sliding mode

Lei,

Lan,

Sun

et al. 2024

Transactions of the Institute of Measurement and Control

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In this paper, a fixed-time convergence scheme for fractional sliding modes is proposed for nonlinear second-order systems. Firstly, a fixed-time fractional-order sliding mode surface is designed by combining the fixed-time theory with fractional-order sliding mode control, which has a faster convergence rate and less chattering. Secondly, the proposed sliding mode controller is applied to a class of second-order nonlinear systems subject to uncertainties and external perturbations to ensure that the system is globally robust fixed-time stable. Then, a continuous fractional order approach law is designed and the proposed sliding mode controller is shown to converge in fixed time by Lyapunov function and the convergence time is related to the choice of controller parameters. Finally, the fixed-time fractional-order sliding mode control strategy is applied to a second-order nonlinear magnetic levitation system system, and the simulation results verify the effectiveness of the proposed method.

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A novel fractional-order neural network for model reduction of large-scale systems with fractional-order nonlinear structure

Cited by 11 publications

References 31 publications

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

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

Fractional Order Neural Transient Modeling of Primary Circuit of ACP1000 Based Nuclear Power Plant in LabVIEW

Fixed-time convergence of second-order nonlinear systems based on nonsingular fractional sliding mode

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