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Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method Research Articles

Yi-fei Pu, Jian Wang,puyifei@scu.edu.cn,wangjiannl@upc.edu.cn

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.1900593

Abstract: We introduce the fractional-order global optimal backpropagation machine, which is trained by an improved (FSDM). This is a fractional-order backpropagation neural network (FBPNN), a state-of-the-art fractional-order branch of the family of backpropagation neural networks (BPNNs), different from the majority of the previous classic first-order BPNNs which are trained by the traditional first-order steepest descent method. The reverse incremental search of the proposed FBPNN is in the negative directions of the approximate fractional-order partial derivatives of the square error. First, the theoretical concept of an FBPNN trained by an improved FSDM is described mathematically. Then, the mathematical proof of fractional-order global optimal convergence, an assumption of the structure, and of the FBPNN are analyzed in detail. Finally, we perform three (types of) experiments to compare the performances of an FBPNN and a classic first-order BPNN, i.e., example function approximation, , and comparison of global search and error fitting abilities with real data. The higher optimal search ability of an FBPNN to determine the global optimal solution is the major advantage that makes the FBPNN superior to a classic first-order BPNN.

Keywords： 分数阶微积分；分数阶反向传播算法；分数阶最速下降法；均方误差；分数阶多尺度全局优化    

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Fractional-order memristive neural synaptic weighting achieved by pulse-based fracmemristor bridge circuit Research Articles

Yifei Pu, Bo Yu, Qiuyan He, Xiao Yuan,heqiuyan789@163.com,yuanxiao@scu.edu.cn

Frontiers of Information Technology & Electronic Engineering 2021, Volume 22, Issue 6,   Pages 862-876 doi: 10.1631/FITEE.2000085

Abstract: We propose a novel circuit for the fractional-order memristive neural synaptic weighting (FMNSW). The introduced circuit is different from the majority of the previous integer-order approaches and offers important advantages. Since the concept of memristor has been generalized from the classic integer-order memristor to the (), a challenging theoretical problem would be whether the can be employed to implement the or not. In this research, characteristics of the FMNSW, realized by a pulse-based bridge circuit, are investigated. First, the circuit configuration of the FMNSW is explained using a pulse-based bridge circuit. Second, the mathematical proof of the fractional-order learning capability of the FMNSW is analyzed. Finally, experimental work and analyses of the electrical characteristics of the FMNSW are presented. Strong ability of the FMNSW in explaining the cellular mechanisms that underlie learning and memory, which is superior to the traditional integer-order memristive neural synaptic weighting, is considered a major advantage for the proposed circuit.

Keywords： 分数阶微积分；分忆抗；分忆抗值；分数阶忆阻；分数阶记忆性突触    

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Discrete fractional watermark technique Correspondence

Zai-rong Wang, Babak Shiri, Dumitru Baleanu,wangzr@njtc.edu.cn,shire_babak@yahoo.com,dumitru@cankaya.edu.tr

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.2000133

Abstract: The fractional logistic map holds rich dynamics and is adopted to generate chaotic series. A image is then encrypted and inserted into the original images. Since the encryption image takes the fractional order within (0, 1], it increases the key space and becomes difficult to attack. This study provides a robust method in the protection of the copyright of hardware, images, and other electronic files.

Keywords： 离散分数阶微积分；图像加密；水印    

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Design of a fractional PI None

Pritesh SHAH, Sudhir AGASHE, Anand J. KULKARNI

Frontiers of Information Technology & Electronic Engineering 2018, Volume 19, Issue 3,   Pages 437-445 doi: 10.1631/FITEE.1601495

Abstract: The cohort intelligence (CI) method has recently evolved as an optimization method based on artificial intelligence. We use the CI method for the first time to optimize the parameters of the fractional proportionalintegral-derivative (PID) controller. The performance of the CI method in designing the fractional PID controller was validated and compared with those of some other popular algorithms such as particle swarm optimization, the genetic algorithm, and the improved electromagnetic algorithm. The CI method yielded improved solutions in terms of the cost function, computing time, and function evaluations in comparison with the other three algorithms. In addition, the standard deviations of the CI method demonstrated the robustness of the proposed algorithm in solving control problems.

Keywords： Cohort intelligence     Fractional calculus     Fractional PID controller     Tuning    

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An improved ROF denoising model based on time-fractional derivative Research Articles

Xing-ran Liao,xrliao_scu@163.com

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.2000067

Abstract: In this study, we discuss mainly the and texture retention issues. Usually, the has an adjustable fractional order to control the diffusion process, and its memory effect can nicely retain the image texture when it is applied to . Therefore, we design a new Rudin-Osher-Fatemi model with a based on a classical one, where the discretization in space is based on the integer-order difference scheme and the discretization in time is the approximation of the (i.e., Caputo-like difference is applied to discretize the ). Stability and convergence of such an explicit scheme are analyzed in detail. We prove that the numerical solution to the new model converges to the exact solution with the order of (+), where , , and are the time step size, fractional order, and space step size, respectively. Finally, various evaluation criteria including the signal-to-noise ratio, feature similarity, and histogram recovery degree are used to evaluate the performance of our new model. Numerical test results show that our improved model has more powerful denoising and texture retention ability than existing ones.

Keywords： 改进ROF去噪模型；时间分数阶导数；Caputo导数；图像去噪    

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A fractional-order multifunctionaln-step honeycomb RLC circuit network Article

Ling ZHOU, Zhi-zhong TAN, Qing-hua ZHANG

Frontiers of Information Technology & Electronic Engineering 2017, Volume 18, Issue 8,   Pages 1186-1196 doi: 10.1631/FITEE.1601560

Abstract: We investigate a multifunctional -step honeycomb network which has not been studied before. By adjusting the circuit parameters, such a network can be transformed into several different networks with a variety of functions, such as a regular ladder network and a triangular network. We derive two new formulae for equivalent resistance in the resistor network and equivalent impedance in the LC network, which are in the fractional-order domain. First, we simplify the complex network into a simple equivalent model. Second, using Kirchhoff’s laws, we establish a fractional difference equation. Third, we construct an equivalent transformation method to obtain a general solution for the nonlinear differential equation. In practical applications, several interesting special results are obtained. In particular, an step impedance LC network is discussed and many new characteristics of complex impedance have been found.

Keywords： Honeycomb network     Equivalent transformation     Fractional differential equation     Impedance characteristics    

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Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux Regular Papers

Karthikeyan RAJAGOPAL, Fahimeh NAZARIMEHR, Anitha KARTHIKEYAN, Ahmed ALSAEDI, Tasawar HAYAT, Viet-Thanh PHAM

Frontiers of Information Technology & Electronic Engineering 2019, Volume 20, Issue 4,   Pages 584-590 doi: 10.1631/FITEE.1800389

Abstract:

We propose a modified Fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integerorder MFNN system (case A) and a fractional-order MFNN system (case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractionalorder magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.

Keywords： Fitzhugh-Nagumo     Chaos     Fractional order     Magnetic flux    

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A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations Research Articles

Li-ping Chen, Hao Yin, Li-guo Yuan, António M. Lopes, J. A. Tenreiro Machado, Ran-chao Wu,lip_chenhut@126.com

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.1900709

Abstract: A novel algorithm based on dynamic deoxyribonucleic acid (DNA) encoding and chaos is presented. A three-neuron fractional-order discrete Hopfield neural network (FODHNN) is employed as a pseudo-random chaotic sequence generator. Its initial value is obtained with the secret key generated by a five-parameter external key and a hash code of the plain image. The external key includes both the FODHNN discrete step size and order. The hash is computed with the SHA-2 function. This ensures a large secret key space and improves the algorithm sensitivity to the plain image. Furthermore, a new three-dimensional projection confusion method is proposed to scramble the pixels among red, green, and blue color components. DNA encoding and diffusion are used to diffuse the image information. Pseudo-random sequences generated by FODHNN are employed to determine the encoding rules for each pixel and to ensure the diversity of the encoding methods. Finally, confusion II and XOR are used to ensure the security of the encryption. Experimental results and the security analysis show that the proposed algorithm has better performance than those reported in the literature and can resist typical attacks.

Keywords： 分数阶离散系统；神经网络；DNA加密；彩色图像加密    

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Controllability of fractional-order damped systems with time-varying delays in control Research Articles

Bin-bin He, Hua-cheng Zhou, Chun-hai Kou,hebinbin45@126.com,hczhou@amss.ac.cn,kouchunhai@dhu.edu.cn

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.1900736

Abstract: In this study, we focus on the of in linear and nonlinear cases with multiple in control. For the linear system based on the Mittag-Leffler matrix function, we define a , which is useful in judging whether the system is controllable or not. Furthermore, in two special cases, we present serval equivalent controllable conditions which are easy to verify. For the nonlinear system, under the of its corresponding linear system, we obtain a sufficient condition on the nonlinear term to ensure that the system is controllable. Finally, two examples are given to illustrate the theory.

Keywords： 可控性；分数阶阻尼系统；时变时滞；Gramian矩阵    

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Intelligent fractional-order integral sliding mode control for PMSM based on an improved cascade observer Research Articles

Lingfei XIAO, Leiming MA, Xinhao HUANG,lfxiao@nuaa.edu.cn

Frontiers of Information Technology & Electronic Engineering 2022, Volume 23, Issue 2,   Pages 328-338 doi: 10.1631/FITEE.2000317

Abstract: In this paper, an intelligent control (FOISMC) strategy based on an improved cascade is proposed. First, an FOISMC strategy is designed to control a . It has good tracking performance, is strongly robust, and can effectively reduce chattering. The proposed FOISMC strategy associates strong points of the integral action (which can eliminate steady-state tracking errors) and the fractional calculus (which is flexible). Second, an improved cascade is proposed to detect the rotor information with a smaller observation error. The proposed combines an adaptive sliding mode and an extended high-gain . In addition, an improved variable-speed grey wolf is designed to enhance controller parameters. The effectiveness of the strategy is tested using simulations and an experiment involving model uncertainty and external disturbance.

Keywords： Permanent magnet synchronous motor     Fractional-order integral sliding mode     Optimization algorithm     Sensorless control     Observer    

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Bifurcation-based fractional-order PI None

Karima RABAH, Samir LADACI, Mohamed LASHAB

Frontiers of Information Technology & Electronic Engineering 2018, Volume 19, Issue 2,   Pages 180-191 doi: 10.1631/FITEE.1601543

Abstract: We propose a novel approach called the robust fractional-order proportional-integral-derivative (FOPID) controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system, we show that the fractional PIλDμ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.

Keywords： Fractional order system     Bifurcation diagram     Fractional PIλDμ controller     Multi-scroll Chen chaotic system     Genesio-Tesi chaotic system    

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Multi-focus image fusion based on fractional-order derivative and intuitionistic fuzzy sets Research Articles

Xue-feng Zhang, Hui Yan, Hao He,zhangxuefeng@mail.neu.edu.cn

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 6,   Pages 809-962 doi: 10.1631/FITEE.1900737

Abstract: Multi-focus is an increasingly important component in , and it plays a key role in imaging. In this paper, we put forward a novel multi-focus method which employs and . The original image is decomposed into a base layer and a detail layer. Furthermore, a new fractional-order spatial frequency is built to reflect the clarity of the image. The fractional-order spatial frequency is used as a rule for detail layers fusion, and are introduced to fuse base layers. Experimental results demonstrate that the proposed fusion method outperforms the state-of-the-art methods for multi-focus .

Keywords： 像融合；分数阶导数；直觉模糊集；多聚焦图像    

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Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation Research Articles

Zahra Sadat Aghayan, Alireza Alfi, J. A. Tenreiro Machado,a_alfi@shahroodut.ac.ir

Frontiers of Information Technology & Electronic Engineering 2021, Volume 22, Issue 10,   Pages 1402-1412 doi: 10.1631/FITEE.2000438

Abstract: This study analyzes the problem of of fractional-order delay systems of neutral type under actuator . A Lyapunov–Krasovskii (LK) function is constructed and conditions of the asymptotic of such systems are given, which are formulated by linear matrix inequalities (LMIs), using the Lyapunov direct method. An algorithm is introduced to compute the gain of the state feedback controller for extending the domain of attraction. The theoretical results are validated using some numerical examples.

Keywords： 分数阶系统；稳定性；中立时滞；鲁棒性；饱和性    

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Observer-based control for fractional-order singular systems with order Research Article

Bingxin LI, Xiangfei ZHAO, Xuefeng ZHANG, Xin ZHAO

Frontiers of Information Technology & Electronic Engineering 2022, Volume 23, Issue 12,   Pages 1862-1870 doi: 10.1631/FITEE.2200294

Abstract: In this paper, for fractional-order with order (0<<1) and is studied. On the basis of the Smith predictor and approximation error, the system with is approximately equivalent to the system without . Furthermore, based on the (LMI) technique, the necessary and sufficient condition of is proposed. Since the condition is a nonstrict LMI, including the equality constraint, it will lead to some trouble when solving problems using toolbox. Thus, the strict LMI-based condition is improved in the paper. Finally, a numerical example and a direct current motor example are given to illustrate the effectiveness of the strict LMI-based condition.

Keywords： Observer-based control     Singular systems     Fractional order     Input delay     Linear matrix inequality    

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Mittag-Leffler stability analysis ofmultiple equilibrium points in impulsive fractional-order quaternion-valued neural networks Research Articles

K. UDHAYAKUMAR, R. RAKKIYAPPAN, Jin-de CAO, Xue-gang TAN

Frontiers of Information Technology & Electronic Engineering 2020, Volume 21, Issue 2,   Pages 234-246 doi: 10.1631/FITEE.1900409

Abstract: In this study, we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with impulses. Using the geometrical properties of activation functions and the Lipschitz condition, the existence of the equilibrium points is analyzed. In addition, the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method. Finally, simulation is performed to illustrate the effectiveness and validity of the main results obtained.

Keywords： Mittag-Leffler stability     Fractional-order     Quaternion-valued neural networks     Impulse    

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Title Author Date Type Operation

Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method

Yi-fei Pu, Jian Wang,puyifei@scu.edu.cn,wangjiannl@upc.edu.cn

Journal Article

Fractional-order memristive neural synaptic weighting achieved by pulse-based fracmemristor bridge circuit

Yifei Pu, Bo Yu, Qiuyan He, Xiao Yuan,heqiuyan789@163.com,yuanxiao@scu.edu.cn

Journal Article

Discrete fractional watermark technique

Zai-rong Wang, Babak Shiri, Dumitru Baleanu,wangzr@njtc.edu.cn,shire_babak@yahoo.com,dumitru@cankaya.edu.tr

Journal Article

Design of a fractional PI

Pritesh SHAH, Sudhir AGASHE, Anand J. KULKARNI

Journal Article

An improved ROF denoising model based on time-fractional derivative

Xing-ran Liao,xrliao_scu@163.com

Journal Article

A fractional-order multifunctionaln-step honeycomb RLC circuit network

Ling ZHOU, Zhi-zhong TAN, Qing-hua ZHANG

Journal Article

Dynamics of a neuron exposed to integer- and fractional-order discontinuous externalmagnetic flux

Karthikeyan RAJAGOPAL, Fahimeh NAZARIMEHR, Anitha KARTHIKEYAN, Ahmed ALSAEDI, Tasawar HAYAT, Viet-Thanh PHAM

Journal Article

A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations

Li-ping Chen, Hao Yin, Li-guo Yuan, António M. Lopes, J. A. Tenreiro Machado, Ran-chao Wu,lip_chenhut@126.com

Journal Article

Controllability of fractional-order damped systems with time-varying delays in control

Bin-bin He, Hua-cheng Zhou, Chun-hai Kou,hebinbin45@126.com,hczhou@amss.ac.cn,kouchunhai@dhu.edu.cn

Journal Article

Intelligent fractional-order integral sliding mode control for PMSM based on an improved cascade observer

Lingfei XIAO, Leiming MA, Xinhao HUANG,lfxiao@nuaa.edu.cn

Journal Article

Bifurcation-based fractional-order PI

Karima RABAH, Samir LADACI, Mohamed LASHAB

Journal Article

Multi-focus image fusion based on fractional-order derivative and intuitionistic fuzzy sets

Xue-feng Zhang, Hui Yan, Hao He,zhangxuefeng@mail.neu.edu.cn

Journal Article

Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation

Zahra Sadat Aghayan, Alireza Alfi, J. A. Tenreiro Machado,a_alfi@shahroodut.ac.ir

Journal Article

Observer-based control for fractional-order singular systems with order

Bingxin LI, Xiangfei ZHAO, Xuefeng ZHANG, Xin ZHAO

Journal Article

Mittag-Leffler stability analysis ofmultiple equilibrium points in impulsive fractional-order quaternion-valued neural networks

K. UDHAYAKUMAR, R. RAKKIYAPPAN, Jin-de CAO, Xue-gang TAN

Journal Article