24 results on '"Wang, Yong"'
Search Results
2. The global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays.
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Wang, Yong and Li, Jinmei
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TIME-varying networks , *FRACTIONAL calculus , *CAPUTO fractional derivatives , *SYNCHRONIZATION , *LYAPUNOV stability - Abstract
This paper investigates the global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays. First, the model of fractional-order inertial memristive neural network with time-varying delays is proposed, which is more universal and less conservative than the integer-order inertial memristive neural network with time-varying delays. Second, one lemma about the compound property of Caputo fractional derivative and integral is given. According to the compound property of Caputo fractional derivative and appropriate variable substitution, the original inertial memristive system translates a routine inertial memristive system. And, using the Filippov discontinuous theory, Lyapunov stability theory, and Mittag-Leffler convergence, several sufficient conditions are derived to ensure the global Mittag-Leffler synchronization of Caputo fractional-order inertial memristive neural networks. An effective feedback controller is proposed for fractional-order inertial memristive neural networks with time-varying delays, such that the global Mittag-Leffler synchronization between the slave system and the master system can be achieved. Finally, a simulation example is given to verify the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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3. Study on fast speed fractional order gradient descent method and its application in neural networks.
- Author
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Wang, Yong, He, Yuli, and Zhu, Zhiguang
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PARTICLE swarm optimization , *FRACTIONAL calculus , *MATHEMATICAL optimization , *SPEED , *RUNNING speed - Abstract
• A novel fractional order gradient descent method based on quadratic loss function is proposed. • A novel two-stage fractional order gradient descent method is proposed with random weight particle swarm optimization algorithm. • The scope of application of the fractional order gradient descent is expanded. This article introduces a novel fractional order gradient descent method for the quadratic loss function. Based on Riemann-Liouville definition, a more practical fractional order gradient descent method with variable initial value is proposed to ensure convergence to the actual extremum. On this basis, the random weight particle swarm optimization algorithm is introduced to select the appropriate initial value, which not only accelerates the convergence speed, but also enhances the global convergence ability of the algorithm. To avoid complicated problems of the chain rule in fractional calculus, the parameters of output layers is trained by the new designed method, while the parameters of hidden layers still use the conventional method. By selecting proper hyper-parameters, the proposed method shows faster convergence speed than others. Finally, numerical examples are given to verify that the proposed algorithm has fast convergence speed and high accuracy under a adequate large number of independent runs. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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4. Description and analysis of the time–domain response of nabla discrete fractional order systems.
- Author
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Wei, Yiheng, Gao, Qing, Cheng, Songsong, and Wang, Yong
- Subjects
FRACTIONAL calculus ,LAPLACE transformation - Abstract
This paper investigates the time–domain response of nabla discrete fractional order systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag–Leffler function. In particular, we find the limitation of discrete Mittag–Leffler when adopted in describing the response. Then we establish two fundamental properties of a nabla discrete fractional order system with nonzero initial instant: i) the existence and uniqueness of the system time–domain response; and ii) the dynamic behavior of the zero input response. Finally, a simulation study is provided to show the validity of the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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5. Modelling and simulation of nabla fractional dynamic systems with nonzero initial conditions.
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Wei, Yiheng, Wang, Jiachang, Tse, Peter W., and Wang, Yong
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DYNAMICAL systems ,SIMULATION methods & models ,FRACTIONAL calculus ,ALGORITHMS ,FINITE, The - Abstract
The paper focuses on the numerical approximation of discrete fractional order systems with the conditions of nonzero initial instant and nonzero initial state. First, the inverse nabla Laplace transform is developed and the equivalent infinite dimensional frequency distributed model of discrete fractional order system is introduced. Then, resorting the nabla discrete Laplace transform, the rationality of the finite dimensional frequency distributed model approaching the infinite one is illuminated. Based on this, an original algorithm to estimate the parameters of the approximate model is proposed with the help of vector fitting method. Additionally, the applicable object is extended from a sum operator to a general system. Three numerical examples are performed to illustrate the applicability and flexibility of the introduced methodology. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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6. Differential flatness‐based ADRC scheme for underactuated fractional‐order systems.
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Li, Zongyang, Wei, Yiheng, Zhou, Xi, Wang, Jiachang, Wang, Jianli, and Wang, Yong
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FRACTIONAL calculus ,ITERATIVE learning control ,FRACTIONAL programming - Abstract
Summary: This article mainly studies the fractional‐order active disturbance rejection control (FOADRC) schemes for the underactuated commensurate fractional‐order systems (FOSs). The FOADRC framework for linear FOSs‐based fractional proportion integration differentiation is constructed by using the fractional‐order tracking differentiator and the fractional‐order extended state observer, and the necessary conditions for the system to have stable controllers are provided. The FOADRC scheme for underactuated FOSs based on differential flatness is proposed. For underactuated FOSs, a set of flat output expressions with a fixed format is given under the controllable condition of the system. Moreover, making the flat output as the equivalent of the system output is simple and easy to analyze and calculate. Subsequently, the FOADRC scheme is designed by using the flat output. Finally, the scheme proposed in this article is verified by a simulation example. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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7. Discussion on the Leibniz rule and Laplace transform of fractional derivatives using series representation.
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Wei, Yiheng, Liu, Da-Yan, Tse, Peter W., and Wang, Yong
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INTEGRAL transforms ,DIFFERENTIABLE functions ,FRACTIONAL calculus ,LAPLACE'S equation - Abstract
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. On this basis, the Lebiniz rule and Laplace transform of fractional calculus is investigated. It is analytically shown that the commonly used Leibniz rule cannot be applied for Caputo derivative. Similarly, the well-known Laplace transform of Riemann–Liouville derivative is doubtful for n-th continuously differentiable function. After pointing out such problems, the exact formula of Caputo Leibniz rule and the explanation of Riemann–Liouville Laplace transform are presented. Finally, three illustrative examples are revisited to confirm the obtained results. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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8. A bias-compensated fractional order normalized least mean square algorithm with noisy inputs.
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Yin, Weidi, Cheng, Songsong, Wei, Yiheng, Shuai, Jianmei, and Wang, Yong
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MEAN square algorithms ,LEAST squares ,FRACTIONAL calculus - Abstract
This paper comes up with a stable bias-compensated fractional order normalized least mean square (BC-FONLMS) algorithm with noisy inputs. This kind of bias-compensated algorithm needs the estimation of input noise variance to avoid the bias caused by noisy inputs. Yet, existing algorithms either cause instability because of the method used to estimate input noise variance, or surmount the instability problems at the price of performance diminishment. This paper introduces fractional order calculus into LMS algorithm to be a new BC-FONLMS algorithm. Then, analyze the stability of the BC-FONLMS algorithm through probing the recursive equations of mean deviation (MD) and mean square deviation (MSD). On the basis of the stability analysis, methods to estimate input noise variance and to adjust step size are suggested to stabilize the algorithm and likewise to enhance the performance such as convergence speed and steady-state error. Numerical simulations are given at last, whose results show that the proposed BC-FONLMS algorithm performs well. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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9. Lyapunov functions for nabla discrete fractional order systems.
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Wei, Yiheng, Chen, Yuquan, Liu, Tianyu, and Wang, Yong
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LYAPUNOV functions ,NONLINEAR systems ,FRACTIONAL calculus - Abstract
Abstract This paper focuses on the fractional difference of Lyapunov functions related to Riemann–Liouville, Caputo and Grünwald–Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for each definition. With the help of the developed inequalities, the sufficient conditions can be obtained to guarantee the asymptotic stability of the nabla discrete fractional order nonlinear systems. Finally, three illustrative examples are presented to demonstrate the validity and feasibility of the proposed theoretical results. Highlights • New method to build Lyapunov functions for discrete fractional order systems. • Five inequalities on the fractional difference of Lyapunov functions. • The applicability of the proposed results for three different definitions. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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10. The numerical algorithms for discrete Mittag-Leffler functions approximation.
- Author
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Li, Ang, Wei, Yiheng, Li, Zongyang, and Wang, Yong
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MATHEMATICAL functions ,DISCRETE geometry ,NUMERICAL analysis ,FRACTIONAL calculus ,MATRIX functions ,APPROXIMATION theory - Abstract
Motivated essentially by the success of the applications of the discrete Mittag-Leffler functions (DMLF) in many areas of science and engineering, the authors present, in a unified manner, a detailed numerical implementation method of the Mittag-Leffler function. With the proposed method, the overflow problem can be well solved. To further improve the practicability, the state transition matrix described by discrete Mittag-Leffler functions are investigated. Some illustrative examples are provided to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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11. Fixed pole based modeling and simulation schemes for fractional order systems.
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Wei, Yiheng, Wang, Jiachang, Liu, Tianyu, and Wang, Yong
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FRACTIONAL calculus ,FRACTIONAL differential equations ,APPROXIMATION theory ,DIFFERENTIAL equations ,ALGORITHMS - Abstract
Abstract This paper mainly investigates the numerical implementation issue of fractional order systems. First, a pattern of fixed pole schemes are developed to approximate fractional integrator/differentiator, whose common is that the poles keep constant for different α. Then, two solutions are proposed to improve the approximation performance around α = 0. Afterwards, the simulation schemes are introduced for two kinds of fractional order systems. In those schemes, the configuration problem of nonzero initial value is considered. Finally, a fair and solid comparison to the classical approximation methods is presented, demonstrating the effectiveness and efficiency of the elaborated algorithms. Highlights • A universal fixed pole approximation algorithm is derived for fractional integrator/differentiator. • The improvement is made to achieve a better performance with smaller order. • Two approximation schemes are presented for implementing fractional transfer function model. • Three approximation schemes are proposed for implementing fractional state space model. • The configuration of nonzero initial system state is discussed for fractional order system. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
12. Fractional Order Systems Time-Optimal Control and Its Application.
- Author
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Wei, Yiheng, Du, Bin, Cheng, Songsong, and Wang, Yong
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FRACTIONAL calculus ,CALCULUS of variations ,OPTIMAL control theory ,ANALYTICAL solutions ,MATHEMATICAL analysis - Abstract
This paper deals with the time-optimal control problem for a class of fractional order systems. An analytic solution of the time-optimal problem is proposed, and the optimal transfer route is provided. Considering it is usually adopted in the discrete situation for actual control system, the sampling date may induce chattering phenomenon, an alternative sub-optimal solution is constructed. Additionally, the special and meaningful application of fractional order tracking differentiator is introduced to explain our main results. The effectiveness and advantages of the proposed method have been illustrated by numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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13. Type Number Based Steady-State Error Analysis on Fractional Order Control Systems.
- Author
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Pan, Jinwen, Gao, Qing, Qiu, Jianbin, and Wang, Yong
- Subjects
FEEDBACK control system stability ,FRACTIONAL calculus ,NONLINEAR differential equations ,ERROR analysis in mathematics ,TRANSFER functions - Abstract
In this paper, steady-state error of fractional order control systems (FOCSs) is analyzed based on the concept of type number. Some practical definitions of the reference and the error for FOCSs with non-unity feedback are first given. Based on these definitions, the type number concept is first introduced to FOCSs with non-unity feedback. Then steady-state error of various types of FOCSs are analyzed respectively via type number concept. It is also shown that FOCSs with type number more than 1 are not able to track particular reference without changing the sign of the tracking error. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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14. A novel self-adaptive fractional multivariable grey model and its application in forecasting energy production and conversion of China.
- Author
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Wang, Yong, Wang, Li, Ye, Lingling, Ma, Xin, Wu, Wenqing, Yang, Zhongsen, He, Xinbo, Zhang, Lei, Zhang, Yuyang, Zhou, Ying, and Luo, Yongxian
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ENERGY conversion , *PROBABILITY density function , *MONTE Carlo method , *PARTICLE swarm optimization , *FRACTIONAL calculus - Abstract
Energy production and conversion have a significant impact on the economic development of all countries in the world. China's energy production and conversion are large. Therefore, accurate mid-to-long term China's energy production and conversion forecasting is becoming more and more important for integrating energy systems and energy strategic planning. For this purpose, a novel fractional grey sequence is proposed based on Grunwald–Letnikov fractional calculus. Furthermore, a novel self-adaptive fractional multivariable grey model is proposed based on the novel sequence. In this article, we compare several classical optimization algorithms and finally choose Particle Swarm Optimization (PSO) to compute the parameters. In addition, Monte-Carlo simulation and probability density analysis (PDA) are presented in this article to verify the model's performance. Monte-Carlo simulation reduces the randomness of the results of the model runs to a certain extent. Probability density analysis visualizes this randomness through kernel density estimation (KDE). This paper compares the new model with the existing seven grey models and predicts the total energy consumption per capita, energy conversion efficiency and total renewable energy in China, respectively. The experimental results show that the new model is superior to the other seven models in terms of stability and prediction accuracy. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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15. Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence.
- Author
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Wang, Yong-Long, Jahanshahi, Hadi, Bekiros, Stelios, Bezzina, Frank, Chu, Yu-Ming, and Aly, Ayman A.
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RECURRENT neural networks , *SLIDING mode control , *FINANCIAL markets , *DEEP learning , *LYAPUNOV stability , *CONFIDENCE - Abstract
• We develop a new finite-time method for controlling and synchronising fractional-order financial systems • A Deep Learning Recurrent Neural Network is integrated by terminal sliding mode control • The proposed technique is applied to a chaotic fractional-order financial model with market confidence under highly complex and time-varying uncertainties • It is shown comparatively that when the disturbances are high, the conventional TSMC methods fail Disturbances are inevitably found in almost every system and, if not rejected, they could jeopardize the effectiveness of control methods. Thereby, employing state-of-the-art observers could improve the reliability and performance of controllers dramatically. Motivated by this, we develop a new finite-time method for controlling and synchronising fractional-order systems. The deep learning recurrent neural network, which is a strong tool in handling highly complex and time-varying uncertainties, is integrated by terminal sliding mode control. On the basis of Lyapunov stability theorem, the finite-time convergence and stability of the closed-loop system are proven. Then, the proposed technique is applied to a chaotic fractional-order financial model with market confidence. In simulations, it is supposed that the system is operating in the presence of complex disturbances. The results of the proposed technique are compared with terminal sliding mode control. Numerical results illustratively confirm the theoretical claims about the robust performance of the deep learning control technique. Also, it is shown that when the disturbances are high, the conventional methods fail. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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16. Stability analysis of fractional-order neural networks: An LMI approach.
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Yang, Ying, He, Yong, Wang, Yong, and Wu, Min
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FRACTIONAL calculus , *ARTIFICIAL neural networks , *LYAPUNOV functions , *LINEAR matrix inequalities , *NUMERICAL analysis - Abstract
This paper analyzes the stability of fractional-order neural networks (FNNs) without and with delay by the fractional Lyapunov direct method and the fractional Razumikhin-type theorem, respectively. S-procedure is applied to handle the nonlinear constraints to obtain a wider parameter selection of the systems. For FNNs without delay, the improved less conservative conditions of the existence and uniqueness of the equilibrium point and the global Mittag-Leffler stability are all derived in the form of linear matrix inequalities (LMIs). Moreover, an LMI-based uniform stability condition of FNNs with time delay is established, which simplifies and extends some previous work. Finally, the validity of the presented results is indicated by some numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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17. Stability analysis for impulsive fractional hybrid systems via variational Lyapunov method.
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Yang, Ying, He, Yong, Wang, Yong, and Wu, Min
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STABILITY theory , *LYAPUNOV functions , *CAPUTO fractional derivatives , *MOMENTS method (Statistics) , *FRACTIONAL calculus - Abstract
This paper investigates the stability properties for a class of impulsive Caputo fractional-order hybrid systems with impulse effects at fixed moments. By utilizing the variational Lyapunov method, a fractional variational comparison principle is established. Some stability and instability criteria in terms of two measures are obtained. These results generalize the known ones, extending the corresponding theory of impulsive fractional differential systems. An example is given to demonstrate their effectiveness. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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- View/download PDF
18. Generalization of the gradient method with fractional order gradient direction.
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Wei, Yiheng, Kang, Yu, Yin, Weidi, and Wang, Yong
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GENERALIZATION , *INFINITE series (Mathematics) , *FRACTIONAL calculus , *ORDER , *PROBLEM solving - Abstract
Fractional calculus is an efficient tool, which has the potential to improve the performance of gradient methods. However, when the first order gradient direction is generalized by fractional order gradient one, the corresponding algorithm converges to the fractional extreme point of the target function which is not equal to the real extreme point. This drawback critically hampers the application of this method. To solve such a convergence problem, the current paper analyzes the specific reasons and proposes three possible solutions. Considering the long memory characteristics of fractional derivative, short memory principle is a prior choice. Apart from the truncation of memory length, two new methods are developed to reach the convergence. The former is the truncation of the infinite series, and the latter is the modification of the constant fractional order. Finally, six illustrative examples are performed to illustrate the effectiveness and practicability of proposed methods. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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19. A novel orthogonalized fractional order filtered-x normalized least mean squares algorithm for feedforward vibration rejection.
- Author
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Yin, Weidi, Wei, Yiheng, Liu, Tianyu, and Wang, Yong
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FRACTIONAL differential equations , *ORTHOGONALIZATION , *VIBRATION (Mechanics) , *FEEDFORWARD control systems , *FRACTIONAL calculus - Abstract
Highlights • The Fx-NLMS algorithm for feedforward vibration rejection is improved. • Fx-NLMS algorithm using fractional order descent method is proposed. • Orth-FONLMS algorithm using orthogonal transform method is formed. Abstract This paper mainly discusses a pattern of vibration rejection by using a feedforward controller. Conventional filtered-x normalized least mean squares (Fx-NLMS) algorithm converges slow especially when signals are not independent on each other. Therefore, a novel orthogonalized fractional order filtered-x normalized least mean squares (Orth-FONLMS) algorithm is proposed to obtain the precise parameters of the feedforward controller. The proposed algorithm is an improved Fx-NLMS algorithm by using fractional calculus and orthogonal transform. To implement the algorithm, fractional order gradient method and adaptive lattice filter are introduced, respectively. Numerical simulation proves that the proposed algorithm outperforms over the Fx-NLMS and fractional order filtered-x normalized least mean squares (Fx-FONLMS) algorithm in terms of convergence rate and accuracy. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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- View/download PDF
20. Design and implementation of fractional differentiators, Part I: System based methods.
- Author
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Wei, Yiheng, Gao, Qing, Chen, Yuquan, and Wang, Yong
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FRACTIONAL calculus , *DIFFERENTIATOR circuits , *AUTOMATIC control systems , *MATHEMATICAL analysis , *COMPUTER systems - Abstract
Abstract The online calculation of fractional derivative is an important technique used in the control engineering area. To achieve satisfactory computing performance, this paper proposes a useful and effective tool named fractional order tracking differentiator (FOTD), which is easy to be implemented. A constructive method for designing the FOTD is developed using a class of asymptotically stable fractional order systems. It is shown that FOTD is the pioneering one to achieve it with simple structure, convenient construction and predominant performance. Finally, several examples are conducted to illustrate the effectiveness and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
21. Fractional central difference Kalman filter with unknown prior information.
- Author
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Liu, Tianyu, Cheng, Songsong, Wei, Yiheng, Li, Ang, and Wang, Yong
- Subjects
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KALMAN filtering , *FRACTIONAL calculus , *ALGORITHMS , *COMPUTATIONAL complexity , *NONLINEAR systems - Abstract
Highlights • A generalized fractional central difference Kalman filter is proposed. • An adaptive fractional central difference Kalman filter is proposed to estimate the system state and noise parameters simultaneously. • The unbiasedness of the proposed adaptive algorithm is analyzed and then an unbiased recursive algorithm is developed. • The approximate accuracy and numerical complexity of the proposed algorithm are analyzed. Abstract In this paper, a generalized fractional central difference Kalman filter for nonlinear discrete fractional dynamic systems is proposed. Based on the Stirling interpolation formula, the presented algorithm can be implemented as no derivatives are needed. Besides, in order to estimate the state with unknown prior information, a maximum a posteriori principle based adaptive fractional central difference Kalman filter is derived. The adaptive algorithm can estimate the noise statistics and system state simultaneously. The unbiasedness of the proposed algorithm is analyzed. Several numerical examples demonstrate the accuracy and effectiveness of the two Kalman filters. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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22. On the series representation of nabla discrete fractional calculus.
- Author
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Wei, Yiheng, Gao, Qing, Liu, Da-Yan, and Wang, Yong
- Subjects
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DISCRETE systems , *FRACTIONAL calculus , *REPRESENTATION theory , *MATHEMATICAL series , *PROBLEM solving - Abstract
Highlights • A new nabla Taylor formula expanded at b ≥ n is derived for a discrete function. • Two kinds of series representations of are derived for nabla discrete fractional sum/difference. • Some essential properties of nabla discrete fractional calculus are investigated. • Besides fixed initial instant case, nabla fractional calculus with fixed memory step are introduced. Abstract This paper addresses the description and analysis problems of nabla discrete fractional calculus. The series representation framework is developed first, including two Taylor series expanded at the initial instant and the current time, respectively. Under this framework, several essential properties of fractional sum/difference are presented and investigated. Notably, the short memory principle is introduced for nabla discrete fractional calculus, along with which two corresponding series are studied. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
23. An innovative fractional order LMS based on variable initial value and gradient order.
- Author
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Cheng, Songsong, Wei, Yiheng, Chen, Yuquan, Li, Yan, and Wang, Yong
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INITIAL value problems , *FRACTIONAL calculus , *MATHEMATICAL variables , *SAMPLING errors , *STOCHASTIC convergence - Abstract
This article presents a novel fractional order LMS (FOLMS) algorithm, which involves a variable gradient order scheme. The fractional order gradient descent method is revisited firstly. A variable initial value scheme is proposed to attenuate the non–locality of fractional order calculus and to ensure the convergence of the proposed FOLMS algorithm. Furthermore, it is noticed that a contradiction between rapidity and accuracy always appears together with the advancement of FOLMS algorithm; namely, a larger value of the gradient order can not only give a faster convergence speed, but also correspond to a larger estimation error. For the purpose of removing the contradiction between rapidity and accuracy, a variable gradient order scheme is designed for the FOLMS algorithm. Based on a sufficient large number of independent runs, the efficiency and superiority of the proposed algorithm are demonstrated in numerical examples finally. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
24. Indirect model reference adaptive control for a class of fractional order systems.
- Author
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Chen, Yuquan, Wei, Yiheng, Liang, Shu, and Wang, Yong
- Subjects
- *
ADAPTIVE control systems , *LYAPUNOV functions , *FRACTIONAL differential equations , *DISTRIBUTION (Probability theory) , *FRACTIONAL calculus , *MATHEMATICAL models - Abstract
This article focuses on the indirect model reference adaptive control problem for fractional order systems. A constrained gradient estimation method was established firstly, since parameter estimation is part and parcel of the whole control problem. Then a novel adaptive control law is designed, from which the two problems, i.e., parameter estimation and reference tracking, can be unified perfectly. On these basis, an effective control scheme is established. The stability of the resulting closed-loop system is analyzed rigorously via indirect Lyapunov method and frequency distributed model. Finally, a careful simulation study is reported to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
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