scholarly journals Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huiming Duan ◽  
Kailiang Shao ◽  
Xinping Xiao ◽  
Jinwei Yang
Keyword(s):  
Fractional Order ◽  
Estimation Method ◽  
Original Data ◽  
Grey Model ◽  
Prediction Errors ◽  
Matrix Perturbation ◽  
Perturbation Bound ◽  
Grey Forecasting ◽  
The Matrix ◽  
The Stability

The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as NDGMp/q) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGMp/q and the NDGMp/q can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGMp/q was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGMp/q and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGMp/q was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

Application of Self-Adaptive MGM (1, n) Model in Dam Deformation Prediction

2013 ◽  
Vol 740 ◽  
pp. 284-288
Author(s):  
He Zhi Liu ◽  
Song Lin Wang ◽  
Jing Yang Liu ◽  
Guang Yang
Keyword(s):  
Estimation Method ◽  
Original Data ◽  
Arch Dam ◽  
Deformation Prediction ◽  
Grey Forecasting ◽  
Forecasting Method ◽  
Forecasting Performance ◽  
Dam Deformation ◽  
Data Group ◽  
Self Adaptive

Considering the characteristics of randomness and uncertainty of dam system and the lack of safety monitoring data in some projects, a grey forecasting method based on self-adaptive MGM (1, n) was proposed in this paper to predict the dam deformation. Firstly, theory of the traditional MGM (1, n) model and the parameter estimation method were introduced. On the basis of this, add these forecasted values into the original data group and eliminate the oldest information, the self-adaptive MGM (1, n) model could be established. This paper employs this improved approach in the dam deformation of an arch dam. By predicting the dam deformation in next 5 days, the validity of such method was proved. Compared with GM (1, 1) model and conventional MGM (1, n) model, the experimental results indicate that the forecasting performance is significantly superior to that of the above mentioned two methods.

A variable-order fractional discrete grey model and its application

2021 ◽  
pp. 1-14
Author(s):  
Huang Meixin ◽  
Liu Caixia
Keyword(s):  
Electricity Consumption ◽  
Grey Model ◽  
Liaoning Province ◽  
Model Parameters ◽  
Variable Order ◽  
Matrix Perturbation ◽  
Application Range ◽  
Whale Optimization ◽  
Grey Models ◽  
The Stability

Fractional order grey model is effective in describing the uncertainty of the system. In this paper, we propose a novel variable-order fractional discrete grey model (short for VOFDGM(1,1)) by combining the discrete grey model and variable-order fractional accumulation, which is a more general form of the DGM(1,1). The detailed modeling procedure of the presented model is first systematically studied, in particular, matrix perturbation theory is used to prove the validity in terms of the stability of the model, and then, the model parameters are optimized by the whale optimization algorithm. The accuracy of the proposed model is verified by comparing it with classical models on six data sequences with different forms. Finally, the model is applied to predict the electricity consumption of Beijing and Liaoning Province of China, and the results show that the model has a better prediction performance compared with the other four commonly-used grey models. To the best of our knowledge, this is the first time that the variable-order fractional accumulation is introduced into the discrete grey model, which greatly increases the prediction accuracy of the DGM(1,1) and extends the application range of grey models.

Composite Model Reference Adaptive Control for a Class of Nonlinear Fractional Order Systems

2015 ◽  
Author(s):  
Yiheng Wei ◽  
Shu Liang ◽  
Yangsheng Hu ◽  
Yong Wang
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Closed Loop ◽  
Tracking Error ◽  
Model Reference Adaptive Control ◽  
Prediction Errors ◽  
Model Reference ◽  
Closed Loop Systems ◽  
The Stability ◽  
Model Reference Adaptive

This article presents a novel model reference adaptive control of fractional order nonlinear systems, which is a generalization of existing method for integer order systems. The formulating adaptive law is in terms of both tracking and prediction errors, whereas existing methods only depends on tracking error. The transient performance of the closed-loop systems with the proposed control strategy improves in the sense of generating smooth system output. The stability and tracking convergence of the resulting closed-loop system are analyzed via the indirect Lyapunov method. Meanwhile, the proposed controller is implemented by employing some fractional order tracking differentiator to generate the required fractional derivatives of a signal. Numerical examples are provided to illustrate the effectiveness of our results.

scholarly journals Geometrical Variable Weights Buffer GM(1,1) Model and Its Application in Forecasting of China’s Energy Consumption

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Li ◽  
Han Xie
Keyword(s):  
Energy Consumption ◽  
Maximum Degree ◽  
Original Data ◽  
Grey Model ◽  
Variable Weights ◽  
Proposed Model ◽  
Term Energy ◽  
Long Term Forecasting ◽  
The Stability

In order to improve the application area and the prediction accuracy of GM(1,1) model, a novel Grey model is proposed in this paper. To remedy the defects about the applications of traditional Grey model and buffer operators in medium- and long-term forecasting, a Variable Weights Buffer Grey model is proposed. The proposed model integrates the variable weights buffer operator with the background value optimized GM(1,1) model to implement dynamic preprocessing of original data. Taking the maximum degree of Grey incidence between fitting value and actual value as objective function, then the optimal buffer factor is chosen, which can improve forecasting precision, make forecasting results embodying the internal trend of original data to the maximum extent, and improve the stability of the prediction. To verify the effectiveness of the proposed model, the energy consumption in China from 2002 to 2009 is used for the modeling to forecast the energy consumption in China from 2010 to 2020, and the forecasting results prove that the GVGM(1,1) model has remarkably improved the forecasting ability of medium- and long-term energy consumption in China.

scholarly journals A New Information Priority Accumulated Grey Model with Hyperbolic Sinusoidal Term and its Application

2021 ◽  
Vol 1 (2) ◽  
pp. 5-19
Author(s):  
Xue Tian ◽  
Wenqing Wu ◽  
Xin Ma ◽  
Peng Zhang
Keyword(s):  
Natural Gas ◽  
Fossil Fuels ◽  
Optimal Parameter ◽  
Estimation Method ◽  
Least Square ◽  
Grey Model ◽  
Grey Forecasting ◽  
New Information ◽  
Proposed Model ◽  
Whale Optimization

Compared to fossil fuels, natural gas is cleaner energy, which has developed rapidly in recent years. Studying the urban supply of natural gas has implications for the development of natural gas. In this paper, the new information priority accumulation method is integrated into the grey forecasting model with the hyperbolic sinusoidal driving term, and then the new grey model is used to predict the urban natural gas supply. The system's linear parameters are calculated by the least square estimation method, and the optimal parameter of the new information accumulated priority is determined by the Whale Optimization Algorithm. Finally, the supply of urban gas is forecasted using the proposed model, and comparative analyses with the four other forecasting models are presented.  

Maximal Bound for Output Feedback Gain in Stabilization of Fixed Points of Fractional-Order Chaotic Systems

2011 ◽  
Vol 6 (3) ◽  
Author(s):  
Mohammad Saleh Tavazoei
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fractional Order ◽  
Output Feedback ◽  
Chaotic Systems ◽  
Feedback Gain ◽  
Static Output Feedback ◽  
Perturbation Bound ◽  
The Stability ◽  
Static Output

This paper deals with the problem of stabilizing the unstable fixed points of a class of fractional-order chaotic systems via using static output feedback. At first, a static output feedback controller designed to stabilize a fixed point of a fractional-order chaotic system is considered. Then, the maximal allowable perturbation bound around the nominal value of the output feedback gain of the designed controller, such that the stability of the intended fixed point in the closed-loop system is guaranteed, is analytically determined. Also, some numerical examples are presented to confirm the validity of the analytical results of the paper.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

scholarly journals Estimation of fractional cycle bias for GPS/BDS-2/Galileo based on international GNSS monitoring and assessment system observations using the uncombined PPP model

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Jin Wang ◽  
Qin Zhang ◽  
Guanwen Huang
Keyword(s):  
Estimation Method ◽  
Satellite Orbit ◽  
Satellite System ◽  
Assessment System ◽  
Navigation Satellite ◽  
Dual Frequency ◽  
Fractional Cycle Bias ◽  
The Stability ◽  
High Consistency ◽  
Global Navigation Satellite

AbstractThe Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP). Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL) and Narrow Lane (NL) combinations, the uncombined PPP model is flexible and effective to generate the FCB products. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS) precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS) observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer coefficients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System (Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles, which indicates a high consistency for the float ambiguities. The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139 cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

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