scholarly journals Parameter Estimation of the Lotka–Volterra Model with Fractional Order Based on the Modulation Function and Its Application

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ying Hao ◽  
Mingshun Guo
Keyword(s):  
Parameter Estimation ◽  
Fractional Order ◽  
Fractional Integration ◽  
Linear Equations ◽  
Volterra Model ◽  
Modulation Function ◽  
Implementation Program ◽  
Shifted Chebyshev Polynomial ◽  
Improved Model ◽  
Universal Applicability

The Lotka–Volterra model is widely applied in various fields, and parameter estimation is important in its application. In this study, the Lotka–Volterra model with universal applicability is established by introducing the fractional order. Modulation function is multiplied by both sides of the Lotka–Volterra model, and the model is converted into linear equations with parameters to be estimated by the fractional integration method. The parameters are obtained by solving the equations. The state of the system is estimated by shifted Chebyshev polynomial. Last, the implementation program of the model is compiled. The concrete implementation method of the improved model is proposed by an example in this study.

CONTINUOUS-TIME FRACTIONAL ORDER LINEAR SYSTEMS IDENTIFICATION USING CHEBYSHEV WAVELET

2020 ◽  
Vol 6 (8(77)) ◽  
pp. 23-28
Author(s):  
Shuen Wang ◽  
Ying Wang ◽  
Yinggan Tang
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Continuous Time ◽  
Fractional Integration ◽  
Operational Matrices ◽  
Computation Complexity ◽  
Order Linear ◽  
Fractional Integration Operator ◽  
Systems Identification ◽  
Chebyshev Wavelet

In this paper, the identification of continuous-time fractional order linear systems (FOLS) is investigated. In order to identify the differentiation or- ders as well as parameters and reduce the computation complexity, a novel identification method based on Chebyshev wavelet is proposed. Firstly, the Chebyshev wavelet operational matrices for fractional integration operator is derived. Then, the FOLS is converted to an algebraic equation by using the the Chebyshev wavelet operational matrices. Finally, the parameters and differentiation orders are estimated by minimizing the error between the output of real system and that of identified systems. Experimental results show the effectiveness of the proposed method.

Initialization of Identification of Fractional Model by Output-Error Technique

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Abir Khadhraoui ◽  
Khaled Jelassi ◽  
Jean-Claude Trigeassou ◽  
Pierre Melchior
Keyword(s):  
Numerical Simulation ◽  
Least Squares ◽  
Fractional Order ◽  
Fractional Integration ◽  
New Approach ◽  
Fractional Model ◽  
Output Error

A bad initialization of output-error (OE) technique can lead to an inappropriate identification results. In this paper, we introduce a solution to this problem; the basic idea is to estimate the parameters and the fractional order of the noninteger system by a new approach of least-squares (LS) method based on repeated fractional integration to initialize OE technique. It will be shown that LS method offers a good initialization to OE algorithm and leads to acceptable identification results. The performance of the proposed method is shown through numerical simulation examples.

Experimental Robot Identification: Advantages of Combining Internal and External Measurements and of Using Periodic Excitation

2001 ◽  
Vol 123 (4) ◽  
pp. 630-636 ◽  
Author(s):  
Walter Verdonck ◽  
Jan Swevers ◽  
Jean-Claude Samin
Keyword(s):  
Signal Processing ◽  
Parameter Estimation ◽  
Effective Means ◽  
Base Plate ◽  
Experimental Results ◽  
Parameter Estimates ◽  
Periodic Excitation ◽  
Identification Method ◽  
Reaction Forces ◽  
Improved Model

This paper discusses the advantages of using periodic excitation and of combining internal and external measurements in experimental robot identification. This discussion is based on the robot identification method developed by Swevers et al., a method that is recognized by industry as an effective means of robot identification that is frequently used, Hirzinger, G., Fischer, M., Brunner, B., Koeppe, R., Otter, M., Grebenstein, M., and Schafer, I, 1999, “Advances is Robotics: The DLR Experiment,” The International Journal of Robotics Research, Vol. 18, No. 11, pp. 1064–1087 [3]. Experimental results on a KUKA IR 361 show that the periodicity of the robot excitation is a key element of this method. Nonperiodic robot excitation complicates the signal processing preceding the parameter estimation, often yielding less accurate parameter estimates. An extension of this identification method combines internal and external measurements, Chenut, X., Samin, J. C., Swevers, J., and Ganseman, C., 2000, “Combining Internal and External robot Models for improved Model Parameter Estimation,” Mechanical Systems and Signal Processing. Vol. 14, No. 5, pp. 691–704 [4], yielding robot models that allow to accurately predict the actuator torques and the reaction forces/torques of the robot on its base plate, which are both important for the path planning. This paper presents and critically discusses the first experimental results obtained with this method.

Adaptive Synchronization of Fractional-Order Coupled Neurons Under Electromagnetic Radiation

2020 ◽  
Vol 30 (03) ◽  
pp. 2050044
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Electromagnetic Radiation ◽  
Fractional Order ◽  
Dynamical Behavior ◽  
Lyapunov Stability Theory ◽  
Neuronal Model ◽  
Adaptive Synchronization ◽  
Dynamical Characteristics ◽  
Single Controller ◽  
Improved Model ◽  
Complex Dynamical Behavior

In this paper, we investigate the dynamical characteristics of four-variable fractional-order Hindmarsh–Rose neuronal model under electromagnetic radiation. The numerical results show that the improved model exhibits more complex dynamical behavior with more bifurcation parameters. Meanwhile, based on the fractional-order Lyapunov stability theory, we propose two adaptive control methods with a single controller to realize chaotic synchronization between two coupled neurons. Finally, numerical simulations show the feasibility and effectiveness of the presented method.

A parameter estimation method for fractional-order nonlinear systems based on improved whale optimization algorithm

2019 ◽  
Vol 33 (07) ◽  
pp. 1950075 ◽  
Author(s):  
Gong Ren ◽  
Renhuan Yang ◽  
Renyu Yang ◽  
Pei Zhang ◽  
Xiuzeng Yang ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Optimization Algorithm ◽  
Fitness Function ◽  
Whale Optimization Algorithm ◽  
Engineering System ◽  
Grasshopper Optimization Algorithm ◽  
Whale Optimization ◽  
System Characteristics

Compared to the integer-order systems, the system characteristics of the fractional system are closer to the system characteristics of the real engineering system, the study found beyond that, strictly speaking, various physical phenomena in nature are nonlinear. The problem of parameter estimation problem of fractional-order nonlinear systems can be transformed into the problem of parameter optimization problem by constructing an appropriate fitness function. This paper proposes a hybrid improvement algorithm based on whale optimization algorithm (WOA) to solve this problem and verify it both in Lorenz system and Lu system. The simulation result shows that the hybrid improved algorithm is superior to genetic algorithm (GA), particle swarm optimization (PSO), grasshopper optimization algorithm (GOA) and WOA in convergence speed and accuracy.

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