Genetic Algorithm-Based Identification of  Fractional-Order Systems

Zhou, Shengxi; Cao, Junyi; Chen, YangQuan

doi:10.3390/e15051624

Cited by 64 publications

(35 citation statements)

References 61 publications

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“…Fractional Calculus (FC) may be considered as a generalisation of integer-order calculus, thus accomplishing what integer-order calculus cannot [20]. As a natural extension of the integer (i.e., classical) derivatives, fractional derivatives provide an excellent tool for the description of memory and hereditary properties of processes [21].…”

Section: Player's Motion From the View Of Fractional Calculusmentioning

confidence: 99%

“…Once again, let us consider the identification of each coordinate ( , ) as = 1, 2 , in such a way that = = . Under those conditions, one can rewrite Equation (20) in the following form:…”

Section: Theorem 2 [28]: the Homogeneous Difference Equation Of (20) mentioning

confidence: 99%

“…In order to study the stability of the homogeneous difference Equation (20), let us truncate the series at = 4 and consider a sampling time of = 1. Once again, let us consider the identification of each coordinate ( , ) as = 1, 2 , in such a way that = = .…”

Section: Theorem 2 [28]: the Homogeneous Difference Equation Of (20) mentioning

confidence: 99%

“…In synthesis, each player should converge to the particular solution * from Equation (19), based on the following theorems [28]: Theorem 1 [28]: All solutions of Equation (20) converge to * (20) is asymptotically stable.…”

Section: It Is Possible To Observe That From Time To Time the Player mentioning

confidence: 99%

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Dynamical Stability and Predictability of Football Players: The Study of One Match

Couceiro

Clemente

Martins

et al. 2014

Entropy

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Abstract:The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player's trajectory. By applying FC, one can benefit from newly OPEN ACCESSEntropy 2014, 16 646 considered modeling perspectives, such as the fractional coefficient, to estimate a player's predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player's process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match.

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Section: Player's Motion From the View Of Fractional Calculusmentioning

confidence: 99%

“…Once again, let us consider the identification of each coordinate ( , ) as = 1, 2 , in such a way that = = . Under those conditions, one can rewrite Equation (20) in the following form:…”

Section: Theorem 2 [28]: the Homogeneous Difference Equation Of (20) mentioning

confidence: 99%

Section: Theorem 2 [28]: the Homogeneous Difference Equation Of (20) mentioning

confidence: 99%

Section: It Is Possible To Observe That From Time To Time the Player mentioning

confidence: 99%

See 2 more Smart Citations

Dynamical Stability and Predictability of Football Players: The Study of One Match

Couceiro

Clemente

Martins

et al. 2014

Entropy

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“…In recent years new optimization methods [34,35,36] and new high-performance languages and tools for technical computing have been developed. Thus, in this contribution we will concentrate mainly on the identification of parameters (including the order of derivatives) for a chosen structure of the model and we compare two different criterions -the first is the sum of squares of the vertical deviations of experimental and theoretical data and the second is the sum of squares of the corresponding orthogonal distances [37,38,39,40].…”

Section: Introductionmentioning

confidence: 99%

Identification of Fractional-Order Dynamical Systems Based on Nonlinear Function Optimization

'ak¹,

Gonzalez²,

'ak³

et al. 2013

Int. J. of Pure and Appl. Math.

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In general, real objects are fractional-order systems and also dynamical processes taking place in them are fractional-order processes, although in some types of systems the order is very close to an integer order. So we consider dynamical system whose mathematical description is a differential equation in which the orders of derivatives can be real numbers. With regard to this, in the task of identification, it is necessary to consider also the fractional order of the dynamical system. In this paper we give suitable numerical solutions of differential equations of this type and subsequently an experimental method of identification in the time domain is given. We will concentrate mainly on the identification of parameters, including the orders of derivatives, for a chosen structure of the dynamical model of the system. Under mentioned assump- tions, we would obtain a system of nonlinear equations to identify the system. More suitable than to solve the system of nonlinear equations is to formulate the identification task as an optimization problem for nonlinear function minimization. As a criterion we have considered the sum of squares of the vertical deviations of experimental and theoretical data and the sum of squares of the corresponding orthogonal distances. The verification was performed on systems with known parameters and also on a laboratory object.

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Fractional‐order system identification based on an improved differential evolution algorithm

Liang

Chen

et al. 2021

Asian Journal of Control

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With the continuous increasing of system modeling accuracy and control performance requirements, the fractional‐order models are applied to describe the dynamic characteristics of the real systems more accurately over traditional integer‐order models. Traditional identification algorithms for fractional‐order system require stringent information on the derivatives of the objective function and initial values of the parameters, which is difficult in practical applications. The differential evolution (DE) algorithm has the advantage of simple implementation and superior performance for solving multi‐dimensional complex optimization problems which is suitable for the identification of fractional‐order systems. Aiming at improving the solution accuracy and convergence speed, an improved DE (IDE) algorithm for fractional‐order system identification is proposed. The movement strategy of the marine predator algorithm (MPA) and the mutation strategy of randomly selecting one from the optimal individual population as the basis vector are both adopted in this proposed IDE algorithm. The parameter information of the successfully mutated individual is archived during the iteration process. The scaling factor and crossover probability factor are adaptively adjusted according to the archived information to enhance the best solution accuracy obtained in the search process. By testing 13 sets of unimodal and multimodal functions with high‐performance optimization algorithms, the accuracy performance of the proposed IDE solution is verified. The IDE algorithm is applied to identify the parameters of the fractional‐order system of permanent magnet synchronous motor with simulation and experiment. The identification results clearly show the effectiveness of the proposed methodology.

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Genetic Algorithm-Based Identification of Fractional-Order Systems

Cited by 64 publications

References 61 publications

Dynamical Stability and Predictability of Football Players: The Study of One Match

Dynamical Stability and Predictability of Football Players: The Study of One Match

Identification of Fractional-Order Dynamical Systems Based on Nonlinear Function Optimization

Fractional‐order system identification based on an improved differential evolution algorithm

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