The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Cet article traite du contrôle de la dynamique chaotique en utilisant les équations système approximées obtenues à l'aide de la programmation génétique (GP). La méthode OGY bien connue utilise des orbites instables déjà existantes intégrées dans l'attracteur chaotique et utilise la linéarisation des équations du système et de petites perturbations pour le contrôle. Cependant, dans la méthode OGY, nous avons besoin d'un temps de transition pour atteindre le contrôle, et le bruit inclus dans la linéalisation des équations déplace à nouveau l'orbite dans une région instable. Dans cet article, nous proposons une méthode de contrôle qui utilise les équations du système estimées obtenues par le GP afin que le contrôle non linéaire direct soit applicable à tout moment à l'orbite instable. Dans le GP, les équations du système sont représentées par des arbres d'analyse et la performance (aptitude) de chaque individu est définie comme l'inversion de l'erreur quadratique moyenne entre les données observées et la sortie de l'équation du système. En sélectionnant une paire d’individus ayant une meilleure forme physique, l’opération de croisement est appliquée pour générer de nouveaux individus. Dans l'étude de simulation, la méthode est appliquée dans un premier temps aux dynamiques chaotiques générées artificiellement telles que la carte Logistique et la carte Hénon. L'erreur d'approximation est évaluée sur la base de l'erreur de prédiction. L'effet du bruit inclus dans la série chronologique sur l'approximation est également discuté. Sous notre contrôle, puisque les équations du système sont estimées, il nous suffit de modifier l'entrée progressivement pour que le système se déplace vers la région stable. En supposant le système dynamique ciblé f(x(t)) avec entrée u(t)=0 est estimé en utilisant le GP (noté
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Yoshikazu IKEDA, Shozo TOKINAGA, "Controlling the Chaotic Dynamics by Using Approximated System Equations Obtained by the Genetic Programming" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 9, pp. 2118-2127, September 2001, doi: .
Abstract: This paper deals with the control of chaotic dynamics by using the approximated system equations which are obtained by using the Genetic Programming (GP). Well known OGY method utilizes already existing unstable orbits embedded in the chaotic attractor, and use linearlization of system equations and small perturbation for control. However, in the OGY method we need transition time to attain the control, and the noise included in the linealization of equations moves the orbit into unstable region again. In this paper we propose a control method which utilize the estimated system equations obtained by the GP so that the direct nonlinear control is applicable to the unstable orbit at any time. In the GP, the system equations are represented by parse trees and the performance (fitness) of each individual is defined as the inversion of the root mean square error between the observed data and the output of the system equation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. In the simulation study, the method is applied at first to the artificially generated chaotic dynamics such as the Logistic map and the Henon map. The error of approximation is evaluated based upon the prediction error. The effect of noise included in the time series on the approximation is also discussed. In our control, since the system equations are estimated, we only need to change the input incrementally so that the system moves to the stable region. By assuming the targeted dynamic system f(x(t)) with input u(t)=0 is estimated by using the GP (denoted
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_9_2118/_p
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@ARTICLE{e84-a_9_2118,
author={Yoshikazu IKEDA, Shozo TOKINAGA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Controlling the Chaotic Dynamics by Using Approximated System Equations Obtained by the Genetic Programming},
year={2001},
volume={E84-A},
number={9},
pages={2118-2127},
abstract={This paper deals with the control of chaotic dynamics by using the approximated system equations which are obtained by using the Genetic Programming (GP). Well known OGY method utilizes already existing unstable orbits embedded in the chaotic attractor, and use linearlization of system equations and small perturbation for control. However, in the OGY method we need transition time to attain the control, and the noise included in the linealization of equations moves the orbit into unstable region again. In this paper we propose a control method which utilize the estimated system equations obtained by the GP so that the direct nonlinear control is applicable to the unstable orbit at any time. In the GP, the system equations are represented by parse trees and the performance (fitness) of each individual is defined as the inversion of the root mean square error between the observed data and the output of the system equation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. In the simulation study, the method is applied at first to the artificially generated chaotic dynamics such as the Logistic map and the Henon map. The error of approximation is evaluated based upon the prediction error. The effect of noise included in the time series on the approximation is also discussed. In our control, since the system equations are estimated, we only need to change the input incrementally so that the system moves to the stable region. By assuming the targeted dynamic system f(x(t)) with input u(t)=0 is estimated by using the GP (denoted
keywords={},
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ISSN={},
month={September},}
Copier
TY - JOUR
TI - Controlling the Chaotic Dynamics by Using Approximated System Equations Obtained by the Genetic Programming
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2118
EP - 2127
AU - Yoshikazu IKEDA
AU - Shozo TOKINAGA
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2001
AB - This paper deals with the control of chaotic dynamics by using the approximated system equations which are obtained by using the Genetic Programming (GP). Well known OGY method utilizes already existing unstable orbits embedded in the chaotic attractor, and use linearlization of system equations and small perturbation for control. However, in the OGY method we need transition time to attain the control, and the noise included in the linealization of equations moves the orbit into unstable region again. In this paper we propose a control method which utilize the estimated system equations obtained by the GP so that the direct nonlinear control is applicable to the unstable orbit at any time. In the GP, the system equations are represented by parse trees and the performance (fitness) of each individual is defined as the inversion of the root mean square error between the observed data and the output of the system equation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. In the simulation study, the method is applied at first to the artificially generated chaotic dynamics such as the Logistic map and the Henon map. The error of approximation is evaluated based upon the prediction error. The effect of noise included in the time series on the approximation is also discussed. In our control, since the system equations are estimated, we only need to change the input incrementally so that the system moves to the stable region. By assuming the targeted dynamic system f(x(t)) with input u(t)=0 is estimated by using the GP (denoted
ER -