Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the...

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Published inChinese physics B Vol. 20; no. 11; pp. 159 - 166
Main Author 张若洵 杨世平
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.11.2011
Subjects
Adaptive control systems
Chaos theory
Control systems
Design engineering
Inequalities
Lyapunov稳定性理论
Simulation
Stabilization
State variable
分数阶
反馈控制器
微分不等式
混沌系统
状态变量
自适应控制理论
镇定
Online AccessGet full text
ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/20/11/110506

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Summary:In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.
Bibliography:Zhang Ruo-Xun,Yang Shi-Ping（a College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China ; b College of Elementary Education, Xingtai University, Xingtai 054001, China）
In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.
stabilization; modified adaptive feedback control;fractional-order chaotic system;chaoscontrol
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ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/20/11/110506