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Author Wang, Yan ♦ Liu, Ling ♦ Liu, Chongxin ♦ Zhu, Ziwei ♦ Sun, Zhenquan
Editor Hosseinnia, S. Hassan
Source Hindawi
Content type Text
Publisher Hindawi
File Format PDF
Copyright Year ©2018
Language English
Abstract In this paper, fractional calculus is applied to establish a novel fractional-order ferroresonance model with fractional-order magnetizing inductance and capacitance. Some basic dynamic behaviors of this fractional-order ferroresonance system are investigated. And then, considering noncommensurate orders of inductance and capacitance and unknown parameters in an actual ferroresonance system, this paper presents a novel fractional-order adaptive backstepping control strategy for a class of noncommensurate fractional-order systems with multiple unknown parameters. The virtual control laws and parameter update laws are designed in each step. Thereafter, a novel fractional-order adaptive controller is designed in terms of the fractional Lyapunov stability theorem. The proposed control strategy requires only one control input and can force the output of the chaotic system to track the reference signal asymptotically. Finally, the proposed method is applied to a noncommensurate fractional-order ferroresonance system with multiple unknown parameters. Numerical simulation confirms the effectiveness of the proposed method. In addition, the proposed control strategy also applies to commensurate fractional-order systems with unknown parameters.
ISSN 1024123X
Learning Resource Type Article
Publisher Date 2018-11-07
Rights License This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
e-ISSN 15635147
Journal Mathematical Problems in Engineering
Volume Number 2018
Page Count 10


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