Fractional-order adaptive backstepping control of a noncommensurate fractional-order ferroresonance system
type: Item
instance of: scholarly article
title: Fractional-order adaptive backstepping control of a noncommensurate fractional-order ferroresonance system
zbMATH Open document ID: 1427.93112
DOI: 10.1155/2018/8091757
author: Yan Wang
author: Ling Liu
author: Ziwei Zhu
author: Zhenquan Sun
author: Chongxin Liu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 93C23
zbMATH DE Number: 7019553
describes a project that uses: Fractional Order Chaotic Systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8091757
OpenAlex ID: W2900336412
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description: scientific article; zbMATH DE number 7019553