PID control of Hopf bifurcation of delayed small-world networks with fractional-order dynamics

Min Xiao; Binbin Tao; Wei Xing Zheng

doi:10.1109/CCTA.2019.8920616

PID control of Hopf bifurcation of delayed small-world networks with fractional-order dynamics

Min Xiao
, Binbin Tao
, Wei Xing Zheng

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

1 Citation (Scopus)

Abstract

This paper investigates the problem of controlling Hopf bifurcation of delayed small-world networks with fractional-order dynamics. Specifically, a fractional-order PID feedback controller is designed to realize control of the Hopf bifurcation that is embedded in delayed small-world networks with fractional-order dynamics. The characteristic equation of the controlled fractional-order network is analyzed, which yields the useful conditions for stability as well as Hopf bifurcation. Moreover, the analysis reveals that the control parameters of the fractional-order PID feedback control scheme may be varied to have a significant effect on the bifurcation dynamics of the controlled small-world network with fractional-order dynamics. The theoretical findings are also confirmed through computer simulations.

Original language	English
Title of host publication	Proceedings IEEE CCTA 2019, 3rd IEEE Conference on Control Technology and Applications, August 19-21, 2019, City University of Hong Kong, Hong Kong, China
Publisher	IEEE
Pages	529-534
Number of pages	6
ISBN (Print)	9781728127675
DOIs	https://doi.org/10.1109/CCTA.2019.8920616
Publication status	Published - 2019
Event	IEEE Conference on Control Technology and Applications - Duration: 19 Aug 2019 → …

Conference

Conference	IEEE Conference on Control Technology and Applications
Period	19/08/19 → …

Keywords

Hopf algebras
feedback control systems
fractional calculus

Access to Document

10.1109/CCTA.2019.8920616

Cite this

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title = "PID control of Hopf bifurcation of delayed small-world networks with fractional-order dynamics",

abstract = "This paper investigates the problem of controlling Hopf bifurcation of delayed small-world networks with fractional-order dynamics. Specifically, a fractional-order PID feedback controller is designed to realize control of the Hopf bifurcation that is embedded in delayed small-world networks with fractional-order dynamics. The characteristic equation of the controlled fractional-order network is analyzed, which yields the useful conditions for stability as well as Hopf bifurcation. Moreover, the analysis reveals that the control parameters of the fractional-order PID feedback control scheme may be varied to have a significant effect on the bifurcation dynamics of the controlled small-world network with fractional-order dynamics. The theoretical findings are also confirmed through computer simulations.",

keywords = "Hopf algebras, feedback control systems, fractional calculus",

author = "Min Xiao and Binbin Tao and Zheng, \{Wei Xing\}",

year = "2019",

doi = "10.1109/CCTA.2019.8920616",

language = "English",

isbn = "9781728127675",

pages = "529--534",

booktitle = "Proceedings IEEE CCTA 2019, 3rd IEEE Conference on Control Technology and Applications, August 19-21, 2019, City University of Hong Kong, Hong Kong, China",

publisher = "IEEE",

note = "IEEE Conference on Control Technology and Applications ; Conference date: 19-08-2019",

}

Xiao, M, Tao, B & Zheng, WX 2019, PID control of Hopf bifurcation of delayed small-world networks with fractional-order dynamics. in Proceedings IEEE CCTA 2019, 3rd IEEE Conference on Control Technology and Applications, August 19-21, 2019, City University of Hong Kong, Hong Kong, China. IEEE, pp. 529-534, IEEE Conference on Control Technology and Applications, 19/08/19. https://doi.org/10.1109/CCTA.2019.8920616

PID control of Hopf bifurcation of delayed small-world networks with fractional-order dynamics. / Xiao, Min; Tao, Binbin; Zheng, Wei Xing.
Proceedings IEEE CCTA 2019, 3rd IEEE Conference on Control Technology and Applications, August 19-21, 2019, City University of Hong Kong, Hong Kong, China. IEEE, 2019. p. 529-534.

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

TY - GEN

T1 - PID control of Hopf bifurcation of delayed small-world networks with fractional-order dynamics

AU - Xiao, Min

AU - Tao, Binbin

AU - Zheng, Wei Xing

PY - 2019

Y1 - 2019

N2 - This paper investigates the problem of controlling Hopf bifurcation of delayed small-world networks with fractional-order dynamics. Specifically, a fractional-order PID feedback controller is designed to realize control of the Hopf bifurcation that is embedded in delayed small-world networks with fractional-order dynamics. The characteristic equation of the controlled fractional-order network is analyzed, which yields the useful conditions for stability as well as Hopf bifurcation. Moreover, the analysis reveals that the control parameters of the fractional-order PID feedback control scheme may be varied to have a significant effect on the bifurcation dynamics of the controlled small-world network with fractional-order dynamics. The theoretical findings are also confirmed through computer simulations.

AB - This paper investigates the problem of controlling Hopf bifurcation of delayed small-world networks with fractional-order dynamics. Specifically, a fractional-order PID feedback controller is designed to realize control of the Hopf bifurcation that is embedded in delayed small-world networks with fractional-order dynamics. The characteristic equation of the controlled fractional-order network is analyzed, which yields the useful conditions for stability as well as Hopf bifurcation. Moreover, the analysis reveals that the control parameters of the fractional-order PID feedback control scheme may be varied to have a significant effect on the bifurcation dynamics of the controlled small-world network with fractional-order dynamics. The theoretical findings are also confirmed through computer simulations.

KW - Hopf algebras

KW - feedback control systems

KW - fractional calculus

UR - http://hdl.handle.net/1959.7/uws:55101

U2 - 10.1109/CCTA.2019.8920616

DO - 10.1109/CCTA.2019.8920616

M3 - Conference Paper

SN - 9781728127675

SP - 529

EP - 534

BT - Proceedings IEEE CCTA 2019, 3rd IEEE Conference on Control Technology and Applications, August 19-21, 2019, City University of Hong Kong, Hong Kong, China

PB - IEEE

T2 - IEEE Conference on Control Technology and Applications

Y2 - 19 August 2019

ER -

PID control of Hopf bifurcation of delayed small-world networks with fractional-order dynamics

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