L2 norm performance index of synchronization and LQR control synthesis of complex networks

Chao Liu; Zhisheng Duan; Guanrong Chen; Lin Huang

doi:10.1016/j.automatica.2009.04.004

L₂norm performance index of synchronization and LQR control synthesis of complex networks

Chao Liu, Zhisheng Duan^*, Guanrong Chen, Lin Huang

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

26 Citations (Scopus)

Abstract

In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means faster network synchronization with lower vibration. The L₂ norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L₂ norm of the error vector e and the H₂ norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H₂ norm of the transfer function G is analyzed. Finally, an LQR controller is designed, according to the LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L₂ norm of the output of the linearized network. © 2009 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	1879-1885
Journal	Automatica
Volume	45
Issue number	8
Online published	15 May 2009
DOIs	https://doi.org/10.1016/j.automatica.2009.04.004
Publication status	Published - Aug 2009

Research Keywords

Complex networks
Control of networks
LQR control
Synchronizability

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@article{d6868919adae440b8cbcbaf0718f6361,

title = "L2 norm performance index of synchronization and LQR control synthesis of complex networks",

abstract = "In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means faster network synchronization with lower vibration. The L2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L2 norm of the error vector e and the H2 norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H2 norm of the transfer function G is analyzed. Finally, an LQR controller is designed, according to the LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L2 norm of the output of the linearized network. {\textcopyright} 2009 Elsevier Ltd. All rights reserved.",

keywords = "Complex networks, Control of networks, LQR control, Synchronizability",

author = "Chao Liu and Zhisheng Duan and Guanrong Chen and Lin Huang",

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journal = "Automatica",

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TY - JOUR

T1 - L2 norm performance index of synchronization and LQR control synthesis of complex networks

AU - Liu, Chao

AU - Duan, Zhisheng

AU - Chen, Guanrong

AU - Huang, Lin

PY - 2009/8

Y1 - 2009/8

N2 - In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means faster network synchronization with lower vibration. The L2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L2 norm of the error vector e and the H2 norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H2 norm of the transfer function G is analyzed. Finally, an LQR controller is designed, according to the LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L2 norm of the output of the linearized network. © 2009 Elsevier Ltd. All rights reserved.

AB - In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means faster network synchronization with lower vibration. The L2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L2 norm of the error vector e and the H2 norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H2 norm of the transfer function G is analyzed. Finally, an LQR controller is designed, according to the LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L2 norm of the output of the linearized network. © 2009 Elsevier Ltd. All rights reserved.

KW - Complex networks

KW - Control of networks

KW - LQR control

KW - Synchronizability

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U2 - 10.1016/j.automatica.2009.04.004

DO - 10.1016/j.automatica.2009.04.004

M3 - RGC 21 - Publication in refereed journal

SN - 0005-1098

VL - 45

SP - 1879

EP - 1885

JO - Automatica

JF - Automatica

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ER -