Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems

Chi Huang; Guisheng Zhai; Gesheng Xu

doi:10.1109/JAS.2018.7511222

Volume 5 Issue 6

Nov. 2018

IEEE/CAA Journal of Automatica Sinica

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Chi Huang, Guisheng Zhai and Gesheng Xu, "Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1044-1053, Nov. 2018. doi: 10.1109/JAS.2018.7511222

Citation:

Chi Huang, Guisheng Zhai and Gesheng Xu, "Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 6, pp. 1044-1053, Nov. 2018. doi: 10.1109/JAS.2018.7511222

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Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems

doi: 10.1109/JAS.2018.7511222

Chi Huang^1
,,
Guisheng Zhai^{2
,
,},
Gesheng Xu^1
,

1.
College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
2.
Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, Japan

Funds:

Japan Ministry of Education, Sciences and Culture C21560471

the National Natural Science Foundation of China 61603268

the Research Project Supported by Shanxi Scholarship Council of China 2015-044

the Fundamental Research Project of Shanxi Province 2015021085

More Information

Author Bio:
Chi Huang (M'15) received the M.S. degree in mathematics and his Ph.D. degree with the Department of Mathematics from the City University of Hong Kong, China, in 2009 and 2012, respectively. His current research interests include multi-agent systems, complex dynamical networks, and sensor networks.
Dr. Huang was the recipient of the Best Paper Award in the 8th Asian Control Conference in 2011.(e-mail: huangchima@gmail.com)

Guisheng Zhai (M'98-SM'01) received his B.S degree from Fudan University, China, in 1988, and received his M.E and Ph.D. degrees, both in system science, from Kobe University, Japan, in 1993 and 1996, respectively.
After two years of industrial experience, Dr. Zhai moved to Wakayama University, Japan, in 1998, and then to Osaka Prefecture University, Japan, in 2004. He held visiting professor positions at University of Notre Dame from August 2001 to July 2002, and at Purdue University from March 2016 through February 2017. In April 2010, he joined the faculty of Shibaura Institute of Technology, Japan, where he currently is a full Professor of Mathematical Sciences. His research interests include large scale and decentralized control systems, robust control, switched systems and switching control, networked control and multi-agent systems, neural networks and signal processing, etc. Dr. Zhai is on the editorial board of several academic journals including IET Control Theory & Applications, International Journal of Applied Mathematics and Computer Science, Journal of Control and Decision, and Frontiers of Mechanical Engineering. He is a Senior Member of IEEE, a member of ISCIE, SICE, JSST and JSME

Gesheng Xu received the B.S. degree in mathematics from Jinzhong University, China, in 2014. He is now an M.S. candidate at Taiyuan University of Technology. His research interests include consensus and formation of multi-agent systems.(e-mail: 260835305@qq.com)
Corresponding author: Guisheng Zhai, e-mail: zhai@shibaura-it.ac.jp
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Received Date: 2017-12-06
Accepted Date: 2018-02-26

Abstract

Abstract

We deal with a consensus control problem for a group of third order agents which are networked by digraphs. Assuming that the control input of each agent is constructed based on weighted difference between its states and those of its neighbor agents, we aim to propose an algorithm on computing the weighting coefficients in the control input. The problem is reduced to designing Hurwitz polynomials with real or complex coefficients. We show that by using Hurwitz polynomials with complex coefficients, a necessary and sufficient condition can be obtained for designing the consensus algorithm. Since the condition is both necessary and sufficient, we provide a kind of parametrization for all the weighting coefficients achieving consensus. Moreover, the condition is a natural extension to second order consensus, and is reasonable and practical due to its comparatively decreased computation burden. The result is also extended to the case where communication delay exists in the control input.
- Communication delay,
- consensus algorithms,
- graph Laplacians,
- Hurwitz polynomials,
- third order multi-agent systems

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References(25)

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Necessary and Sufficient Conditions for Consensus in Third Order Multi-Agent Systems

doi: 10.1109/JAS.2018.7511222

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