TY - JOUR
T1 - Necessary and sufficient conditions for consensus in third order multi-agent systems
AU - Huang, Chi
AU - Zhai, Guisheng
AU - Xu, Gesheng
N1 - Funding Information:
Manuscript received December 6, 2017; accepted February 26, 2018. This work was supported by 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), and the Fundamental Research Project of Shanxi Province (2015021085). Recommended by Associate Editor Long Chen. (Corresponding author: Guisheng Zhai.) Citation: C. Huang, G. Zhai, and G. S. Xu, “Necessary and sufficient conditions for consensus in third order multi-agent systems,” IEEE/CAA J. of Autom. Sinica, vol. 5, no. 6, pp. 1044−1053, Nov. 2018.
Publisher Copyright:
© 2014 Chinese Association of Automation.
PY - 2018/11
Y1 - 2018/11
N2 - 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.
AB - 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.
KW - Communication delay
KW - Hurwitz polynomials
KW - consensus algorithms
KW - graph Laplacians
KW - third order multi-agent systems
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U2 - 10.1109/JAS.2018.7511222
DO - 10.1109/JAS.2018.7511222
M3 - Article
AN - SCOPUS:85051840649
SN - 2329-9266
VL - 5
SP - 1044
EP - 1053
JO - IEEE/CAA Journal of Automatica Sinica
JF - IEEE/CAA Journal of Automatica Sinica
IS - 6
M1 - 8436488
ER -