Necessary and sufficient conditions for consensus in third order multi-agent systems

Chi Huang, Guisheng Zhai, Gesheng Xu

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Article number8436488
Pages (from-to)1044-1053
Number of pages10
JournalIEEE/CAA Journal of Automatica Sinica
Volume5
Issue number6
DOIs
Publication statusPublished - 2018 Nov 1

Fingerprint

Multi agent systems
Polynomials
Communication

Keywords

  • Communication delay
  • consensus algorithms
  • graph Laplacians
  • Hurwitz polynomials
  • third order multi-agent systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems
  • Artificial Intelligence

Cite this

Necessary and sufficient conditions for consensus in third order multi-agent systems. / Huang, Chi; Zhai, Guisheng; Xu, Gesheng.

In: IEEE/CAA Journal of Automatica Sinica, Vol. 5, No. 6, 8436488, 01.11.2018, p. 1044-1053.

Research output: Contribution to journalArticle

@article{dba0f76c435b4be0809c35d661cc14e3,
title = "Necessary and sufficient conditions for consensus in third order multi-agent systems",
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.",
keywords = "Communication delay, consensus algorithms, graph Laplacians, Hurwitz polynomials, third order multi-agent systems",
author = "Chi Huang and Guisheng Zhai and Gesheng Xu",
year = "2018",
month = "11",
day = "1",
doi = "10.1109/JAS.2018.7511222",
language = "English",
volume = "5",
pages = "1044--1053",
journal = "IEEE/CAA Journal of Automatica Sinica",
issn = "2329-9266",
publisher = "IEEE Advancing Technology for Humanity",
number = "6",

}

TY - JOUR

T1 - Necessary and sufficient conditions for consensus in third order multi-agent systems

AU - Huang, Chi

AU - Zhai, Guisheng

AU - Xu, Gesheng

PY - 2018/11/1

Y1 - 2018/11/1

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 - consensus algorithms

KW - graph Laplacians

KW - Hurwitz polynomials

KW - third order multi-agent systems

UR - http://www.scopus.com/inward/record.url?scp=85051840649&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051840649&partnerID=8YFLogxK

U2 - 10.1109/JAS.2018.7511222

DO - 10.1109/JAS.2018.7511222

M3 - Article

AN - SCOPUS:85051840649

VL - 5

SP - 1044

EP - 1053

JO - IEEE/CAA Journal of Automatica Sinica

JF - IEEE/CAA Journal of Automatica Sinica

SN - 2329-9266

IS - 6

M1 - 8436488

ER -