### Abstract

In this paper, we deal with a consensus control problem for a group of high dimensional agents which are networked by digraphs. Assuming that the control input of each agent is constructed based on the 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 complex coefficients. Focusing on the case of three dimensional systems, we show that by using Hurwitz polynomials with complex coefficients, we obtain a necessary and sufficient condition for the consensus algorithm. The condition is a natural extension to second order consensus, and is reasonable and practical due to its comparatively less computation burden. Two numerical examples show effectiveness of the proposed condition and the consensus algorithm.

Original language | English |
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Title of host publication | Proceedings of the 36th Chinese Control Conference, CCC 2017 |

Publisher | IEEE Computer Society |

Pages | 8293-8298 |

Number of pages | 6 |

ISBN (Electronic) | 9789881563934 |

DOIs | |

Publication status | Published - 2017 Sep 7 |

Event | 36th Chinese Control Conference, CCC 2017 - Dalian, China Duration: 2017 Jul 26 → 2017 Jul 28 |

### Other

Other | 36th Chinese Control Conference, CCC 2017 |
---|---|

Country | China |

City | Dalian |

Period | 17/7/26 → 17/7/28 |

### Fingerprint

### Keywords

- consensus algorithm
- graph Laplacian
- Hurwitz polynomials with complex coefficients
- Networked high dimensional agents

### ASJC Scopus subject areas

- Computer Science Applications
- Control and Systems Engineering
- Applied Mathematics
- Modelling and Simulation

### Cite this

*Proceedings of the 36th Chinese Control Conference, CCC 2017*(pp. 8293-8298). [8028670] IEEE Computer Society. https://doi.org/10.23919/ChiCC.2017.8028670

**An algebraic approach to designing consensus algorithm of networked high dimensional agents.** / Huang, Chi; Zhai, Guisheng; Xu, Gesheng.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 36th Chinese Control Conference, CCC 2017.*, 8028670, IEEE Computer Society, pp. 8293-8298, 36th Chinese Control Conference, CCC 2017, Dalian, China, 17/7/26. https://doi.org/10.23919/ChiCC.2017.8028670

}

TY - GEN

T1 - An algebraic approach to designing consensus algorithm of networked high dimensional agents

AU - Huang, Chi

AU - Zhai, Guisheng

AU - Xu, Gesheng

PY - 2017/9/7

Y1 - 2017/9/7

N2 - In this paper, we deal with a consensus control problem for a group of high dimensional agents which are networked by digraphs. Assuming that the control input of each agent is constructed based on the 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 complex coefficients. Focusing on the case of three dimensional systems, we show that by using Hurwitz polynomials with complex coefficients, we obtain a necessary and sufficient condition for the consensus algorithm. The condition is a natural extension to second order consensus, and is reasonable and practical due to its comparatively less computation burden. Two numerical examples show effectiveness of the proposed condition and the consensus algorithm.

AB - In this paper, we deal with a consensus control problem for a group of high dimensional agents which are networked by digraphs. Assuming that the control input of each agent is constructed based on the 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 complex coefficients. Focusing on the case of three dimensional systems, we show that by using Hurwitz polynomials with complex coefficients, we obtain a necessary and sufficient condition for the consensus algorithm. The condition is a natural extension to second order consensus, and is reasonable and practical due to its comparatively less computation burden. Two numerical examples show effectiveness of the proposed condition and the consensus algorithm.

KW - consensus algorithm

KW - graph Laplacian

KW - Hurwitz polynomials with complex coefficients

KW - Networked high dimensional agents

UR - http://www.scopus.com/inward/record.url?scp=85032207538&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032207538&partnerID=8YFLogxK

U2 - 10.23919/ChiCC.2017.8028670

DO - 10.23919/ChiCC.2017.8028670

M3 - Conference contribution

AN - SCOPUS:85032207538

SP - 8293

EP - 8298

BT - Proceedings of the 36th Chinese Control Conference, CCC 2017

PB - IEEE Computer Society

ER -