### Abstract

In this paper, we study an extended consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The concept extended consensus means that a combination of each agent's state elements is required to converge to the same vector. For this extended consensus problem, we propose to reduce the problem to a stabilization problem with an appropriate transformation, and thus obtain a strict matrix inequality with respect to a Lyapunov matrix and a structured controller gain matrix. We then utilize a homotopy based method for solving the matrix inequality effectively, and show validity of the result by an example. The feature of the present algorithm is that it can deal with various additional control requirements such as convergence rate specification and actuator limitations.

Original language | English |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Pages | 4772-4777 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai Duration: 2009 Dec 15 → 2009 Dec 18 |

### Other

Other | 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 |
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City | Shanghai |

Period | 09/12/15 → 09/12/18 |

### Fingerprint

### Keywords

- Extended consensus
- Graph laplacian
- Homotopy method
- LMI
- Matrix inequality
- Multi-agent systems

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 4772-4777). [5400168] https://doi.org/10.1109/CDC.2009.5400168

**An extended consensus algorithm for multi-agent systems.** / Zhai, Guisheng; Okuno, Shohei; Imae, Joe; Kobayashi, Tomoaki.

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

*Proceedings of the IEEE Conference on Decision and Control.*, 5400168, pp. 4772-4777, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, 09/12/15. https://doi.org/10.1109/CDC.2009.5400168

}

TY - GEN

T1 - An extended consensus algorithm for multi-agent systems

AU - Zhai, Guisheng

AU - Okuno, Shohei

AU - Imae, Joe

AU - Kobayashi, Tomoaki

PY - 2009

Y1 - 2009

N2 - In this paper, we study an extended consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The concept extended consensus means that a combination of each agent's state elements is required to converge to the same vector. For this extended consensus problem, we propose to reduce the problem to a stabilization problem with an appropriate transformation, and thus obtain a strict matrix inequality with respect to a Lyapunov matrix and a structured controller gain matrix. We then utilize a homotopy based method for solving the matrix inequality effectively, and show validity of the result by an example. The feature of the present algorithm is that it can deal with various additional control requirements such as convergence rate specification and actuator limitations.

AB - In this paper, we study an extended consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The concept extended consensus means that a combination of each agent's state elements is required to converge to the same vector. For this extended consensus problem, we propose to reduce the problem to a stabilization problem with an appropriate transformation, and thus obtain a strict matrix inequality with respect to a Lyapunov matrix and a structured controller gain matrix. We then utilize a homotopy based method for solving the matrix inequality effectively, and show validity of the result by an example. The feature of the present algorithm is that it can deal with various additional control requirements such as convergence rate specification and actuator limitations.

KW - Extended consensus

KW - Graph laplacian

KW - Homotopy method

KW - LMI

KW - Matrix inequality

KW - Multi-agent systems

UR - http://www.scopus.com/inward/record.url?scp=77950829058&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950829058&partnerID=8YFLogxK

U2 - 10.1109/CDC.2009.5400168

DO - 10.1109/CDC.2009.5400168

M3 - Conference contribution

AN - SCOPUS:77950829058

SN - 9781424438716

SP - 4772

EP - 4777

BT - Proceedings of the IEEE Conference on Decision and Control

ER -