A matrix inequality based design method for consensus problems in multi-agent systems

Shohei Okuno; Joe Imae; Tomoaki Kobayashi

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 4, page 639-646
  • ISSN: 1641-876X

Abstract

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In this paper, we study a consensus problem in 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 existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.

How to cite

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Shohei Okuno, Joe Imae, and Tomoaki Kobayashi. "A matrix inequality based design method for consensus problems in multi-agent systems." International Journal of Applied Mathematics and Computer Science 19.4 (2009): 639-646. <http://eudml.org/doc/207962>.

@article{ShoheiOkuno2009,
abstract = {In this paper, we study a consensus problem in 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 existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.},
author = {Shohei Okuno, Joe Imae, Tomoaki Kobayashi},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {multi-agent systems; consensus; decentralized control; graph Laplacian; matrix inequality; LMI},
language = {eng},
number = {4},
pages = {639-646},
title = {A matrix inequality based design method for consensus problems in multi-agent systems},
url = {http://eudml.org/doc/207962},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Shohei Okuno
AU - Joe Imae
AU - Tomoaki Kobayashi
TI - A matrix inequality based design method for consensus problems in multi-agent systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 4
SP - 639
EP - 646
AB - In this paper, we study a consensus problem in 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 existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.
LA - eng
KW - multi-agent systems; consensus; decentralized control; graph Laplacian; matrix inequality; LMI
UR - http://eudml.org/doc/207962
ER -

References

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  9. Olfati-Saber, R. and Murray, R. M. (2003). Consensus protocols for networks of dynamic agents, Proceedings of the 2003 American Control Conference, Denver, CO, USA, pp. 951-956. 
  10. Olfati-Saber, R. and Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control 49(9): 1520-1533. 
  11. Mohar, B. (1991). The Laplacian spectrum of graphs, in Y. Alavi, G. Chartrand, O. Ollermann and A. Schwenk (Eds.), Graph Theory, Combinatorics, and Applications, Wiley, New York, NY, pp. 871-898. Zbl0840.05059
  12. Pogromsky, A., Santoboni, G. and Nijmeijer, H. (2002). Partial synchronization: From symmetry towards stability, Physica D 172(1): 65-87. Zbl1008.37012
  13. Wang, J., Cheng, D. and Hu, X. (2008). Consensus of multiagent linear dynamic systems, Asian Journal of Control 10(2): 144-155. 
  14. Zhai, G., Ikeda, M. and Fujisaki, Y. (2001). Decentralized H ∞ controller design: A matrix inequality approach using a homotopy method, Automatica 37(4): 565-572. Zbl0982.93035

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