Geodesic
A matrix inequality based design method for consensus problems in multi-agent systems
International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 4, pp. 639-646.

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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.
Keywords: multi-agent systems, consensus, decentralized control, graph Laplacian, matrix inequality, LMI
Mots-clés : system wieloagentowy, konsensus, sterowanie zdecentralizowane, nierówność macierzy, LMI 
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Zhai, G.; Okuno, S.; Imae, J.; Kobayashi, T. A matrix inequality based design method for consensus problems in multi-agent systems. International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 4, pp. 639-646. http://geodesic.mathdoc.fr/item/IJAMCS_2009_19_4_a10/

[1] Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.

[2] Fax, J. A. (2001). Optimal and Cooperative Control of Vehicle Formations, Ph.D. dissertation, Control Dynamical Systems, California Institute of Technology, Pasadena, CA.

[3] Fax, J. A. and Murray, R. M. (2004). Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control 49(9): 1465-1476.

[4] Gahinet, P., Nemirovskii, A., Laub, A. and Chilali, M. (1994). The LMI control toolbox, Proceedings of the 33rd IEEE Conference on Decision and Control, Orlando, FL, USA, pp. 2038-2041.

[5] Godsil, C. and Royle, G. (2001). Algebraic Graph Theory, Springer-Verlag, Berlin.

[6] Khalil, H. K. (2002). Nonlinear Systems, 2nd Edn., Prentice Hall, Upper Saddle River, NJ.

[7] Lancaster, P. and Tismenetsky, M. (1985). The Theory of Matrices with Applications, 2nd Edn., Academic Press, Orlando, FL.

[8] Olfati-Saber, R., Fax, J. A. and Murray, R. M. (2007). Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE 95(1): 215-233.

[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.

[12] Pogromsky, A., Santoboni, G. and Nijmeijer, H. (2002). Partial synchronization: From symmetry towards stability, Physica D 172(1): 65-87.

[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.