# EECI09: Distributed control

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In this lecture we introduce the problem of distributed control of a multi-agent system. As an analysis tool, we prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also consider several design paradigms for decentralized and distributed control systems.

## Lecture Materials

- Lecture notes: Distributed control systems

## Further Reading

J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations",

*IEEE T. Automatic Control*, 49(9):1465-1476, 2004.S. K. Mitter and A. Sahai, "Information and control: Witsenhausen revisited," in

*Learning, Control and Hybrid Systems: Lecture Notes in Control and Information Sciences*, 241, Y. Yamamoto and S. Hara, Eds. New York, NY: Springer, 1999, pp. 281-293.V. Gupta, B. Hassibi and R. M. Murray, "On the Synthesis of Control Laws for a Network of Autonomous Agents", Proceedings of the American Control Conference 2004, vol. 6, pp. 4927-4932, 2004.

R. D'Andrea and G. E. Dullerud, "Distributed Control Design for Spatially Interconnected Systems",

*IEEE Transactions on Automatic Control*, vol. 48, no. 9, pp 1478-1495, 2003.C. Langbort, R. S. Chandra and R. D'Andrea, "Distributed Control Design for Systems Interconnected over an Arbitrary Graph",

*IEEE Transactions on Automatic Control*, vol. 49, no. 9, pp. 1502-1519, Sep. 2004.M. Rotkowitz and S. Lall, "A Characterization of Convex Problems in Decentralized Control",

*IEEE Transactions on Automatic Control*, vol. 51, no. 2, pp.274-286, Feb. 2006.