Networked and Multi-agent Control Systems (ELL805)

Time and Venue

  • Tuesday: 3:30 P.M. - 5:00 P.M. (LH 517)

  • Friday: 3:30 P.M. - 5:00 P.M. (LH 517)


  • Introduction:- Multi-agent systems (practical examples); Agreement/Consensus protocol; Control problems: formation, consensus and synchronization.

  • Graph Theory:- Graphs and digraphs: path, cycle, tree, strongly connected digraph, balanced diagraph, induced subgraph; Operations (union and intersection) on subgraphs; Graph associated matrices: adjacency matrix, incidence matrix, Laplacian matrix; Edge Laplacian matrix, Stochastic matrix; Cycle space; Algebraic and spectral graph theory.

  • Agreement/Consensus protocol:- Agreement protocol in undirected and directed networks: agreement subspace, convergence rate to the agreement space, spanning rooted out-branching, Gersgorin disc, edge agreement protocol and its convergence; Lyapunov and LaSalle's analysis for convergence.

  • Formation Control:- Framework; Graph rigidity: rigidity, infinitesimal rigidity and rigidity matrix; Formation specifications: shapes, relative states; Shape-based control; Relative state-based control; Rendezvous.

  • Consensus and Synchronization Control:- Disagreement dynamics and error system dynamics; Coupling gain; State feedback control; Observer based feedback control.

Lecture Notes


  • Assignment: 10% (We will have interactive session on the day of assignment submission)

  • Minor 1: 25%

  • Minor 2: 25%

  • Major: 40%

Suggested References

  1. M. Mesbahi and M. Egerstedt, “Graph Theoretic Methods in Multiagent Networks”, Princeton Univercity Press, NJ, 2010.

  2. W. Ren and R.W. Beard, “Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Application”, Springer-Verlag, London, 2008.

  3. F. Lewis, H. Zhang, K. Hengster-Movric and A. Das, “Cooperative Control of Multi-Agent Systems: Optimal and Adaptive Design Approaches”, Springer-verlag, London, 2014.

  4. R. B. Bapat, “Graphs and Matrices”, Hindustan Book Agency, Springer-Verlag, London, 2011.

  5. L. Krick, M. E. Broucke and B. A. Francis “Stabilisation of infinitesimally rigid formations of multi-robot networks”, International Journal of Control, Vol. 82, No. 3, 2009.

  6. W. Ren, R. W. Beard, and E. M. Atkins, “Information Consensus in Multivehicle Cooperative Control”, IEEE Control Systems Magazine, April-2007.

  7. Z. Li, Z. Duan, G. Chen and L. Huang, “Consensus of Multi-agent Systems and Synchronization of Complex Networks: A Unified Viewpoint”, IEEE Transactions on Circuits and Systems-I: Regular Papers, Vol. 57-1, 2010.

  8. H. Zhang, F. L. Lewis and A. Das, “Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback”, IEEE Transactions on Automatic Control, vol. 56, no. 8, 2011.