Networked and Multi-agent Control Systems (ELL805)

Time and Venue (Semester-I, 2023-24)

• Tuesday: 10 AM - 11 AM (LH 527)

• Wednesday: 10 AM - 11 AM (LH 527)

• Friday: 10 AM - 11 AM (LH 527)

Syllabus

• Introduction: On multi-agent systems (Lecture 1)

• Graph Theory

  • Some Definitions on Graphs and digraphs (Lecture 2)

  • Graph associated matrices and results: Adjacency matrix, Incidence matrix, Laplacian matrix; Edge Laplacian matrix, Cycle space (Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lecture 10)

• Consensus (Scalar Agent Dynamics)

  • Undirected Network Topology (continuous-time case): agreement subspace, convergence analysis, average consensus (Lecture 11, Lecture 12)

  • Undirected Network Topology (discrete-time case): Stochastic matrix, Perron-Frobenius results, Primitive matrix, Gersgorin disc theorem, Convergence analysis (Lecture 13, Lecture 14, Lecture 15, Lecture 16)

  • Directed Network Topology (continuous-time case): Spanning rooted out-branching, Consensus control (Lecture 17, Lecture 18)

  • Edge Consensus (Lecture 19)

• Formation Control

  • Formation specification, Formation invariants (scale, translation and rotation), Formation control, Rendezvous (Lecture 20, Lecture 21, Lecture 22), Rigid framework, Infinitesimal rigidity, Rigidity matrix, Minimally rigid framework, Gradient based control (Lecture 23, Lecture 24-25, Lecture 26)

• Consensus (General Dynamics): Distributed static state feedback control (Lecture 27-29)

• Leader-Follower Synchronization: Distributed static state feedback control (Lecture 30-31)

• Output Consensus: Distributed output feedback control, Classical control system based design (Article-1, Article-2)

Evaluation

• Minor Exam: 35%

• Major Exam: 45%

• Course Project: 20%

• If you are Auditing, then you need to score at least “C” grade to get Audit pass (NP).

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

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

5. 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.

6. S. Datta, “Consensus in Multi-agent Systems: A Transfer Function Based Controller Design Approach”, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.: 69(11), pp: 4384-4388, 2022.

7. 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.

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.