Syllabus

Introduction to multi-agent systems, Graph Theory: Graphs and digraphs, Adjacency matrix, Incidence matrix, Laplacian matrix, Edge Laplacian matrix [8]

Consensus: agreement subspace, convergence analysis, average consensus, Stochastic matrix, Perron-Frobenius results, Primitive matrix, Gersgorin disc theorem, Convergence analysis, Spanning rooted out-branching, Consensus control [8]

Formation Control: Formation specification, Formation invariants (scale, translation and rotation), Formation control, Rigid framework, Infinitesimal rigidity, Rigidity matrix, Minimally rigid framework, Gradient-based control [8]

Consensus (General Dynamics): Distributed static state feedback control, Leader-Follower consensus, Distributed output feedback control [6]

To introduce the fundamental concepts of multi-agent systems (MAS) and their applications in cooperative control, coordination, and distributed decision-making.

To develop a strong mathematical foundation using graph theory for modelling and analysing the communication topology among interacting agents.

To understand consensus algorithms and analyse convergence properties using matrix theory, eigenvalue analysis, and stability concepts.

To study formation control strategies and the role of rigidity theory in maintaining and controlling geometric formations among multiple agents.

To design distributed control laws for consensus and formation under general agent dynamics, including leader–follower and output feedback scenarios.

Model multi-agent systems using graph-theoretic tools such as adjacency, incidence, Laplacian, and edge Laplacian matrices.

Analyze and ensure consensus in multi-agent networks using stochastic matrices, Perron–Frobenius theory, and convergence analysis techniques.

Apply Gersgorin’s theorem and algebraic connectivity concepts to evaluate system stability and rate of convergence in distributed coordination problems.

Design and implement formation control laws based on rigidity theory, gradient-based methods, and formation invariants (translation, rotation, and scaling).

Develop distributed control strategies for leader–follower and output-feedback-based consensus problems in linear multi-agent systems.

Francesco Bullo, Lectures on Network Systems, Kindle Direct Publishing , Edition 1.7, Apr 2024

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

M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks, Princeton University Press , NJ, 2010

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.

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.