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Introduction to Multi-Agent Systems

NPTEL via Swayam

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ABOUT THE COURSE:This course introduces foundational and some advanced concepts in multi-agent systems with a focus on its applications in various domains. Students will explore mathematical tools from linear algebra, systems theory and algebraic and spectral graph theory to model and analyse the inter-agent interactions in coordinated frameworks. Thereafter, we will study some protocols to achieve consensus among the agents. The course will conclude with some applications of consensus protocols in the areas of path planning and coordination of multi-robot systems, networks of coupled oscillators and mathematical sociology.

Syllabus

Week 1: Introduction to Networked Dynamical Systems, Motivational examples.
Week 2:Mathematical Preliminaries - Linear algebra and Matrix theory.
Week 3:Elementary Graph theory - Graphs, digraphs, subgraphs, walks and connectivity.
Week 4:Algebraic Graph theory - Adjacency matrix, Spectral graph theory, Algebraic connectivity, Averaging systems.
Week 5:Controllability in multi-agent systems.
Week 6:Centrality indices and their applications
Week 7:Incidence matrix, Laplacian flows.
Week 8:Dynamical systems and stability notions, Applications in formation control problems.
Week 9:Opinion evolution in social networks.
Week 10:Distributed strategies in autonomous vehicles
Week 11:Consensus protocols for cyber-physical systems.
Week 12:Consensus protocols in coupled oscillator networks.