Overview
This course introduces modeling, analysis, and design for networked (multi-agent) dynamical systems using graph theory, dynamical systems, and optimization. Topics include consensus, formation control, performance analysis, and applications to robotic and aerospace systems.
See the handout PDF for the authoritative syllabus and policies.
Syllabus (topics)
- Graph theory; algebraic & spectral graph theory
- Consensus protocols (undirected, directed, switching, random)
- Relative sensing networks (formation control, distributed estimation)
- Networks as systems: stability, performance (H2/H∞), controllability, observability
- Nonlinear models (Kuramoto, interconnected passive systems)
- Connectivity maintenance & maximization
- Rigid formations for control & localization; graph design
- Applications in robotics and aerospace
Grading Policy
- Homeworks 30% 4–6 sets (work in groups encouraged, submission individually)
- Midterm Project 25% (take-home; individual).
- Final Project 45% (details TBA).
Tentative Weekly Outline
- Intro & graph theory fundamentals; algebraic graph theory
- Consensus: undirected, directed
- Consensus: switching; connectivity maintenance
- Consensus feedback for linear systems
- Networks as systems—controllability, observability
- Stability & performance; edge agreement
- Rigidity theory (formation control)
- Distance-based formation control
- Bearing-based formation control
- Consensus design & synthesis
- Nonlinear consensus—Kuramoto; passive systems
- Advanced topics / projects
- Advanced topics / projects
Lecture Notes
Zoom Recordings
Homeworks
Suggested Textbooks
- Mesbahi & Egerstedt, Graph Theoretic Methods in Multiagent Networks
- Bullo, Lectures on Network Systems
- Lunze, Networked Control of Multi-Agent Systems
- Godsil & Royle, Algebraic Graph Theory
- Horn & Johnson, Matrix Analysis
- Bai, Arcak, Wen, Cooperative Control Design
- Ren & Beard, Distributed Consensus in Multi-Vehicle Cooperative Control
- Bullo, Cortés, Martínez, Distributed Control of Robotic Networks