# Distributed Control of Multi-Agent Networks

## AAE59000

3

### Learning Objective:

To know frontier topics in robotics especially their coordination and collaborations for tasks well beyond the capability of individual robots; To learn key concepts in control, networks, graph theories, optimizations, and their integration; To prepare basic background for future research in machine learnings; To enhance independent research capability.

### Description:

This graduate-level course introduces distributed control of multi-agent networks, which achieves global objectives through local coordination among nearby neighboring agents. The course will prepare students with basic concepts in control (Lyapunov stability theory, exponential convergence, Perron-Frobenius theorem), graph theories (adjacency matrix, Laplacian matrix, incidence matrix, rigidity matrix), matrix theories (stochastic matrices, double stochastic matrices), and optimizations (gradient descent methods, ADMM). Topics of applications to be covered include flocking (by consensus), sensor networks (by distributed averaging), distributed fusion (by distributed linear equation solver), multi-robot formation (by distributed gradient descent method), cyber-security (by resilient information fusion), and increasing autonomy of multi-robot coordination through machine learnings.

### Topics Covered:

• Fundamental concepts in linear algebra: Matrix and norm; Eigenvalues and Eigenvectors; Jordan form of matrices; Stochastic matrices.
• Important techniques in control and optimizations: Convergence of continuous and discrete time systems; Laypunov stability theory; Perron-Frobenius Theorem.
• Basic methods in optimizations: Gradient descent method; Alternating Direction Method of Multiplier (ADMM).
• Key tools in graph theories for networks: Adjacency/Laplacian/Incidence/Rigidity matrices; Graph connectivity and composition.
• Research Topic: Flocking of robot swarms (consensus algorithms)
• Research Topic: Distributed averaging (gossiping algorithms) with applications in sensor networks.
• Research Topic: Distributed algorithms for solving linear/nonlinear equations with applications in distributed fusion/estimation.
• Research Topic: Distributed formation control of multiple robots
• Research Topic: Distributed optimizations with applications into machine learning.

### Prerequisites:

Basic linear algebra and control background.

20 / 80

### Textbooks:

Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department. No required text. Textbook recommendations include:
• Lectures on Network Systems (by Prof. Francessco Bullo) https://ucsb.app.box.com/v/book-lns
• Graph Theoretic Methods in Multiagent Networks (by Mehran Mesbahi, Magnus Egerstedt)
• Distributed Coordination of Multi-agent networks (by Wei Ren, Yongcan Cao)

### Other Requirements:

MATLAB skills required

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