The project considers the problem of coordination between dynamical systems that exchange information over directed graphs. The analysis of these systems turns out to be extremely challenging not only due to the potential complexity of each agent interacting in the system, but also due to the asymmetric information exchange resulting from the directed graphs. Commonly used analysis tools for studying these systems, such as passivity or dissipasivity theory, are not amenable to asymmetric interconnections. This project aims to study this problem by considering new approaches at the intersection of differential geometry, nonlinear optimization, and graph theory. A motivating application for this are the synchronization and formation control problems.
