Robust Synchronization and Model Reduction of Multi-Agent Systems

A networked multi-agent system is a dynamic system that consists of multipleinterconnected subsystems called agents. These agents are interconnectedaccording to a certain communication topology: the network graph.An important problem in the theory of multi-agent systems is the problem ofrobust synchronization. Here, the dynamics of agents are uncertain. While thedynamics of the individual agents are not known precisely, they are close to agiven nominal dynamics. The goal is to find communication protocols that achievesynchronization despite this uncertainty. A network is said to be synchronizedif the states of the agents converge to a common trajectory. In the first partof this thesis, we provide protocols that achieve synchronization robustly fornetworks where the agent dynamics are uncertain in the sense that the nominaldynamics has been perturbed by coprime factor perturbations.Another well-known problem is that of model reduction: given a complex,large-scale system, can we find less complex models that accurately approximateour original system? Applying existing techniques to networks in general leadsto unsatisfying results, because the model reduction step destroys the structureof the network. In the second part of this thesis, we investigate two differenttechniques that preserve the structure of the network. The first technique isbased on clustering. Here, the agents are divided into groups and each group isrepresented by a single agent in the reduced network. The second techniqueinstead reduces the network graph by removing cycles, thus reducing thecomplexity of the communication topology