Robust Synchronization and Model Reduction of Multi-Agent Systems

A networked multi-agent system is a dynamic system that consists of multiple interconnected subsystems called agents. These agents are interconnected according to a certain communication topology: the network graph. An important problem in the theory of multi-agent systems is the problem of robust synchronization. Here, the dynamics of agents are uncertain. While the dynamics of the individual agents are not known precisely, they are close to a given nominal dynamics. The goal is to find communication protocols that achieve synchronization despite this uncertainty. A network is said to be synchronized if the states of the agents converge to a common trajectory. In the first part of this thesis, we provide protocols that achieve synchronization robustly for networks where the agent dynamics are uncertain in the sense that the nominal dynamics 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 approximate our original system? Applying existing techniques to networks in general leads to unsatisfying results, because the model reduction step destroys the structure of the network. In the second part of this thesis, we investigate two different techniques that preserve the structure of the network. The first technique is based on clustering. Here, the agents are divided into groups and each group is represented by a single agent in the reduced network. The second technique instead reduces the network graph by removing cycles, thus reducing the complexity of the communication topology