• Communication networks
• Network analysis and control
• Networked control systems

This work investigates the issue of how to make decentralized networks amenable to external control, i.e. how to ensure that they are appropriately organized so that they can be effectively "reprogrammed". In particular, we study networked systems whose
interaction dynamics are given by a nearest-neighbor averaging
rule. And, by letting one node in the network take on the role of a leader
in the sense that this node provides the control input to the entire
system, we can ask questions concerning the controllability of this setup.
The important result in this work is that the controllable subspaces associated with
such systems have a direct, graph theoretic interpretation in terms of
so-called quotient graphs. These graphs thus provide us with smaller
networks that behave exactly like the original networks from a
controllability point-of-view.
Furthermore, a method to overcome
the problem of the uncontrollability of
symmetric single leader networks is then provided.
The main result in this work is that using equitable partition
concepts we can provide a necessary and sufficient
condition for the controllability of single leader networks. In
particular a direct interpretation of the
controllability properties of multi-agent systems can be given simply by
inspecting the geometry of the graph associated to the network.