Topology-Based Controllability Problem in Network Systems

In network systems with a huge number of nodes, it is not possible to apply input signals to all network nodes to control them. In this paper, we show that this issue can be addressed by designing a network topology so that the nodes in the network system are controllable by a few nodes in the system. A theoretical framework that provides the basic link between structural controllability of network systems and the topology design problem is developed. The results also shed light on how new nodes can be added to the network system without having to introduce new control nodes. Hence, the results are useful in dealing with topology design to obtain a controllable network. Moreover, the results also show under what circumstances a network system with multiple identical nodes is uncontrollable. In many applications, groups of identical nodes are connected to each other which is called network of groups. Here, we address the structural controllability problem for multiple groups of network systems which provides information on proper topology design at both network level (i.e., interconnection of groups) and node level (i.e., interconnection of nodes within a group).