  Controllability of complex networks arises in many technological problems
involving social, financial, road, communication, and smart grid networks. In
many practical situations, the underlying topology might change randomly with
time, due to link failures such as changing friendships, road blocks or sensor
malfunctions. Thus, it leads to poorly controlled dynamics if randomness is not
properly accounted for. We consider the problem of controlling the network
state when the topology varies randomly with time. Our problem concerns target
states that are bandlimited over the graph; these are states that have nonzero
frequency content only on a specific graph frequency band. We thus leverage
graph signal processing and exploit the bandlimited model to drive the network
state from a fixed set of control nodes. When controlling the state from a few
nodes, we observe that spurious, out-of-band frequency content is created.
Therefore, we focus on controlling the network state over the desired frequency
band, and then use a graph filter to get rid of the unwanted frequency content.
To account for the topological randomness, we develop the concept of
controllability in the mean, which consists of driving the expected network
state towards the target state. A detailed mean squared error analysis is
performed to quantify the statistical deviation between the final controlled
state on a particular graph realization and the actual target state. Finally,
we propose different control strategies and evaluate their effectiveness on
synthetic network models and social networks.
