Controllability of bandlimited graph processes over random time varying graphs

Controllability of bandlimited graph processes over random time varying graphs

Gama, F. (University of Pennsylvania)
Isufi, E. (TU Delft Multimedia Computing)
Ribeiro, Alejandro (University of Pennsylvania)
Leus, G.J.T. (TU Delft Signal Processing Systems)

2019

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.

graph process
Graph signal processing
graph signals
linear systems on graphs
network controllability
random graphs

http://resolver.tudelft.nl/uuid:c0a1eea6-e9bd-4cf7-be70-3241f6d81893

https://doi.org/10.1109/TSP.2019.2952053

2020-06-15

1053-587X

IEEE Transactions on Signal Processing, 67 (24), 6440-6454

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2019 F. Gama, E. Isufi, Alejandro Ribeiro, G.J.T. Leus