Controllability of bandlimited graph processes over random time varying graphs

Fernando Gama, Elvin Isufi, Alejandro Ribeiro, Geert Leus

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
7 Downloads (Pure)

Abstract

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.

Original languageEnglish
Article number8892652
Pages (from-to)6440-6454
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume67
Issue number24
DOIs
Publication statusPublished - 2019

Keywords

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

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