Optimal sparse network topology under sparse control in Laplacian networks

Wentao Tang, Pedro H. Constantino, Prodromos Daoutidis

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


Understanding the effect of network topology on its controllability or control performance helps to explain the emergence and evolution of different topological features in biological or social networks, and to provide principles of designing networked engineering systems. In natural and artificial systems, networks have sparse topology and are controlled by sparse feedback controllers. Therefore, the optimal network topology and controllers are specified by a trade-off between the control performance and the sparsity of the network and the controllers. In this work, by considering Laplacian networks and adopting an H2-optimal control framework that incorporates the network Laplacian matrix as an optimization variable and promotes the network sparsity and controller sparsity, we simultaneously optimize the network topology and the feedback gain matrix through the alternating direction method of multipliers (ADMM). We observe that with increasing sparsity, modular and hierarchical topological features emerge along with distributed and hierarchical control architectures, which is consistent with observations in biological networks and allows an evolutionary interpretation of their emergence.

Original languageEnglish (US)
Pages (from-to)273-278
Number of pages6
Issue number20
StatePublished - 2019
Event8th IFAC Workshop on Distributed Estimation and Control in Networked Systems, NECSYS 2019 - Chicago, United States
Duration: Sep 16 2019Sep 17 2019

Bibliographical note

Publisher Copyright:
© 2019 IFAC-PapersOnLine. All rights reseved.

Copyright 2020 Elsevier B.V., All rights reserved.


  • Network topology
  • hierarchy
  • modularity
  • optimal control
  • sparsity


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