Decentralized gain adaptation for optimal pinning controllability of complex networks

Anna Di Meglio*, Pietro De Lellis, Mario Di Bernardo

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)


Coordinating ensembles of dynamical systems in a decentralized manner is of central importance when controlling complex networks. Pinning control is a much used technique where only a small fraction of the network nodes is directly controlled, with control gains being typically selected uniformly across the control layer. In this letter, we tackle the problem of optimally selecting the control gains of a pinning control strategy. Indeed, in networks of nonlinear dynamical systems fulfilling the so-called QUAD assumption, pinning controllability improves as the smallest eigenvalue \lambda -{1} of an extended Laplacian matrix increases. Based on this observation, we pose a constrained optimization problem on the network. Rather than solving it in a centralized fashion, we propose a fully decentralized multilayer approach. Specifically, one layer is used to evaluate the sensitivity of \lambda -{1} to the variation of the gains, while the second layer uses such an estimate to dynamically tune the control gains. The effectiveness of the approach is demonstrated via a representative example.

Original languageEnglish
Article number8738815
Pages (from-to)253-258
Number of pages6
JournalIEEE Control Systems Letters
Issue number1
Early online date18 Jun 2019
Publication statusPublished - 1 Jan 2020

Bibliographical note

Acceptance date is provisional - author emailed for acceptance date and AAM.


  • adaptive control
  • Control of networks
  • decentralized control
  • optimization


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