On the structural target controllability of undirected networks

Jingqi Li, Ximing Chen, Sergio Pequito, George J. Pappas, Victor M. Preciado

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

In this paper, we study the target controllability problem of networked dynamical systems, in which we are tasked to steer a subset of network nodes towards a desired objective. More specifically, we derive necessary and sufficient conditions for the structural target controllability of linear time-invariant (LTI) systems with symmetric state matrices, such as those representing undirected dynamical networks with unknown link weights. To achieve our goal, we first characterize the generic rank of symmetrically structured matrices, as well as the modes of any numerical realization. Subsequently, we provide graph-theoretic necessary and sufficient conditions for the structural target controllability of undirected networks with multiple control nodes. In addition, we show that these results can be extended and lead to a necessary and sufficient condition of the structural output controllability. However, different from structural target controllability, we prove that verifying the proposed conditions on structural output controllability in undirected networks is NP-hard.

Original languageEnglish
Pages (from-to)8
JournalIEEE Transactions on Automatic Control
DOIs
Publication statusE-pub ahead of print - 2021

Keywords

  • Computational complexity
  • Controllability
  • Dynamical systems
  • Graph theory
  • Linear systems
  • networked control systems
  • structured linear systems
  • Symmetric matrices
  • Target controllability
  • Tools

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