On the structural target controllability of undirected networks
Jingqi Li (University of California)
Ximing Chen (University of Pennsylvania)
Sergio Pequito (TU Delft - Team Tamas Keviczky)
George J. Pappas (University of Pennsylvania)
Victor M. Preciado (University of Pennsylvania)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
In this article, we study the target controllability problem of networked dynamical systems,in which we are tasked to steer a subset of network nodes toward 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.