On the Computation of the Distance-based Lower Bound on Strong Structural Controllability in Networks

Mudassir Shabbir, Waseem Abbas, Yasin Yazicioglu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

A network of agents with linear dynamics is strong structurally controllable if agents can be maneuvered from any initial state to any final state independently of the coupling strengths between agents. If a network is not strong structurally controllable with given input nodes (leaders), then the dimension of strong structurally controllable subspace quantifies the extent to which a network can be controlled by the same inputs. Computing this dimension exactly is computationally challenging. In this paper, we study the problem of computing a sharp lower bound on the dimension of strong structurally controllable subspace in networks with Laplacian dynamics. The bound is based on a sequence of vectors containing distances between leaders and the remaining nodes in the underlying network graph. Such vectors are referred to as the distance-to-leader vectors. We provide a polynomial time algorithm to compute a desired sequence of distance-to-leader vectors with a fixed set of leaders, which directly provides a lower bound on the dimension of strong structurally controllable subspace. We also present a linearithmic approximation algorithm to compute such a sequence, which provides near optimal solutions in practice. Finally, we numerically evaluate and compare our bound with other bounds in the literature on various networks.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5468-5473
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

Fingerprint Dive into the research topics of 'On the Computation of the Distance-based Lower Bound on Strong Structural Controllability in Networks'. Together they form a unique fingerprint.

  • Cite this

    Shabbir, M., Abbas, W., & Yazicioglu, Y. (2019). On the Computation of the Distance-based Lower Bound on Strong Structural Controllability in Networks. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 5468-5473). [9029413] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029413