We study the strong structural controllability (SSC) of diffusively coupled networks, where the external control inputs are injected to only some nodes, namely the leaders. For such systems, one measure of controllability is the dimension of strong structurally controllable subspace, which is equal to the smallest possible rank of controllability matrix under admissible (positive) coupling weights. In this paper, we compare two tight lower bounds on the dimension of strong structurally controllable subspace: one based on the distances of followers to leaders, and the other based on the graph coloring process known as zero forcing. We show that the distance-based lower bound is usually better than the zero-forcing-based bound when the leaders do not constitute a zero-forcing set. On the other hand, we also show that any set of leaders that can be shown to achieve complete SSC via the distance-based bound is necessarily a zero-forcing set. Furthermore, we present a novel bound based on the combination of these two approaches, which is always at least as good as, and in some cases strictly greater than, the maximum of the two bounds. Finally, we present some numerical results to compare the bounds on various graphs.
|Original language||English (US)|
|Title of host publication||2020 59th IEEE Conference on Decision and Control, CDC 2020|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - Dec 14 2020|
|Event||59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of|
Duration: Dec 14 2020 → Dec 18 2020
|Name||Proceedings of the IEEE Conference on Decision and Control|
|Conference||59th IEEE Conference on Decision and Control, CDC 2020|
|Country/Territory||Korea, Republic of|
|City||Virtual, Jeju Island|
|Period||12/14/20 → 12/18/20|
Bibliographical noteFunding Information:
Yasin Yazıcıog˘lu is with the Department of Electrical and Computer Engineering at the University of Minnesota, Minneapolis, MN, USA. Email: email@example.com Mudassir Shabbir is with the Computer Science Department at the Information Technology University, Lahore, Punjab, Pakistan. Email: firstname.lastname@example.org Waseem Abbas and Xenofon Koutsoukos are with the Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN, USA (e-mails: email@example.com, firstname.lastname@example.org). Their work was supported in part by the National Institute of Standards and Technology under Grant 70NANB18H198.
© 2020 IEEE.