TY - GEN

T1 - On the Computation of the Distance-based Lower Bound on Strong Structural Controllability in Networks

AU - Shabbir, Mudassir

AU - Abbas, Waseem

AU - Yazicioglu, Yasin

PY - 2019/12

Y1 - 2019/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85082485239&partnerID=8YFLogxK

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U2 - 10.1109/CDC40024.2019.9029413

DO - 10.1109/CDC40024.2019.9029413

M3 - Conference contribution

AN - SCOPUS:85082485239

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5468

EP - 5473

BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 58th IEEE Conference on Decision and Control, CDC 2019

Y2 - 11 December 2019 through 13 December 2019

ER -