TY - JOUR

T1 - Tradeoff between Controllability and Robustness in Diffusively Coupled Networks

AU - Abbas, Waseem

AU - Shabbir, Mudassir

AU - Yazicioglu, A. Yasin

AU - Akber, Aqsa

N1 - Publisher Copyright:
© 2014 IEEE.

PY - 2020/12

Y1 - 2020/12

N2 - In this article, we demonstrate a conflicting relationship between two crucial properties - controllability and robustness - in linear dynamical networks of diffusively coupled agents. In particular, for any given number of nodes N and diameter D, we identify networks that are maximally robust using the notion of Kirchhoff's index and then analyze their strong structural controllability. For this, we compute the minimum number of leaders, which are the nodes directly receiving external control inputs, needed to make such networks controllable under all feasible coupling weights between agents. Then, for any N and D, we obtain a sharp upper bound on the minimum number of leaders needed to design strong structurally controllable networks with N nodes and D diameter. We also discuss that the bound is best possible for arbitrary N and D. Moreover, we construct a family of graphs for any N and D such that the graphs have maximal edge sets (maximal robustness) while being strong structurally controllable with the number of leaders in the proposed sharp bound. We then analyze the robustness of this graph family. The results suggest that optimizing robustness increases the number of leaders needed for strong structural controllability. Our analysis is based on graph-theoretic methods and can be applied to exploit network structure to co-optimize robustness and controllability in networks.

AB - In this article, we demonstrate a conflicting relationship between two crucial properties - controllability and robustness - in linear dynamical networks of diffusively coupled agents. In particular, for any given number of nodes N and diameter D, we identify networks that are maximally robust using the notion of Kirchhoff's index and then analyze their strong structural controllability. For this, we compute the minimum number of leaders, which are the nodes directly receiving external control inputs, needed to make such networks controllable under all feasible coupling weights between agents. Then, for any N and D, we obtain a sharp upper bound on the minimum number of leaders needed to design strong structurally controllable networks with N nodes and D diameter. We also discuss that the bound is best possible for arbitrary N and D. Moreover, we construct a family of graphs for any N and D such that the graphs have maximal edge sets (maximal robustness) while being strong structurally controllable with the number of leaders in the proposed sharp bound. We then analyze the robustness of this graph family. The results suggest that optimizing robustness increases the number of leaders needed for strong structural controllability. Our analysis is based on graph-theoretic methods and can be applied to exploit network structure to co-optimize robustness and controllability in networks.

KW - Network controllability

KW - network robustness

KW - network structure

UR - http://www.scopus.com/inward/record.url?scp=85097939038&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85097939038&partnerID=8YFLogxK

U2 - 10.1109/TCNS.2020.3011814

DO - 10.1109/TCNS.2020.3011814

M3 - Article

AN - SCOPUS:85097939038

VL - 7

SP - 1891

EP - 1902

JO - IEEE Transactions on Control of Network Systems

JF - IEEE Transactions on Control of Network Systems

SN - 2325-5870

IS - 4

M1 - 9146993

ER -