TY - JOUR

T1 - Finite-time weighted average consensus and generalized consensus over a subset

AU - Shang, Yilun

PY - 2016/6/13

Y1 - 2016/6/13

N2 - In this paper, the finite-time consensus for arbitrary undirected graphs is discussed. We develop a parametric distributed algorithm as a function of a linear operator defined on the underlying graph and provide a necessary and sufficient condition guaranteeing weighted average consensus in K steps, where K is the number of distinct eigenvalues of the underlying operator. Based on the novel framework of generalized consensus meaning that consensus is reached only by a subset of nodes, we show that the finite-time weighted average consensus can always be reached by a subset corresponding to the non-zero variables of the eigenvector associated with a simple eigenvalue of the operator. It is interesting that the final consensus state is shown to be freely adjustable if a smaller subset of consensus is admitted. Numerical examples, including synthetic and real-world networks, are presented to illustrate the theoretical results. Our approach is inspired by the recent method of successive nulling of eigenvalues by Safavi and Khan.

AB - In this paper, the finite-time consensus for arbitrary undirected graphs is discussed. We develop a parametric distributed algorithm as a function of a linear operator defined on the underlying graph and provide a necessary and sufficient condition guaranteeing weighted average consensus in K steps, where K is the number of distinct eigenvalues of the underlying operator. Based on the novel framework of generalized consensus meaning that consensus is reached only by a subset of nodes, we show that the finite-time weighted average consensus can always be reached by a subset corresponding to the non-zero variables of the eigenvector associated with a simple eigenvalue of the operator. It is interesting that the final consensus state is shown to be freely adjustable if a smaller subset of consensus is admitted. Numerical examples, including synthetic and real-world networks, are presented to illustrate the theoretical results. Our approach is inspired by the recent method of successive nulling of eigenvalues by Safavi and Khan.

KW - Weighted average consensus

KW - generalized consensus

KW - finite-time

KW - discrete-time

KW - distributed algorithm

U2 - 10.1109/ACCESS.2016.2570518

DO - 10.1109/ACCESS.2016.2570518

M3 - Article

SN - 2169-3536

VL - 4

SP - 2615

EP - 2620

JO - IEEE Access

JF - IEEE Access

ER -