TY - JOUR

T1 - Approximate projected consensus for convex intersection computation

T2 - Convergence analysis and critical error angle

AU - Lou, Youcheng

AU - Shi, Guodong

AU - Johansson, Karl Henrik

AU - Hong, Yiguang

PY - 2014/7

Y1 - 2014/7

N2 - In this paper, we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets, where each set corresponds to one network node. Instead of assuming exact convex projection that each node can compute, we allow each node to compute an approximate projection with respect to its own set. After receiving the approximate projection information, nodes update their states by weighted averaging with the neighbors over a directed and time-varying communication graph. The approximate projections are related to projection angle errors, which introduces state-dependent disturbance in the iterative algorithm. Projection accuracy conditions are presented for the considered algorithm to converge. The results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected. In addition, we show that is a critical angle for the error of the projection approximation to ensure the boundedness. Finally, the results are illustrated by simulations.

AB - In this paper, we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets, where each set corresponds to one network node. Instead of assuming exact convex projection that each node can compute, we allow each node to compute an approximate projection with respect to its own set. After receiving the approximate projection information, nodes update their states by weighted averaging with the neighbors over a directed and time-varying communication graph. The approximate projections are related to projection angle errors, which introduces state-dependent disturbance in the iterative algorithm. Projection accuracy conditions are presented for the considered algorithm to converge. The results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected. In addition, we show that is a critical angle for the error of the projection approximation to ensure the boundedness. Finally, the results are illustrated by simulations.

KW - Multi-agent systems

KW - approximate projection

KW - intersection computation

KW - optimal consensus

UR - http://www.scopus.com/inward/record.url?scp=84903287276&partnerID=8YFLogxK

U2 - 10.1109/TAC.2014.2309261

DO - 10.1109/TAC.2014.2309261

M3 - Article

SN - 0018-9286

VL - 59

SP - 1722

EP - 1736

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 7

M1 - 6750701

ER -