On matrix factorization and finite-time average-consensus

Abstract

Abstract-We study the finite-time average-consensus problem for arbitrary connected networks. Viewing this consensus problem as a factorization of 1 n 11T by suitable families of matrices, we prove the existence of a finite factorization and provide tight bounds on the size of the minimal factorization by exhibiting finite-time average-consensus algorithms and bounding their runtimes. We also show that basic matrix theory yields insights into the structure of finite-time consensus algorithms.

Distributed Model Predictive Control of linear discrete-time systems with local and global constraints

“…However, such a centralized approach is not desirable due to its communication requirement. This section describes a distributed approach using the finite-time average consensus algorithm (Hendrickx, Jungers, Olshevsky, & Vankeerberghen, 2014;Hendrickx, Shi, & Johansson, 2015;Ko & Gao, 2009;Sundaram & Hadjicostis, 2007;Yuan, Stan, Shi, Barahona, & Goncalves, 2013). The main idea of a finite-time average consensus algorithm is given next.…”

Graph Laplacian based matrix design for finite-time distributed average consensus

“…In [11], based on properties of de Bruijn's graph and block Kronecker product, it has been shown that the average consensus problem can be reached in finite time if the number of nodes is an exact power of the out-degree of the communication graph. Another interesting contribution is that in [12] where finite-time average consensus problem is formulated as a matrix factorization problem. However, the proposed approach is fully centralized and requires scheduling of nodes connection.…”

Distributed Design of Finite-time Average Consensus Protocols

“…The existence issue has been deeply considered in Ko (2010) and Georgopoulos (2011). It has been pointed out that no solution exists if the factor matrices W t are all equal except if the graph is complete.…”

“…Therefore, the computational cost is the weakness of these methods. In Ko (2010) and Georgopoulos (2011), the finite-time average consensus was formulated as a matrix factorization problem. The resulting solution yields a link scheduling on the complete graph to achieve finite time consensus.…”