Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method

Thi-Minh-Dung Tran (1) , Alain Kibangou (1)

1 NECS - Networked Controlled Systems

This paper presents a new method for estimating the eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system. Given an approximate value of the average of the initial condition of the network state and some intermediate values of the network state when performing a Laplacian-based average consensus, the estimation of the Laplacian eigenvalues is obtained by solving the factorization of the averaging matrix. For this purpose, in contrast to the state of the art, we formulate a convex optimization problem that is solved in a distributed way by means of the Alternating Direction Method of Multipliers (ADMM). The main variables in the optimization problem are the coefficients of a polynomial whose roots are precisely the inverse of the distinct nonzero Laplacian eigenvalues. The performance of the proposed method is evaluated by means of simulation results.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Automatique / Robotique

Thi-Minh-Dung Tran, Alain Kibangou. Distributed Estimation of Graph Laplacian Eigenvalues by the Alternating Direction of Multipliers Method. IFAC WC 2014 - 19th IFAC World Congress, Aug 2014, Le Cap, South Africa. ⟨hal-00968419⟩