Performance and robustness of averaging algorithms

Abstract

This chapter has the goal of introducing more instruments for the study of consensus algorithms. We will define several performance metrics: Each proposed metric highlights a specific aspect of the algorithm, possibly in relation with a field of application. Namely, we shall consider the speed of convergence in Sect. 4.1, a quadratic control cost in Sect. 4.2, the robustness to noise in Sect. 4.3, and the estimation error in a distributed inference problem in Sect. 4.5. The metrics that we describe share the following feature: under suitable assumptions of symmetry of the update matrix, they can be evaluated as functions of the eigenvalues of the update matrix.