On Measurement Disturbances in Distributed Least Squares Solvers for Linear Equations

Abstract: This paper aims at distributed algorithms for solving a system of linear algebraic equations. Different from most existing formulations for this problem, we assume that the local data at each node is not accurately measured but subject to some disturbances. To be specific, the local measurement consists of two parts: a nominal value and a multiple sinusoidal disturbance. By introducing an identifier-enhanced observer to estimate the disturbance, we present a novel distributed least squares solver for the linear equations using noisy measurements. The proposed solver is proven to be able to recover the least squares solution to the linear equations associated with the nominal values irrespective of any multi-sinusoidal disturbance even with unknown frequencies. We also show the robustness of the distributed solvers under standard conditions against unstructured perturbations. The effectiveness of our design is verified by a numerical example.