Discrete-Time Distributed Least Square Algorithms for Linear Equations via Layered Coordination

This paper is concerned with the problem of designing discrete-time distributed algorithms for the least squares solution of over-determined linear equations via layered coordination. A row-column partition and a column-row partition are provided to partition the augmented matrix associated with the linear equations into several block matrices, respectively. By assigning an equation solver layer to computation and a data integration layer to data exchanges, a row-column partition-based discrete-time distributed algorithm and a column-row partition-based discrete-time distributed algorithm are proposed for solving over-determined linear equations, respectively. It is shown that the distributed algorithms proposed can reach a consensus exponentially on the least squares solution of linear equations. Finally, the effectiveness of the distributed algorithms proposed is validated via a numerical simulation.