### Jorge Cortés

#### Professor

Solving linear equations with separable problem data
over directed networks

P. Srivastava, J. Cortés

IEEE Control Systems Letters, submitted

### Abstract

This paper deals with linear algebraic equations where the global
coefficient matrix and constant vector are given respectively, by
the summation of the coefficient matrices and constant vectors of
the individual agents. Our approach is based on reformulating the
original problem as an unconstrained optimization. Based on this
exact reformulation, we first provide a gradient-based, centralized
algorithm which serves as a reference for the ensuing design of
distributed algorithms. We propose two sets of exponentially stable
continuous-time distributed algorithms that do not require the
individual agent matrices to be invertible, and are based on
estimating non-distributed terms in the centralized algorithm using
dynamic average consensus. The first algorithm works for
time-varying weight-balanced directed networks, and the second
algorithm works for general directed networks for which the
communication graphs might not be balanced. Numerical simulations
illustrate our results.

pdf

Mechanical and Aerospace Engineering,
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