Finite-Time Distributed Linear Equation Solver for Solutions With Minimum $l_1$-Norm

Abstract

This paper proposes a continuous-time distributed algorithm for multiagent networks to achieve a solution with the minimum l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm to underdetermined linear equations. The proposed algorithm comes from a combination of the Filippov set-valued map with the projection-consensus flow. Given the underlying network is undirected and fixed, it is shown that the proposed algorithm drives all agents' individual states to converge in finite time to a common value, which is the minimum l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm solution.