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

This paper proposes a continuous-time distributed algorithm for multiagent networks to achieve a solution with the minimum l
₁
-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
₁
-norm solution.