Distributed Continuous-Time Algorithm to Solve a Linear Matrix Equation

摘要

We study the distributed solving process of one class of linear matrix equations such as Σ_x=1^{rAiXBi = Σ_i=1rCi, using a continuous-time optimization method over multi-agent networks. In the problem formulation, each agent i is aware of Ai, Bi, Ci and communicates with its neighbors. Next, a continuous-time distributed algorithm presented is to solve its least squares solution from a distributed constrained optimization viewpoint. With help of the Lyapunov stability and semi-stability analysis, we prove the convergence of the algorithm and provide two numerical examples.}