Distributed Solving Linear Algebraic Equations with Switched Fractional Order Dynamics

This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations. Firstly, the authors proposed "Consensus + Projection" flow with fractional order dynamics, which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms. Moreover, the authors prove that the proposed algorithm is convergent under certain iteration order and step-size. Furthermore, the authors develop iteration order switching scheme with initial condition design to improve the convergence performance of the proposed algorithm. Finally, the authors illustrate the effectiveness of the proposed method with several numerical examples.