Distributed algorithms for solving linear algebraic equations: An optimal control perspective

Designing superior distributed algorithms for solving linear algebraic equations (LAEs) plays a crucial role in engineering and computer science fields. This paper proposes two discrete distributed algorithms for solving LAEs from the perspective of optimal control. By benefiting from the devised error system and constructed performance index, the presented algorithms can converge R-linearly to a solution of LAEs without solving algebraic Riccati equations. In particular, the full-row rank requirements on sub-matrices are eliminated in row partitioning framework. Moreover, the need for communication exchange among all agents within the same cluster is alleviated, and only one state variable is updated in the row-wise arbitrary column partitioning framework. Simulation results demonstrate that the proposed distributed algorithms outperform non-optimal control design algorithms in terms of convergence performance.