Distributed Optimization Design of Iterative Refinement Technique for Algebraic Riccati Equations

This article focuses on the problem of a distributed computation of continuous-time algebraic Riccati equations (CARE), where information of matrices is split and known by multiple agents. This article proposes a distributed optimization design of the iterative refinement technique (IRM), a well-established centralized method for CARE. By assuming that each agent only knows partial information of CARE, we reformulate IRM for CARE as three classes of distributed optimization subproblems with different formulations and constraints. Then, we propose distributed algorithms for obtained distributed optimization subproblems and prove convergence properties of proposed algorithms. Numerical results show the efficacy of the proposed distributed IRM.