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.

I. Introduction

Distributed algorithms implemented on multiagent systems, each agent of which knows local information and communicates with its connected agents for global objectives, have received a continuous interest in the control system community for a few decades [1], [2]. This interest primarily stems from a large number of applications in formation control [3], machine learning [4], and load sharing of power grids [5], due to various reasons, such as big data, privacies, and securities.