Suboptimal distributed LQR design for physically coupled systems

In this paper, we propose a suboptimal distributed LQR control method, applicable to systems coupled through both physical interconnections and the quadratic cost to be minimized. Thanks to a novel suboptimal but distributed cost-to-go matrix update that enforces block-diagonality, the suboptimal LQR gain matrix is structured, making the overall control scheme distributed. Moreover, the proposed control design algorithm is scalable. Theoretical properties of the method, including the stability of the closed-loop system, are investigated. A case study is shown to illustrate the features of the approach.