Sparse Linear-Quadratic-Gaussian Control in Networked Systems. Issue 1 (July 2017) - Lin, Fu; Bopardikar, Shaunak D.
Abstract: We consider the sparsity-promoting Linear Quadratic Gaussian (LQG) control for a network of linear systems. A sparse LQG controller requires fewer communication channels with the networked system. The bidirectional communication implies that the column-block-sparsity pattern of the Kalman filter and the row-block-sparsity pattern of the state feedback controller must be the same. We develop a two-step procedure: the first step being a sparsity-promoting design of the Kalman filter and the second step leveraging the structure identified in the first step to design the respective controllers. In both steps we employ the Alternating Directions Method of Multipliers (ADMM) and show its effectiveness for the identification and the structural LQG design. In particular, ADMM allows us to decompose the structured LQG problem into a sequence of convex quadratic problems that can be solved efficiently. We demonstrate via numerical experiments that our approach results in sparse controllers whose performance is comparable to that of the fully centralized controllers.