Sparse Feedback Implementation for Sender-Receiver Transportation Linear-Quadratic Control

We study a sparse linear-quadratic problem for transportation dynamics. The goal is to compute the optimal control signal without applying the usually dense optimal feedback gain directly. We show that the optimal feedback gain can be factorized as the product of a sparse matrix and the inverse of another sparse matrix from the right. This factorization enables the control signal to be computed with much less computational effort than direct multiplication by the dense gain. The factorization also enables a distributed implementation. The main message is that linear quadratic control need not appear dense when expressed in graph-adapted coordinates, and that intrinsic sparsity can be revealed under the proposed formulation.