Algebraic Riccati equation approach for network distributed optimal H2 synthesis

In this paper, we solve the optimal ${\mathcal{H}}_{2}$ control problem distributed over networks with an arbitrary graph, with the assumption that the controller network has no delays but only sparsity constraints. Our solution extends the previous approach valid for strongly connected graphs. Under the quadratic invariance structure assumption, we follow the Youla parameterization framework for the distributed control synthesis setup. We show that the optimal solution is finite-dimensional and can be computed by solving three algebraic Riccati equations: two are standard for centralized ${\mathcal{H}}_{2}$ control, while the third emerges from the sparsity constraints imposed by the network. We present a 4-car platoon example for method validation.