Identification of sparse communication graphs in consensus networks

We consider the design of distributed controller architectures for undirected networks of single-integrators. In the presence of stochastic disturbances, we identify communication topologies that balance the variance amplification of the network with the number of communication links. This is achieved by solving a parameterized family of sparsity-promoting optimal control problems whose solution traces the optimal tradeoff curve that starts at the centralized controller and ends at the controller with sparse communication links. We show that the optimal control problem can be formulated as a semidefinite program whose global solution can be computed efficiently. An example is provided to illustrate the utility of the developed approach.