Edge addition in directed consensus networks
Sepideh Hassan-Moghaddam, Xiaofan Wu, Mihailo R. Jovanović · 2017
We study the problem of performance enhancement in stochastically-forced directed consensus networks by adding edges to an existing topology. We formulate the problem as a feedback control design, and represent the links as the elements of the controller graph Laplacian matrix. The topology design of the controller network can be cast as an ℓ1regularized version of the ℋ2optimal control problem. The goal is to optimize the performance of the network by selecting a controller graph with low communication requirements. To deal with the structural constraints that arise from the absence of absolute measurements, we introduce a coordinate transformation to eliminate the average mode and assure convergence of all states to the average of the initial node values. By exploiting structure of the optimization problem, we develop a customized algorithm based on the alternating direction method of multipliers to design a sparse controller network that improves the performance of the closed-loop system.