Topology design for stochastically-forced consensus networks
arXiv:1506.03437 · doi:10.1109/TCNS.2017.2674962
Abstract
We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected network, with a known graph Laplacian, in order to optimally enhance closed-loop performance. To promote controller sparsity, we introduce -regularization into the optimal formulation and cast the design problem as a semidefinite program. We derive a Lagrange dual, provide interpretation of dual variables, and exploit structure of the optimality conditions for undirected networks to develop customized proximal gradient and Newton algorithms that are well-suited for large problems. We illustrate that our algorithms can solve the problems with more than million edges in the controller graph in a few minutes, on a PC. We also exploit structure of connected resistive networks to demonstrate how additional edges can be systematically added in order to minimize the norm of the closed-loop system.
11 pages; 5 figures