1Algorithms for Leader Selection in Stochastically Forced Consensus Networks
Lin Fu, Makan Fardad, Mihailo R. Jovanović, Senior Member · 2016
Abstract—We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular for-mations and localization in sensor networks. For networks with leaders subject to noise, we show that the Boolean constraints (which indicate whether a node is a leader) are the only source of nonconvexity. By relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value. We also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound. For networks with leaders that perfectly follow their desired trajectories, we identify an additional source of nonconvexity in the form of a rank constraint. Removal of the rank constraint and relaxation of the Boolean constraints yields a semidefinite program for which we develop a customized algo-rithm well-suited for large networks. Several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms. Index Terms—Alternating direction method of multipliers (ADMMs), consensus networks, convex optimization, convex re-laxations, greedy algorithm, leader selection, performance bounds, semidefinite programming (SDP), sensor selection, variance amplification. I.