Submodular Optimization for Consensus Networks with Noise-Corrupted Leaders

We consider the leader selection problem in a network with consensus dynamics where both leader and follower agents are subject to stochastic external disturbances. The performance of the system is quantified by the total steadystate variance of the node states, and the goal is to identify the set of leaders that minimizes this variance. We first show that this performance measure can be expressed as a submodular set function over the nodes in the network. We then use this result to analyze the performance of two greedy, polynomialtime algorithms for leader selection, showing that the leader sets produced by the greedy algorithms are within provable bounds of optimal.