Submodular Optimization for Consensus Networks with Noise-Corrupted Leaders

TL;DR

This paper addresses leader selection in noisy consensus networks by formulating the problem as a submodular optimization task, enabling efficient algorithms with provable performance bounds.

Contribution

It demonstrates that the network's performance measure is submodular and analyzes greedy algorithms for leader selection with guaranteed approximation bounds.

Findings

Performance measure is a submodular function.

Greedy algorithms achieve near-optimal leader sets.

Provable bounds for algorithm performance.

Abstract

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 steady-state 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, polynomial-time algorithms for leader selection, showing that the leader sets produced by the greedy algorithms are within provable bounds of optimal.