Numerically Efficient Agents-to-Group H∞ Analysis

Abstract

This paper proposes a numerically efficient approach for computing the maximal/minimal impact a subset of agents has on the cooperative system. For instance, if one is able to disturb/bolster several agents so as to maximally disturb/bolster the entire team, which agents to choose and what kind of inputs to apply? We quantify the agents-to-team impacts in terms of H∞ norm whereas output synchronization is taken as the underlying cooperative control scheme. Sufficient conditions on agents’ parameters, synchronization gains and topology are provided such that the associated H∞ norm attains its maximum for constant agents’ disturbances. Linear second-order agent dynamics and weighted undirected topologies are considered. Our analyses also provide directions towards improving graph design and tuning/selecting cooperative control mechanisms. Lastly, numerical examples, some of which include forty thousand agents, are provided.