Numerically efficient [formula omitted] analysis of cooperative multi-agent systems

Abstract

This article proposes a numerically efficient approach for computing the maximal (or minimal) impact one agent has on the cooperative system it belongs to. For example, if one is able to disturb/bolster merely one agent in order to maximally disturb/bolster the entire team, which agent to choose? We quantify the agent-to-system impact in terms of H∞ norm whereas output synchronization is taken as the underlying cooperative control scheme. The agent dynamics are homogeneous, second order and linear whilst communication graphs are weighted and undirected. We devise simple sufficient conditions on agent dynamics, topology and output synchronization parameters rendering all agent-to-system H∞ norms to attain their maxima in the origin (that is, when constant disturbances are applied). Essentially, we quickly identify bottlenecks and weak/strong spots in multi-agent systems without resorting to intense computations, which becomes even more important as the number of agents grows. Our analyses also provide directions towards improving communication graph design and tuning/selecting cooperative control mechanisms. Lastly, numerical examples with a large number of agents and experimental verification employing off-the-shelf nano quadrotors are provided.