Containment Control of Multi-Human Multi-Agent Systems Under Time Delays

This article considers the containment of heterogeneous linear time-invariant multi-human multi-agent systems with a distributed dynamic state feedback control law. The unique aspect of this problem lies in the presence of multiple human operators. Each operator commands a subset of the agents while observing the same or a different subset. Commanding based on their observation approach of the human operators makes them integral components of the network rather than simple providers of reference signals. This setup requires a new set of conditions distinct from the standard containment problem literature. Considering fixed-time delays in human reactions and information exchange between human operators and agents, it is shown that the containment problem is solved if the delayed closed-loop system is exponentially stable under the new set of conditions. Encompassing different graphs, system scales, and human parameters, we evaluate the largest delay without losing the closed-loop stability under various scenarios through numerical examples. The results highlight the potential for effective coordination of a large fleet of autonomous vehicles facilitated by a limited number of human operators.