Communication preserving min-max time consensus tracking

A collection of double integrator agents is considered, where each agent has bounded input and a limited range for receiving information from other agents. One autonomous node (the Root) generates an unknown reference trajectory to which other agents are required to converge in minimum possible time, using only locally available information. A distributed algorithm is proposed to identify a directed spanning tree rooted at the Root agent. The child agent of each edge of this selected tree uses min-max time control strategies to converge to the states of the parent node. Necessary and sufficient conditions are derived for limiting the inter-agent distance so as to preserve the tree communication structure chosen. Under these conditions, the proposed control strategy turns out to be the global communication preserving min-max strategy for the entire collection.