Tracking Protocol for Network of Double-Integrator Systems With Heterogeneous Time Delays

This article studies the consensus tracking problem for a group of double-integrator agents in the presence of heterogeneous communication and input delays. We consider a tracking protocol comprising a consensus-based estimator for the desired trajectory with a simple tracking controller for each agent, which ensures bounded tracking under input delays. As a part of the protocol design, we employ the simplest communication topology, wherein each agent either has the desired trajectory information or receives an estimate of the trajectory from only one other agent. We study the stable tracking conditions for two different estimator structures, viz., conventional double-integrator structure and coupled single-integrator structure. We show that our protocol can ensure uniformly ultimately bounded tracking errors for a trajectory with unbounded acceleration but bounded jerk. We find necessary and sufficient conditions on estimator gains such that the double-integrator estimator yields higher delay margin than the coupled single-integrator estimator, and vice versa. Simulation results demonstrate these findings and the performance of this protocol vis-à-vis existing works.