Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication

This paper studies a distributed discrete-time coordinated tracking problem where a team of vehicles communicating with their local neighbors at discrete-time instants tracks a time-varying reference state available to only a subset of the team members. We propose a PD-like discrete-time consensus algorithm to address the problem under a fixed communication graph. We then study the condition on the communication graph, the sampling period, and the control gain to ensure stability and give the quantitative bound of the tracking errors. It is shown that the ultimate bound of the tracking errors is proportional to the sampling period. The benefit of the proposed PD-like discrete-time consensus algorithm is also demonstrated through comparison with an existing P-like discrete-time consensus algorithm. Simulation results are presented as a proof of concept.