Distributed Average Tracking for Double-integrator Multi-agent Systems with Reduced Requirement on Velocity Measurements

Abstract

This paper addresses distributed average tracking for a group of physical double-integrator agents under an undirected graph with reduced requirement on velocity measurements. The idea is that multiple agents track the average of multiple time-varying input signals, each of which is available to only one agent, under local interaction with neighbors. We consider two cases. First, a distributed discontinuous algorithm and filter are proposed, where each agent needs the relative positions between itself and its neighbors and its neighbors' filter outputs obtained through communication but the requirement for either absolute or relative velocity measurements is removed. The agents' positions and velocities must be initialized correctly, but the algorithm can deal with a wide class of input signals with bounded acceleration deviations. Second, a distributed discontinuous algorithm and filter are proposed to remove the requirement for communication and accurate initialization. Here each agent needs to measure the relative position between itself and its neighbors and its own velocity but the requirement for relative velocity measurements between itself and its neighbors is removed. The algorithm can deal with the case where the input signals and their velocities and accelerations are all bounded. Numerical simulations are also presented to illustrate the theoretical results.