Robust consensus tracking for double-integrator dynamics without velocity measurements

This paper investigates the robust second-order tracking problem of multi-agent systems without velocity measurements on detailed balanced directed communication topologies, where agents´ dynamics are subject to uncertain and external disturbances. We first construct the controller for multi-agent systems without uncertain and external disturbances. Then, combined with the controller, one modifying uncertainty and disturbance estimator (UDE) is proposed to approximate the situation where neither the velocity measurements nor its asymptotic estimation is available. It is shown that the synchronization errors are bounded and their ultimate bounds could be arbitrarily small by choosing some parameters appropriately. Simulation results are presented to show the effectiveness of the controllers.