Tracking the average of time-varying nonsmooth signals for double-integrator agents with a fixed topology

In this paper, the average tracking problem for coupled multiagent systems with double-integrator dynamics is considered. The accelerations of the reference signals, which could be discontinuous, are assumed to be upper bounded. A sliding-mode surface is designed such that the trajectory on the surface will solve the average tracking problem. For this purpose, a discontinuous control algorithm is proposed to guarantee that the system trajectory reaches the surface in finite time. It is shown that if the communication graph is connected, then by properly choosing the control gain the average tracking problem is solved.