Robust cooperative tracking for multiple non-identical second-order nonlinear systems

In this paper, a distributed cooperative tracking problem is studied for a group of non-identical second-order nonlinear systems with bounded external disturbances. The control goal is to drive the states of the followers to converge to those of a time-varying leader in the presence of only local information interactions from the leader to the followers and between the followers. We first propose a simple distributed control algorithm for the case when both the relative position and relative velocity measurements are available for feedback. It is shown that distributed cooperative tracking can be achieved if in the sensing topology the leader has directed paths to all followers. Then, the extension to the case when the velocity measurements are not available is studied. We consider two different scenarios, i.e., when the absolute position measurements and local communication between neighbors are available and only the relative position measurements are available. Distributed observers and distributed control inputs are designed to address these two scenarios. Numerical studies are carried out to illustrate the theoretical results.