On distributed finite-time observer design and finite-time coordinated tracking of multiple double integrator systems via local interactions

This paper studies finite-time coordinated tracking problem for multiple double integrator systems with a time-varying leader's velocity and bounded external disturbances. We consider the dynamic feedback designs for two different cases. In the first case, the velocities of the followers and the leader are assumed to be unavailable, and the communication topology is assumed to be undirected and fixed. In the second case, the velocities of the followers and the leader are assumed to be available, and the communication topology is assumed to be directed and switching. Distributed finite-time observers are designed, respectively, to obtain the velocity information in the first case and the relative state information in the second case. The states of these observers are then used to design control inputs that achieve finite time robust coordinated tracking of multiple double integrator systems in the presence of bounded disturbances for these two cases. Simulation results are provided to validate the effectiveness of these theoretical results.