Finite-time consensus tracking of multiple coupled harmonic oscillations via bounded control

This paper considers the problem of finite-time consensus tracking for multiple harmonic oscillators with a leader-follower architecture. By using the techniques of finite-time control and saturation control, a class of bounded finite-time controllers are first proposed. Then to address the case in the presence of external disturbance, a finite-time convergent disturbance observer is constructed to estimate the disturbance in a finite time. Finally, a disturbance observer-based bounded finite-time controller is developed. Rigorous proof shows that the systems states can reach consensus in a finite time and the final consensus states are the leader´s states.