Distributed finite-time tracking control for harmonic oscillators via output feedback control

This paper addresses the finite-time control problems for a single harmonic oscillator and multiple harmonic oscillators. First of all, an output feedback controller is adopted to solve the finite-time stabilization problem for a single harmonic oscillator. Rigorous proof shows that the harmonic oscillator can be stabilized in finite time. Then, the finite-time consensus tracking for a group of harmonic oscillators is investigated, where each agent can only share its position states with its neighbors. A new type of observer-based control algorithm is proposed to achieve the finite-time consensus tracking in multi-agent systems with a virtual leader. The communication topology among the followers is undirected and only a subset of followers can obtain the information from the leader. By using the homogeneous theory, it is theoretically shown that the states of the followers can track that of the leader in finite time. Numerical simulations are finally given to illustrate the theoretical results.