Distributed attitude tracking for multiple flexible spacecraft described by partial differential equations

In this study, two distributed control strategies without or with a Partial Differential Equation (PDE) observer are proposed for a team of flexible spacecraft to track the attitude of a virtual leader under an undirected and connected graph. The PDE is used to describe the dynamics of each spacecraft with an appendage, which is simplified as a hub-beam system. It is assumed that both the hub and the free tip of the beam are actuated directly. The desired attitude angle, i.e., the state of the virtual leader, is only available for one spacecraft in the team. A distributed controller with the state measurements of the hub and the free tip of the beam is proposed first. Then a PDE observer is presented to estimate the states of the whole beam from the information of the hub only. A novel distributed controller with such a PDE observer is developed to drive the team to track the virtual leader. It is indicated by rigorous proof that the two controllers can actuate the team to the desired attitude without any residual vibration asymptotically. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed controllers.