Fully-actuated system method for prescribed-time elliptical orbital spacecraft rendezvous

This paper addresses the prescribed-time control design problem for a linear time-varying spacecraft rendezvous system. This linear time-varying spacecraft rendezvous system is first transformed into a linear periodic system via the linear invertible transformation and then reduced into a simpler linear system. When both the relative position and the relative velocity are available, a composite linear periodic time-delay state-feedback control is designed for this simpler linear system based on the smooth periodic time-delay feedback control method. When only the relative position is available, a prescribed-time state observer is constructed to estimate the system state. Then, using this estimated state, a composite linear periodic time-delay output-feedback control is designed for this simpler linear system via the same smooth periodic time-delay feedback framework. In both cases, the spacecraft rendezvous mission can be accomplished within the prescribed time. Finally, the effectiveness and practicality of the proposed method are demonstrated through two numerical examples based on realistic spacecraft rendezvous scenarios.