Prescribed-time feedback control design of nonlinear elliptical orbital spacecraft rendezvous system

This article addresses the prescribed-time feedback control design problem of nonlinear spacecraft rendezvous system in elliptical orbit. First, nonlinear spacecraft rendezvous system is transformed into a nonlinear periodic system by using an invertible linear transformation. Then this nonlinear periodic system is simplified into a linear periodic system according to the fully actuated system approach. Second, combining the periodic time delay feedback control approach and the parametric Lyapunov equation approach, a composite nonlinear periodic time-delay feedback control is designed for the nonlinear periodic system. Under the obtained feedback control, the stabilisation of the nonlinear periodic system can be achieved in the prescribed time. Therefore, the prescribed-time feedback control is designed for nonlinear spacecraft rendezvous system to successfully accomplish the rendezvous mission in any prescribed time. Finally, the practicability of the control design approach proposed in this paper is verified through an example of the elliptical orbital spacecraft rendezvous.