Periodic Event-Triggered and Self-Triggered Control of Spacecraft Rendezvous System With Input Delay

This paper solves the problem of spacecraft rendezvous with input delay by designing the periodic event-triggered control (PETC) and periodic self-triggered control (PSTC), respectively. Firstly, a PETC based on the discrete-time parametric Lyapunov equation (DPLE) is designed to stabilize the delayed spacecraft rendezvous systems. Moreover, in order to avoid monitoring the measurement errors, a PSTC algorithm that the updates of the next control law depend on the previous triggered states is also designed. Specially, by using the properties of the DPLE, this new approach is not only simple, but also provides an easy and explicit condition on the only parameter of DPLE to guarantee the non-triviality of the designed PETC and PSTC. Finally, the effectiveness of theoretical results is verified by simulations. Note to Practitioners—Although this paper was inspired by the problem of spacecraft rendezvous, the designed algorithms can also be applied to other time-delay systems. Existing general event-triggered control methods have been used to solve the problem of spacecraft rendezvous for reducing the communication load, although this often complicates the design of the controller due to preventing the occurrence of Zeno phenomenon. To overcome this drawback, This paper proposes a periodic event-triggered control to achieve the spacecraft rendezvous with input delay, which naturally avoids the occurrence of Zeno phenomenon. In addition, a periodic self-triggered control is also designed, which has never been designed to solve the problem of delayed spacecraft rendezvous.