Adaptive time-varying sliding mode control for autonomous spacecraft rendezvous

In this paper, two types optimal adaptive time-varying sliding mode control (ATVSMC) for a class of spacecraft rendezvous systems are proposed. The sliding surfaces pass through the initial point of system at the beginning and then move towards the origin of the error state space. By designing the ATVSMC law, the reaching phase is eliminated, and the system's robustness to unknown bounded parameter uncertainties and external disturbances is guaranteed from the beginning. The existence of global siding mode is proved by Lyapunov method. Furthermore, the parameters of sliding surfaces are obtained by minimizing the integral of the infinite norm of relative position tracking error. An example is included to illustrate the obtained results.