Predefined-Time Disturbance Observer Based Predefined-Time Sliding Mode Control for Space Triangle Tethered Formation System

In this paper, the control problem of spinning formation deployment for space triangle tethered formation systems is studied at the predefined-time convergence. First, based on the Euler-Lagrange dynamic model, a nominal predefined-time sliding mode controller is proposed for formation deployment, whose convergence time can be tuned by the setting-time parameter in advance. Second, a novel predefined-time disturbance observer is designed to estimate the lumped disturbances. Moreover, the stability of the predefined-time disturbance observer and the predefined-time controller is proved by the Lyapunov theory. The simulation results of predefined-time convergence show that the proposed control mechanism is successful.