Adaptive Fixed-Time Control for the Postcapture Tethered Spacecraft with Full-State Constraints

This article studies the fixed-time control problem for the postcapture tethered spacecraft subject to full-state constraints and uncertainties. A $\mathcal {C}^{1}$ smooth adaptive fixed-time controller is constructed via introducing a smooth switch between fractional and quadratic form feedback, such that the undesired chattering and singularity issues are removed. With the aid of universal transformed function technique, the proposed controller not only ensures that the constraint boundaries are not violated, but also eliminates the feasibility condition existing in the traditional barrier Lyapunov functions-based control solutions. Furthermore, by incorporating the generalized first-order filter and adaptive laws into control design procedure, the fixed-time stability of the closed-loop system can be guaranteed. The validity of the proposed control scheme is demonstrated by a simulation example.