Global fixed-time attitude tracking control for the rigid spacecraft with actuator saturation and faults

This paper investigates the global finite-time attitude tracking problem for the rigid spacecraft subject to inertial uncertainties, external disturbances, actuator faults, and input saturation constraints. The exponential coordinates vector in conjunction with a hysteretic-based jump condition is introduced to overcome the topological obstacles of global stability on the special orthogonal group. A novel nonsingular fixed-time-based sliding mode is designed, which not only avoids the singularity but also guarantees that the convergence time of tracking errors along the sliding surface is independent of the state value. Then, an adaptive fault-tolerant control law is constructed to enforce the system state to reach a neighborhood of the sliding surface in the sense of the fixed-time concept, which can accommodate actuator failures under limited control torque. The total convergence time is independent of the initial conditions information. A rigorous mathematical stability Proof is given. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed finite-time controller.