Fixed-Time L₂ Attitude Control Guaranteeing Anti-Unwinding Performance and Energy Efficiency

This article deals with the challenging problem of fixed-time L₂ control for flexible spacecraft attitude system with a focus on energy-efficiency, anti-unwinding property, and reducing conservativeness in estimating the settling time upper bound. To this end, we first introduce a novel fixed-time stable system which is applicable to spacecraft attitude system represented by unit quaternion. It provides a more accurate estimation of the settling time. Based on the proposed fixed-time system, we define a singularity-free, anti-unwinding sliding surface that does not include any piecewise continuous functions to address singularity issues due to the use of fractional power. This sliding surface contains the initial scalar part of the quaternion to guarantee fixed-time convergence for both equilibrium points, removing the unwinding problem. Considering the sliding variable as the performance vector, the proposed control framework guarantees that the fixed-time L₂ gain of lumped disturbance attenuation is less than a predetermined value. The performance of the proposed control framework is established through numerical simulations and validated using a Speedgoat real-time experimental setup.