Fixed-time formation control for spacecraft with prescribed performance guarantee under input saturation

This paper investigates the fixed-time stability of spacecraft formation flying by considering input saturation and prescribed performance constraints, including the safe distance constraint between members and control accuracy. By analyzing the relationship between the positional tracking error and the minimum safe distance between spacecrafts, a new form of the prescribed performance function with fixed-time convergence is developed to constrain the overshoot and accuracy of the tracking error. A nonsingular saturated terminal sliding-mode surface is developed to stabilize the system states in fixed time. A fixed-time coordinated tracking controller with input and rate saturation is finally developed by combining sliding-mode control, the back-stepping method, fixed-time observers, an anti-windup saturation compensator, and an auxiliary system. The stability of the closed-loop system is validated by Lyapunov stability theory. The results of simulation verified the effectiveness of the proposed control algorithm.