Distributed appointed-time prescribed performance attitude coordinated tracking for multiple rigid spacecraft under directed communication topology

This paper addresses appointed-time attitude coordinated control problem of multiple spacecraft under the directed communication topology in presence of input saturation. With only a subset of spacecrafts being able to access the information of the reference trajectory, a distributed observer is developed for each spacecraft to estimate the virtual leader's state in fixed time. Subsequently, to ensure the tracking error can achieve the preassigned transient and steady state performance, an adaptive backstepping controller is synthesized by incorporating an appointed-time performance function with the asymmetric tan-type barrier Lyapunov function (BLF). Furthermore, to tackle the input saturation constraint, a Nussbaum-type function is incorporated to compensate for the time-varying nonlinear gain arising from the derivative of the nonlinear approximation function. Different from most existing finite-time coordination protocols, the convergence time can be appointed by the user without resorting to judicious control parameters selection. Finally, numerical simulation is conducted to assess the efficacy of the theoretical results.