Distributed event-triggered fixed-time formation tracking control for multi-spacecraft systems based on adaptive immersion and invariance technique

In this study, the problem of fixed-time formation tracking for multi-spacecraft systems without internal collisions was investigated. Aiming to ensure that the formation members can accurately realize and maintain the required configuration within the user-given time, we designed a novel adaptive immersion and invariance (I&I)-based control protocol. The novelty here lies in two aspects. First and foremost, this study was based on the adaptive I&I technique, combined with a new artificial potential function, to achieve the desired formation tracking without internal collision. Second, unlike the asymptotic convergence of the traditional I&I-related works, to guarantee the fixed-time stability, the proposed protocol introduced the prescribed performance control, which can also alleviate the possible system performance degradation caused by the non-periodic control signal update of the event-triggered mechanism. Further, the introduction of the event-triggered mechanism can reduce the unnecessary information interaction. Lyapunov stability analysis shows that this proposed protocol can enable the defined implicit manifold to converge to the origin for the most initial conditions. Also, benefiting from the prescribed performance techniques, the convergence time can eliminate the dependence of the system on designed controller parameters or initial system conditions, relying only on the actual mission requirements. In addition, we adopted a linear extended state observer to deal with the parameter uncertainties and external disturbances, and used the I&I adaption to estimate the observer errors, thus further improving the system performance. Moreover, a new exponential-type artificial potential function was designed to avoid close proximity between formation members and prevent internal collisions. Finally, numerical simulations were conducted to verify the theoretical results.