Neural network-based distributed adaptive configuration containment control for satellite formations

Considering unknown perturbations and model uncertainties, this paper investigates the configuration containment control for satellite formations based on directed communication topologies. We consider that there are multiple leader satellites with constant relative velocities, while only a subset of follower satellites have access to the leaders. First, a distributed velocity observer is proposed for each follower to obtain velocity information of the leaders. Then, a distributed adaptive configuration containment control algorithm is proposed in which the model nonlinear uncertainties are approximated and compensated through neural networks, while the perturbations and approximation errors are compensated by adaptive gain technique. Furthermore, subject to the chattering caused by sign functions, an improved continuous containment strategy is developed. We use graph theory, Lyapunov theory, and Barbalat lemma to demonstrate that both proposed methods can make all the follower satellites converge to the convex hull spanned by the leader satellites. Numerical examples and comparisons are provided to show the effectiveness and performances of the proposed control strategies.