The ‘New Space’ mentality is gaining in popularity and is at the basis of the growing size of satellite constellations. These satellite constellations are used for technologies such as satellite navigation and internet, but a clear framework to controlling large satellite constellations is missing. Therefore, a new approach is developed to work efficiently with thousands of satellitesby finding a suitable model, controller and problem formulation.

A new model is developed that is linear time-invariant, fully based on physics and can include J2 perturbations. Furthermore, it can work well for both in-plane and out-of-plane movements. This model is paired with the lumped System-Level Synthesis control framework: a robust control algorithm that optimises the closed-loop transfer function. Due to a modification, the applied controller is less conservative than the original controller and faster than other modifications. The problem formulation is rewritten to a standard quadratic problem to significantly increase the rate at which these problems can be solved. This includes rewriting
one-norms and infinity norms, but also a new formulation for these System-Level Synthesis problems in general.

These findings are tested in a simulation of over two hundred satellites, where the satellites are controlled with the new model, the robust controller, the new problem formulation and collision avoidance constraint. These collision avoidance constraints are added to ensure that satellites keep a safe distance between themselves at all times. This includes constraints between satellites within the same plane, but also between satellites that cross each other’s orbit while close to each other.