Application of Active Feedback Control for Investigation of Debris Mitigation Strategies on a Density-Based Model of the Population Evolution

The population of objects in space faced an unforeseeable growth in the last decades. There-fore, it is now imperative to reiterate the debris mitigation guidelines and reconsider the approach to the debris proliferation problem. Different counteractions are available to deal with the sit-uation. However, how to efficiently combine and apply these methods for sustainable use of the space environment is still an open question. To respond to this need, the GREEN SPECIES project, funded by a consolidator grant of the European Research Council, will develop a con-trolled model of the space debris population to define optimal mitigation policies. In its current version, the system exploits a statistical model in which debris and intact objects move in a one-dimensional domain in orbital radius and binned in spherical shells. The evolution of the environment is modelled in terms of the objects' density dynamics. The system includes the effect of atmospheric drag, sources as launches and in-orbit fragmentations, and artificial sink mechanisms such as post mission disposals and active debris removals. The resulting set of ordi-nary differential equations is integrated with a state-dependent linear feedback controller to tune different inputs and reach a predefined target. The novel appraoch exploits the benefits of control techniques to investigate the effectiveness of diversified rules in space and time to mitigate the debris proliferation and its risk to missions in low Earth orbit.