Drag-Free and Attitude Control System for the LISA Space Mission: An $H_{\infty}$ Constrained Decoupling Approach

This article presents an approach to drag-free and attitude control for the laser interferometer space antenna (LISA) space mission, based on a constrained decoupling $H_{\infty}$ approach. LISA will be a space-based gravitational wave observatory, which is expected to be launched by the European Space Agency (ESA) in 2034. The LISA concept consists of a constellation of three satellites that exchange a bidirectional laser link to perform interferometry. The gravitational waves can be detected by measuring the relative distance variations, by means of laser interferometers, between two free-falling bodies located at a far distance, called the test masses (TMs). In this framework, the spacecraft (SC) drag-free attitude control plays a key role since it allows the TMs to move in free-fall conditions, rejecting external disturbances and noises, at the nanoscopic level, that can compromise the quality of scientific measurements. To this end, we propose an $H_\infty$ drag-free attitude controller, based on a constrained decoupling of the SC linearized dynamics, where the pseudoinverse of the control matrix is obtained by minimizing the inversion error. Moreover, we provide sufficient conditions for stability of the closed-loop, in order to ensure that the decoupling inversion error does not affect the closed-loop stability. The effectiveness of the proposed approach is confirmed by means of an extensive Monte Carlo campaign, carried out employing a high-fidelity simulator.