Momentum-Based Learning of Nash Equilibria for LISA Pointing Acquisition

Abstract

This paper addresses the pointing acquisition phase of the Laser Interferometer Space Antenna (LISA) mission as a guidance problem. It is formulated in a cooperative game setup, which solution is a sequence of corrections that can be used as a tracking reference to align all the spacecraft' laser beams simultaneously within the tolerances required for gravitational wave detection. We propose a model-free learning algorithm based on residual-feedback and momentum, for accelerated convergence to stable solutions, i.e. Nash Equilibria. Each spacecraft has 4 degrees of freedom, and the only measured output considered are laser misalignments with the local interferometer sensors. Simulation results demonstrate that the proposed strategy manages to achieve absolute misalignment errors $<1\mu$rad in a timely manner.