Covariance Control for Stochastic Low-Thrust Trajectory Optimization

This paper outlines a novel approach to the design of optimal space trajectories under significant uncertainty. Finite-horizon covariance control, i.e., the steering of a system from an initial probability distribution to a desired one at a prescribed time, is employed to plan an optimal nominal path along with a robust feedback controller that compensates for exogenous in-flight disturbances. The major contribution of the present paper is a mindful convexification strategy to recast the nonlinear covariance control problem as a deterministic convex optimization problem. The convexification is based on a convenient change of variables that allows to relax the covariance matrix discrete-time propagation into a set of semidefinite cone constraints. While featuring a larger feasible space, the relaxed problem shares the same optimal solution as the original one, as proven by numerical experiments, hence demonstrating that the proposed relaxation is lossless. Monte Carlo campaigns are carried out to validate the in-flight performance of the attained control policies. © 2022, American Institute of Aeronautics and Astronautics Inc.. All rights reserved.