Convex Approach to Covariance Control for Low-Thrust Trajectory Optimization with Mass Uncertainty

This paper presents a convex approach to the design of optimal space trajectories while explicitly accounting for uncertainty. A covariance control problem aimed at driving a stochastic system from an initial probability distribution to a desired one at a final time is formulated to retrieve an optimal nominal trajectory and an additive state feedback controller that can compensate for exogenous in-flight disturbances. The feedback controller regulates the thrust magnitude and, consequently, the propellant mass consumption. As a result, mass is a random state variable with a significant variance if high disturbances are considered. The propagation of the mass variance is considered in the optimization to retrieve a control policy that is robust to mass uncertainties. Convexification strategies, including changes of variables, lossless relaxations, and successive linearization, are used to obtain a deterministic convex optimization problem solvable with low computational complexity. A numerical example consisting of a low-thrust transfer from the Earth to Mars is considered. Extensive Monte Carlo campaigns are carried out to assess the effectiveness and performance of the attained control policy.